1
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Litman Y, Kapil V, Feldman YMY, Tisi D, Begušić T, Fidanyan K, Fraux G, Higer J, Kellner M, Li TE, Pós ES, Stocco E, Trenins G, Hirshberg B, Rossi M, Ceriotti M. i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations. J Chem Phys 2024; 161:062504. [PMID: 39140447 DOI: 10.1063/5.0215869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2024] [Accepted: 07/11/2024] [Indexed: 08/15/2024] Open
Abstract
Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.
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Affiliation(s)
- Yair Litman
- Y. Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Venkat Kapil
- Y. Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Physics and Astronomy, University College London, 17-19 Gordon St, London WC1H 0AH, United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology, 19 Gordon St, London WC1H 0AH, United Kingdom
| | | | - Davide Tisi
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Tomislav Begušić
- Div. of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Karen Fidanyan
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Guillaume Fraux
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Jacob Higer
- School of Physics, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Matthias Kellner
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Tao E Li
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Eszter S Pós
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Elia Stocco
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - George Trenins
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Barak Hirshberg
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Mariana Rossi
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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2
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Ke Y, Richardson JO. Quantum nature of reactivity modification in vibrational polariton chemistry. J Chem Phys 2024; 161:054104. [PMID: 39087532 DOI: 10.1063/5.0220908] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
In this work, we present a mixed quantum-classical open quantum system dynamics method for studying rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. In this approach, the cavity radiation mode is treated classically with a mean-field nuclear force averaging over the remaining degrees of freedom, both within the system and the environment, which are handled quantum mechanically within the hierarchical equations of motion framework. Using this approach, we conduct a comparative analysis by juxtaposing the mixed quantum-classical results with fully quantum-mechanical simulations. After eliminating spurious peaks that can occur when not using the rigorous definition of the rate constant, we confirm the crucial role of the quantum nature of the cavity radiation mode in reproducing the resonant peak observed in the cavity frequency-dependent rate profile. In other words, it appears necessary to explicitly consider the quantized photonic states in studying reactivity modification in vibrational polariton chemistry (at least for the model systems studied in this work), as these phenomena stem from cavity-induced reaction pathways involving resonant energy exchanges between photons and molecular vibrational transitions.
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Affiliation(s)
- Yaling Ke
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
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3
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Morshed O, Amin M, Cogan NMB, Koessler ER, Collison R, Tumiel TM, Girten W, Awan F, Mathis L, Huo P, Vamivakas AN, Odom TW, Krauss TD. Room-temperature strong coupling between CdSe nanoplatelets and a metal-DBR Fabry-Pérot cavity. J Chem Phys 2024; 161:014710. [PMID: 38953450 DOI: 10.1063/5.0210700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 05/27/2024] [Indexed: 07/04/2024] Open
Abstract
The generation of exciton-polaritons through strong light-matter interactions represents an emerging platform for exploring quantum phenomena. A significant challenge in colloidal nanocrystal-based polaritonic systems is the ability to operate at room temperature with high fidelity. Here, we demonstrate the generation of room-temperature exciton-polaritons through the coupling of CdSe nanoplatelets (NPLs) with a Fabry-Pérot optical cavity, leading to a Rabi splitting of 74.6 meV. Quantum-classical calculations accurately predict the complex dynamics between the many dark state excitons and the optically allowed polariton states, including the experimentally observed lower polariton photoluminescence emission, and the concentration of photoluminescence intensities at higher in-plane momenta as the cavity becomes more negatively detuned. The Rabi splitting measured at 5 K is similar to that at 300 K, validating the feasibility of the temperature-independent operation of this polaritonic system. Overall, these results show that CdSe NPLs are an excellent material to facilitate the development of room-temperature quantum technologies.
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Affiliation(s)
- Ovishek Morshed
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Mitesh Amin
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Nicole M B Cogan
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Eric R Koessler
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Robert Collison
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Trevor M Tumiel
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - William Girten
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Farwa Awan
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Lele Mathis
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Pengfei Huo
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - A Nickolas Vamivakas
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Teri W Odom
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - Todd D Krauss
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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4
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Li TE. Mesoscale Molecular Simulations of Fabry-Pérot Vibrational Strong Coupling. J Chem Theory Comput 2024. [PMID: 38912683 DOI: 10.1021/acs.jctc.4c00349] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/25/2024]
Abstract
Developing theoretical frameworks for vibrational strong coupling (VSC) beyond the single-mode approximation is crucial for a comprehensive understanding of experiments with planar Fabry-Pérot cavities. Herein, a generalized cavity molecular dynamics (CavMD) scheme is developed to simulate VSC of a large ensemble of realistic molecules coupled to an arbitrary 1D or 2D photonic environment. This approach is built upon the Power-Zienau-Woolley Hamiltonian in the normal mode basis and uses a grid representation of the molecular ensembles to reduce the computational cost. When simulating the polariton dispersion relation for a homogeneous distribution of molecules in planar Fabry-Pérot cavities, our data highlight the importance of preserving the in-plane translational symmetry of the molecular distribution. In this homogeneous limit, CavMD yields the consistent polariton dispersion relation as an analytic theory, i.e., incorporating many cavity modes with varying in-plane wave vectors (k∥) produces the same spectrum as the system with a single cavity mode. Furthermore, CavMD reveals that the validity of the single-mode approximation is challenged when nonequilibrium polariton dynamics are considered, as polariton-polariton scattering occurs between modes with the nearest neighbor k∥. The procedure for numerically approaching the macroscopic limit is also demonstrated with CavMD by increasing the system size. Looking forward, our generalized CavMD approach may facilitate understanding vibrational polariton transport and condensation.
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Affiliation(s)
- Tao E Li
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
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5
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Tian Z, Xu D, Yang S, Wang B, Zhang Z. Highly ordered nanocavity as photonic-plasmonic-polaritonic resonator for single molecule miRNA SERS detection. Biosens Bioelectron 2024; 254:116231. [PMID: 38513540 DOI: 10.1016/j.bios.2024.116231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Revised: 03/11/2024] [Accepted: 03/15/2024] [Indexed: 03/23/2024]
Abstract
Strong light-matter coupling between molecules and electromagnetic field lead to the formation of hybrid polaritonic states for surface enhanced Raman scattering (SERS) detection. However, owing to the inefficient interaction between zero-point fluctuations of photons/plasmons and molecular electronic transitions, the Raman enhancement is limited in relative low levels. Here, we propose and fabricate a TiOx/Cu2-xSe/R6G nanocavity based photonic-plasmonic-polaritonic resonator for single molecular SERS detection. Through precisely matching the energy levels of illuminated photon, generated plasmon, and molecular polariton, an extremely high Raman enhancement factor of 2.6 × 109 is implemented. The rationally designed SERS substrate allows sensitive detection of miRNA-21 in single molecular level with a detection limit of 1.58 aM. The hybrid SERS mechanism both from electromagnetic and chemical perspectives in this photonic-plasmonic-polaritonic resonance strategy provides insight into polaritonic semiconductor systems, thus paving the way for new experimental possibilities in light-matter hybrids.
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Affiliation(s)
- Zheng Tian
- State Key Laboratory of Molecular & Process Engineering, Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200241, China
| | - Dawei Xu
- State Key Laboratory of Molecular & Process Engineering, Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200241, China
| | - Shenbo Yang
- Hongzhiwei Technology (Shanghai) CO.LTD., 1599 Xinjinqiao Road, Pudong, Shanghai, China
| | - Bing Wang
- Department of Oncological Surgery, Minhang Branch, Shanghai Cancer Center, Fudan University, Shanghai, 200240, China
| | - Zhonghai Zhang
- State Key Laboratory of Molecular & Process Engineering, Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200241, China; Institute of Eco-Chongming, East China Normal University, 20 Cuiniao Road, Chongming District, Shanghai, 202162, China.
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6
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Ke Y, Richardson JO. Insights into the mechanisms of optical cavity-modified ground-state chemical reactions. J Chem Phys 2024; 160:224704. [PMID: 38856061 DOI: 10.1063/5.0200410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 05/27/2024] [Indexed: 06/11/2024] Open
Abstract
In this work, we systematically investigate the mechanisms underlying the rate modification of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. We employ a symmetric double-well description of the molecular potential energy surface and a numerically exact open quantum system approach-the hierarchical equations of motion in twin space with a matrix product state solver. Our results predict the existence of multiple peaks in the photon frequency-dependent rate profile for a strongly anharmonic molecular system with multiple vibrational transition energies. The emergence of a new peak in the rate profile is attributed to the opening of an intramolecular reaction pathway, energetically fueled by the cavity photon bath through a resonant cavity mode. The peak intensity is determined jointly by kinetic factors. Going beyond the single-molecule limit, we examine the effects of the collective coupling of two molecules to the cavity. We find that when two identical molecules are simultaneously coupled to the same resonant cavity mode, the reaction rate is further increased. This additional increase is associated with the activation of a cavity-induced intermolecular reaction channel. Furthermore, the rate modification due to these cavity-promoted reaction pathways remains unaffected, regardless of whether the molecular dipole moments are aligned in the same or opposite direction as the light polarization.
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Affiliation(s)
- Yaling Ke
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
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7
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Fábri C, Császár AG, Halász GJ, Cederbaum LS, Vibók Á. Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description. J Chem Phys 2024; 160:214308. [PMID: 38836455 DOI: 10.1063/5.0205048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 05/20/2024] [Indexed: 06/06/2024] Open
Abstract
The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schrödinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work, we compare numerically the Lindblad and Schrödinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schrödinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.
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Affiliation(s)
- Csaba Fábri
- HUN-REN-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Attila G Császár
- HUN-REN-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Gábor J Halász
- Department of Information Technology, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Ágnes Vibók
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
- ELI-ALPS, ELI-HU Non-Profit Ltd., Dugonics tér 13, H-6720 Szeged, Hungary
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8
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Patrahau B, Piejko M, Mayer RJ, Antheaume C, Sangchai T, Ragazzon G, Jayachandran A, Devaux E, Genet C, Moran J, Ebbesen TW. Direct Observation of Polaritonic Chemistry by Nuclear Magnetic Resonance Spectroscopy. Angew Chem Int Ed Engl 2024; 63:e202401368. [PMID: 38584127 DOI: 10.1002/anie.202401368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 04/01/2024] [Accepted: 04/05/2024] [Indexed: 04/09/2024]
Abstract
Polaritonic chemistry is emerging as a powerful approach to modifying the properties and reactivity of molecules and materials. However, probing how the electronics and dynamics of molecular systems change under strong coupling has been challenging due to the narrow range of spectroscopic techniques that can be applied in situ. Here we develop microfluidic optical cavities for vibrational strong coupling (VSC) that are compatible with nuclear magnetic resonance (NMR) spectroscopy using standard liquid NMR tubes. VSC is shown to influence the equilibrium between two conformations of a molecular balance sensitive to London dispersion forces, revealing an apparent change in the equilibrium constant under VSC. In all compounds studied, VSC does not induce detectable changes in chemical shifts, J-couplings, or spin-lattice relaxation times. This unexpected finding indicates that VSC does not substantially affect molecular electron density distributions, and in turn has profound implications for the possible mechanisms at play in polaritonic chemistry under VSC and suggests that the emergence of collective behavior is critical.
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Affiliation(s)
- B Patrahau
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - M Piejko
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - R J Mayer
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - C Antheaume
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - T Sangchai
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - G Ragazzon
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - A Jayachandran
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - E Devaux
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - C Genet
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - J Moran
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - T W Ebbesen
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
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9
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Rider MS, Johnson EC, Bates D, Wardley WP, Gordon RH, Oliver RDJ, Armes SP, Leggett GJ, Barnes WL. Strong coupling in molecular systems: a simple predictor employing routine optical measurements. NANOPHOTONICS 2024; 13:2453-2467. [PMID: 38836102 PMCID: PMC11147498 DOI: 10.1515/nanoph-2023-0879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Accepted: 03/08/2024] [Indexed: 06/06/2024]
Abstract
We provide a simple method that enables readily acquired experimental data to be used to predict whether or not a candidate molecular material may exhibit strong coupling. Specifically, we explore the relationship between the hybrid molecular/photonic (polaritonic) states and the bulk optical response of the molecular material. For a given material, this approach enables a prediction of the maximum extent of strong coupling (vacuum Rabi splitting), irrespective of the nature of the confined light field. We provide formulae for the upper limit of the splitting in terms of the molar absorption coefficient, the attenuation coefficient, the extinction coefficient (imaginary part of the refractive index) and the absorbance. To illustrate this approach, we provide a number of examples, and we also discuss some of the limitations of our approach.
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Affiliation(s)
- Marie S. Rider
- Department of Physics and Astronomy, University of Exeter, Stocker Road, DevonEX4 4QL, UK
| | - Edwin C. Johnson
- Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, S3 7HF, UK
| | - Demetris Bates
- Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, S3 7HF, UK
| | - William P. Wardley
- Department of Physics and Astronomy, University of Exeter, Stocker Road, DevonEX4 4QL, UK
| | - Robert H. Gordon
- Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK
| | - Robert D. J. Oliver
- Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK
- Department of Materials Science and Engineering, University of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, UK
| | - Steven P. Armes
- Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, S3 7HF, UK
| | - Graham J. Leggett
- Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, S3 7HF, UK
| | - William L. Barnes
- Department of Physics and Astronomy, University of Exeter, Stocker Road, DevonEX4 4QL, UK
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10
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Thomas PA, Barnes WL. Strong coupling-induced frequency shifts of highly detuned photonic modes in multimode cavities. J Chem Phys 2024; 160:204303. [PMID: 38804495 DOI: 10.1063/5.0208379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2024] [Accepted: 05/07/2024] [Indexed: 05/29/2024] Open
Abstract
Strong coupling between light and molecules is a fascinating topic exploring the implications of the hybridization of photonic and molecular states. For example, many recent experiments have explored the possibility that strong coupling of photonic and vibrational modes might modify chemical reaction rates. In these experiments, reactants are introduced into a planar cavity, and the vibrational mode of a chemical bond strongly couples to one of the many photonic modes supported by the cavity. Some experiments quantify reaction rates by tracking the spectral shift of higher-order cavity modes that are highly detuned from the vibrational mode of the reactant. Here, we show that the spectral position of these cavity modes, even though they are highly detuned, can still be influenced by strong coupling. We highlight the need to consider this strong coupling-induced frequency shift of cavity modes if one is to avoid underestimating cavity-induced reaction rate changes. We anticipate that our work will assist in the re-analysis of several high-profile results and has implications for the design of future strong coupling experiments.
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Affiliation(s)
- Philip A Thomas
- Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom
| | - William L Barnes
- Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom
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11
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Sidler D, Schnappinger T, Obzhirov A, Ruggenthaler M, Kowalewski M, Rubio A. Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling. J Phys Chem Lett 2024; 15:5208-5214. [PMID: 38717382 PMCID: PMC11103705 DOI: 10.1021/acs.jpclett.4c00913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Revised: 05/01/2024] [Accepted: 05/03/2024] [Indexed: 05/22/2024]
Abstract
We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full nonrelativistic Pauli-Fierz problem of an ensemble of strongly coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus, collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.
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Affiliation(s)
- Dominik Sidler
- Laboratory
for Materials Simulations, Paul Scherrer
Institute, 5232 Villigen PSI, Switzerland
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Thomas Schnappinger
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106
91 Stockholm, Sweden
| | - Anatoly Obzhirov
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael Ruggenthaler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Markus Kowalewski
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106
91 Stockholm, Sweden
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron
Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Nano-Bio
Spectroscopy Group, University of the Basque
Country (UPV/EHU), 20018 San Sebastián, Spain
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12
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Fábri C, Halász GJ, Cederbaum LS, Vibók Á. Impact of Cavity on Molecular Ionization Spectra. J Phys Chem Lett 2024; 15:4655-4661. [PMID: 38647546 DOI: 10.1021/acs.jpclett.4c00247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
Ionization phenomena have been widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of a cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.
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Affiliation(s)
- Csaba Fábri
- HUN-REN-ELTE Complex Chemical Systems Research Group, H-1518 Budapest 112, Hungary
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Gábor J Halász
- Department of Information Technology, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Ágnes Vibók
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
- ELI-ALPS, ELI-HU Non-Profit Ltd, Dugonics tér 13, H-6720 Szeged, Hungary
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13
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Phuc NT. Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities. J Chem Theory Comput 2024; 20:3019-3027. [PMID: 38608260 DOI: 10.1021/acs.jctc.4c00078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2024]
Abstract
It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.
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Affiliation(s)
- Nguyen Thanh Phuc
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
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14
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Xiang B, Xiong W. Molecular Polaritons for Chemistry, Photonics and Quantum Technologies. Chem Rev 2024; 124:2512-2552. [PMID: 38416701 PMCID: PMC10941193 DOI: 10.1021/acs.chemrev.3c00662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Revised: 01/22/2024] [Accepted: 02/08/2024] [Indexed: 03/01/2024]
Abstract
Molecular polaritons are quasiparticles resulting from the hybridization between molecular and photonic modes. These composite entities, bearing characteristics inherited from both constituents, exhibit modified energy levels and wave functions, thereby capturing the attention of chemists in the past decade. The potential to modify chemical reactions has spurred many investigations, alongside efforts to enhance and manipulate optical responses for photonic and quantum applications. This Review centers on the experimental advances in this burgeoning field. Commencing with an introduction of the fundamentals, including theoretical foundations and various cavity architectures, we discuss outcomes of polariton-modified chemical reactions. Furthermore, we navigate through the ongoing debates and uncertainties surrounding the underpinning mechanism of this innovative method of controlling chemistry. Emphasis is placed on gaining a comprehensive understanding of the energy dynamics of molecular polaritons, in particular, vibrational molecular polaritons─a pivotal facet in steering chemical reactions. Additionally, we discuss the unique capability of coherent two-dimensional spectroscopy to dissect polariton and dark mode dynamics, offering insights into the critical components within the cavity that alter chemical reactions. We further expand to the potential utility of molecular polaritons in quantum applications as well as precise manipulation of molecular and photonic polarizations, notably in the context of chiral phenomena. This discussion aspires to ignite deeper curiosity and engagement in revealing the physics underpinning polariton-modified molecular properties, and a broad fascination with harnessing photonic environments to control chemistry.
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Affiliation(s)
- Bo Xiang
- Department
of Chemistry, School of Science and Research Center for Industries
of the Future, Westlake University, Hangzhou, Zhejiang 310030, China
| | - Wei Xiong
- Department
of Chemistry and Biochemistry, University
of California, San Diego, California 92126, United States
- Materials
Science and Engineering Program, University
of California, San Diego, California 92126, United States
- Department
of Electrical and Computer Engineering, University of California, San
Diego, California 92126, United States
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15
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Thomas PA, Barnes WL. Selection Bias in Strong Coupling Experiments. J Phys Chem Lett 2024; 15:1708-1710. [PMID: 38356453 PMCID: PMC10875671 DOI: 10.1021/acs.jpclett.3c03546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Revised: 01/30/2024] [Accepted: 01/31/2024] [Indexed: 02/16/2024]
Abstract
The strong coupling of light and molecules offers a potential new pathway to modify the properties of photonic modes and molecules. There are many reasons to be optimistic about the prospects of strong coupling; however, progress in this field is currently hindered by challenges in reproducibility, problems associated with differentiating between strong coupling and other effects, and the lack of a clear theoretical model to describe the reported effects. Concerning the question of differentiating between strong coupling and other possible mechanisms when examining experimental data, here, we show how cognitive bias can lead us to place undue emphasis on a given interpretation of unsystematic experimental data. We hope that this Viewpoint will, where appropriate, help readers to plan strong coupling experiments more carefully and evaluate the significance of the data obtained from them.
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Affiliation(s)
- Philip A. Thomas
- Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United
Kingdom
| | - William L. Barnes
- Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United
Kingdom
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16
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Vu N, Mejia-Rodriguez D, Bauman NP, Panyala A, Mutlu E, Govind N, Foley JJ. Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction Theory. J Chem Theory Comput 2024; 20:1214-1227. [PMID: 38291561 PMCID: PMC10876286 DOI: 10.1021/acs.jctc.3c01207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Revised: 12/21/2023] [Accepted: 12/26/2023] [Indexed: 02/01/2024]
Abstract
Polariton chemistry has attracted great attention as a potential route to modify chemical structure, properties, and reactivity through strong interactions among molecular electronic, vibrational, or rovibrational degrees of freedom. A rigorous theoretical treatment of molecular polaritons requires the treatment of matter and photon degrees of freedom on equal quantum mechanical footing. In the limit of molecular electronic strong or ultrastrong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach we refer to as ab initio cavity quantum electrodynamics, where the photon degrees of freedom are treated at the level of cavity quantum electrodynamics. Here, we present an approach called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction theory to provide ground- and excited-state polaritonic surfaces with a balanced description of strong correlation effects among electronic and photonic degrees of freedom. This method provides a platform for ab initio cavity quantum electrodynamics when both strong electron correlation and strong light-matter coupling are important and is an important step toward computational approaches that yield multiple polaritonic potential energy surfaces and couplings that can be leveraged for ab initio molecular dynamics simulations of polariton chemistry.
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Affiliation(s)
- Nam Vu
- Department
of Chemistry, University of North Carolina
Charlotte, 9201 University City Blvd., Charlotte, North Carolina 28223, United States
| | - Daniel Mejia-Rodriguez
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Nicholas P. Bauman
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Ajay Panyala
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Erdal Mutlu
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Jonathan J. Foley
- Department
of Chemistry, University of North Carolina
Charlotte, 9201 University City Blvd., Charlotte, North Carolina 28223, United States
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17
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Hassan M, Pavošević F, Wang DS, Flick J. Simulating Polaritonic Ground States on Noisy Quantum Devices. J Phys Chem Lett 2024; 15:1373-1381. [PMID: 38287217 DOI: 10.1021/acs.jpclett.3c02875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2024]
Abstract
The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.
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Affiliation(s)
- Mohammad Hassan
- Department of Physics, City College of New York, New York, New York 10031, United States
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
| | | | - Derek S Wang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Department of Physics, City College of New York, New York, New York 10031, United States
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
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18
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Rana B, Hohenstein EG, Martínez TJ. Simulating the Excited-State Dynamics of Polaritons with Ab Initio Multiple Spawning. J Phys Chem A 2024; 128:139-151. [PMID: 38110364 DOI: 10.1021/acs.jpca.3c06607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2023]
Abstract
Over the past decade, there has been a growth of interest in polaritonic chemistry, where the formation of hybrid light-matter states (polaritons) can alter the course of photochemical reactions. These hybrid states are created by strong coupling between molecules and photons in resonant optical cavities and can even occur in the absence of light when the molecule is strongly coupled with the electromagnetic fluctuations of the vacuum field. We present a first-principles model to simulate nonadiabatic dynamics of such polaritonic states inside optical cavities by leveraging graphical processing units (GPUs). Our first implementation of this model is specialized for a single molecule coupled to a single-photon mode confined inside the optical cavity but with any number of excited states computed using complete active space configuration interaction (CASCI) and a Jaynes-Cummings-type Hamiltonian. Using this model, we have simulated the excited-state dynamics of a single salicylideneaniline (SA) molecule strongly coupled to a cavity photon with the ab initio multiple spawning (AIMS) method. We demonstrate how the branching ratios of the photodeactivation pathways for this molecule can be manipulated by coupling to the cavity. We also show how one can stop the photoreaction from happening inside of an optical cavity. Finally, we also investigate cavity-based control of the ordering of two excited states (one optically bright and the other optically dark) inside a cavity for a set of molecules, where the dark and bright states are close in energy.
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Affiliation(s)
- Bhaskar Rana
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
| | - Edward G Hohenstein
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
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19
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Calderón LF, Triviño H, Pachón LA. Quantum to Classical Cavity Chemistry Electrodynamics. J Phys Chem Lett 2023; 14:11725-11734. [PMID: 38112558 DOI: 10.1021/acs.jpclett.3c02870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
Polaritonic chemistry has ushered in new avenues for controlling molecular dynamics. However, two key questions remain: (i) Can classical light sources elicit the same effects as certain quantum light sources on molecular systems? (ii) Can semiclassical treatments of light-matter interactions capture nontrivial quantum effects observed in molecular dynamics? This work presents a quantum-classical approach addressing issues of realizing cavity chemistry effects without actual cavities. It also highlights the limitations of the standard semiclassical light-matter interaction. It is demonstrated that classical light sources can mimic quantum effects up to the second order of light-matter interaction provided that the mean-field contribution, the symmetrized two-time correlation function, and the linear response function are the same in both situations. Numerical simulations show that the quantum-classical method aligns more closely with exact quantum molecular-only dynamics for quantum light states such as Fock states, superpositions of Fock states, and vacuum squeezed states than does the conventional semiclassical approach.
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Affiliation(s)
- Leonardo F Calderón
- Grupo de Física Teórica y Matemática Aplicada, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia; Calle 70 No. 52-21, 500001 Medellín, Colombia
- Grupo de Física Computacional en Materia Condensada, Escuela de Física, Facultad de Ciencias, Universidad Industrial de Santander UIS; Cra 27 Calle 9 Ciudad Universitaria, 680002 Bucaramanga, Colombia
| | - Humberto Triviño
- Grupo de Física Teórica y Matemática Aplicada, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia; Calle 70 No. 52-21, 500001 Medellín, Colombia
| | - Leonardo A Pachón
- Grupo de Física Teórica y Matemática Aplicada, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia; Calle 70 No. 52-21, 500001 Medellín, Colombia
- Grupo de Física Atómica y Molecular, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia; Calle 70 No. 52-21, 500001 Medellín, Colombia
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20
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Pavošević F, Smith RL, Rubio A. Cavity Click Chemistry: Cavity-Catalyzed Azide-Alkyne Cycloaddition. J Phys Chem A 2023; 127:10184-10188. [PMID: 37992280 DOI: 10.1021/acs.jpca.3c06285] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2023]
Abstract
Click chemistry, which refers to chemical reactions that are fast and selective with high product yields, has become a powerful approach in organic synthesis and chemical biology. Due to the cytotoxicity of the transition metals employed in click chemistry reactions, a search for novel metal-free alternatives continues. Herein, we demonstrate that an optical cavity can be utilized as a metal-free alternative in the click chemistry cycloaddition reaction between cyanoacetylene and formylazide using the quantum electrodynamics coupled cluster method. We show that by changing the molecular orientation with respect to the polarization of the cavity mode(s), the reaction can be selectively catalyzed to form a major 1,4-disubstituted or 1,5-disubstituted product. This work highlights that a cavity has the same effect on the investigated cycloaddition as the transition metal catalysts traditionally employed in click chemistry reactions. We expect our findings to further stimulate research on cavity-assisted click chemistry reactions.
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Affiliation(s)
- Fabijan Pavošević
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Algorithmiq Ltd, Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Robert L Smith
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Angel Rubio
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
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21
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Fidler AP, Chen L, McKillop AM, Weichman ML. Ultrafast dynamics of CN radical reactions with chloroform solvent under vibrational strong coupling. J Chem Phys 2023; 159:164302. [PMID: 37870135 DOI: 10.1063/5.0167410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 08/21/2023] [Indexed: 10/24/2023] Open
Abstract
Polariton chemistry may provide a new means to control molecular reactivity, permitting remote, reversible modification of reaction energetics, kinetics, and product yields. A considerable body of experimental and theoretical work has already demonstrated that strong coupling between a molecular vibrational mode and the confined electromagnetic field of an optical cavity can alter chemical reactivity without external illumination. However, the mechanisms underlying cavity-altered chemistry remain unclear in large part because the experimental systems examined previously are too complex for detailed analysis of their reaction dynamics. Here, we experimentally investigate photolysis-induced reactions of cyanide radicals with strongly-coupled chloroform (CHCl3) solvent molecules and examine the intracavity rates of photofragment recombination, solvent complexation, and hydrogen abstraction. We use a microfluidic optical cavity fitted with dichroic mirrors to facilitate vibrational strong coupling (VSC) of the C-H stretching mode of CHCl3 while simultaneously permitting optical access at visible wavelengths. Ultrafast transient absorption experiments performed with cavities tuned on- and off-resonance reveal that VSC of the CHCl3 C-H stretching transition does not significantly modify any measured rate constants, including those associated with the hydrogen abstraction reaction. This work represents, to the best of our knowledge, the first experimental study of an elementary bimolecular reaction under VSC. We discuss how the conspicuous absence of cavity-altered effects in this system may provide insights into the mechanisms of modified ground state reactivity under VSC and help bridge the divide between experimental results and theoretical predictions in vibrational polariton chemistry.
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Affiliation(s)
- Ashley P Fidler
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Liying Chen
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | | | - Marissa L Weichman
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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22
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Sokolovskii I, Tichauer RH, Morozov D, Feist J, Groenhof G. Multi-scale molecular dynamics simulations of enhanced energy transfer in organic molecules under strong coupling. Nat Commun 2023; 14:6613. [PMID: 37857599 PMCID: PMC10587084 DOI: 10.1038/s41467-023-42067-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Accepted: 09/21/2023] [Indexed: 10/21/2023] Open
Abstract
Exciton transport can be enhanced in the strong coupling regime where excitons hybridize with confined light modes to form polaritons. Because polaritons have group velocity, their propagation should be ballistic and long-ranged. However, experiments indicate that organic polaritons propagate in a diffusive manner and more slowly than their group velocity. Here, we resolve this controversy by means of molecular dynamics simulations of Rhodamine molecules in a Fabry-Pérot cavity. Our results suggest that polariton propagation is limited by the cavity lifetime and appears diffusive due to reversible population transfers between polaritonic states that propagate ballistically at their group velocity, and dark states that are stationary. Furthermore, because long-lived dark states transiently trap the excitation, propagation is observed on timescales beyond the intrinsic polariton lifetime. These insights not only help to better understand and interpret experimental observations, but also pave the way towards rational design of molecule-cavity systems for coherent exciton transport.
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Affiliation(s)
- Ilia Sokolovskii
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, Jyväskylä, 40014, Finland
| | - Ruth H Tichauer
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, Jyväskylä, 40014, Finland
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - Dmitry Morozov
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, Jyväskylä, 40014, Finland
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - Gerrit Groenhof
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, Jyväskylä, 40014, Finland.
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23
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Philbin JP, Haugland TS, Ghosh TK, Ronca E, Chen M, Narang P, Koch H. Molecular van der Waals Fluids in Cavity Quantum Electrodynamics. J Phys Chem Lett 2023; 14:8988-8993. [PMID: 37774379 PMCID: PMC10578074 DOI: 10.1021/acs.jpclett.3c01790] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 09/14/2023] [Indexed: 10/01/2023]
Abstract
Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. In this work, we demonstrate that strong light-matter coupling can be used to control the thermodynamic properties of many-molecule systems. Our analyses reveal orientation dependent single molecule energies and interaction energies for van der Waals molecules. For example, we find intermolecular interactions that depend on the distance between the molecules R as R-3 and R0. Moreover, we employ ab initio cavity quantum electrodynamics calculations to develop machine-learning-based interaction potentials for molecules inside optical cavities. By simulating systems ranging from 12 H2 to 144 H2 molecules, we observe varying degrees of orientational order because of cavity-modified interactions, and we explain how quantum nuclear effects, light-matter coupling strengths, number of cavity modes, molecular anisotropies, and system size all impact the extent of orientational order.
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Affiliation(s)
- John P. Philbin
- Harvard
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
- College
of Letters and Science, University of California, Los Angeles, California 90095, United States
| | - Tor S. Haugland
- Department
of Chemistry, Norwegian University of Science
and Technology, 7491 Trondheim, Norway
| | - Tushar K. Ghosh
- Department
of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Enrico Ronca
- Dipartimento
di Chimica, Biologia e Biotecnologie, Università
degli Studi di Perugia, Via Elce di Sotto, 8, 06123 Perugia, Italy
- Max Planck
Institute for the Structure and Dynamics of Matter and Center Free-Electron
Laser Science, Luruper
Chaussee 149, 22761 Hamburg, Germany
| | - Ming Chen
- Department
of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Prineha Narang
- Harvard
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
- College
of Letters and Science, University of California, Los Angeles, California 90095, United States
| | - Henrik Koch
- Department
of Chemistry, Norwegian University of Science
and Technology, 7491 Trondheim, Norway
- Scuola
Normale Superiore, Piazza dei Cavalieri, 7, 56124 Pisa, Italy
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24
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Severi M, Zerbetto F. Polaritonic Chemistry: Hindering and Easing Ground State Polyenic Isomerization via Breakdown of σ-π Separation. J Phys Chem Lett 2023; 14:9145-9149. [PMID: 37796008 PMCID: PMC10577679 DOI: 10.1021/acs.jpclett.3c02081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 09/06/2023] [Indexed: 10/06/2023]
Abstract
The ground state conformational isomerization in polyenes is a symmetry allowed process. Its low energy barrier is governed by electron density transfer from the formal single bond that is rotated to the nearby formal double bonds. Along the reaction pathway, the transition state is therefore destabilized. The rules of polaritonic chemistry, i.e., chemistry in a nanocavity with reflecting windows, are barely beginning to be laid out. The standing electric field of the nanocavity couples strongly with the molecular wave function and modifies the potential energy curve in unexpected ways. A quantum electrodynamics approach, applied to the torsional degree of freedom of the central bond of butadiene, shows that formation of the polariton mixes the σ-π frameworks thereby stabilizing/destabilizing the planar, reactant-like conformations. The values of the fundamental mode of the cavity field used in the absence of the cavity do not trigger this mechanism.
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Affiliation(s)
- Marco Severi
- Department
of Chemistry G. Ciamician, University of
Bologna, Via F. Selmi 2, 40126 Bologna, Italy
| | - Francesco Zerbetto
- Department
of Chemistry G. Ciamician, University of
Bologna, Via F. Selmi 2, 40126 Bologna, Italy
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25
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Villaseco Arribas E, Vindel-Zandbergen P, Roy S, Maitra NT. Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics. Phys Chem Chem Phys 2023; 25:26380-26395. [PMID: 37750820 DOI: 10.1039/d3cp03464j] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/27/2023]
Abstract
The exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron-ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron-nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.
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Affiliation(s)
| | - Patricia Vindel-Zandbergen
- Department of Physics, Rutgers University, Newark 07102, New Jersey, USA.
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Saswata Roy
- Department of Physics, Rutgers University, Newark 07102, New Jersey, USA.
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark 07102, New Jersey, USA.
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26
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Bhuyan R, Mony J, Kotov O, Castellanos GW, Gómez Rivas J, Shegai TO, Börjesson K. The Rise and Current Status of Polaritonic Photochemistry and Photophysics. Chem Rev 2023; 123:10877-10919. [PMID: 37683254 PMCID: PMC10540218 DOI: 10.1021/acs.chemrev.2c00895] [Citation(s) in RCA: 12] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Indexed: 09/10/2023]
Abstract
The interaction between molecular electronic transitions and electromagnetic fields can be enlarged to the point where distinct hybrid light-matter states, polaritons, emerge. The photonic contribution to these states results in increased complexity as well as an opening to modify the photophysics and photochemistry beyond what normally can be seen in organic molecules. It is today evident that polaritons offer opportunities for molecular photochemistry and photophysics, which has caused an ever-rising interest in the field. Focusing on the experimental landmarks, this review takes its reader from the advent of the field of polaritonic chemistry, over the split into polariton chemistry and photochemistry, to present day status within polaritonic photochemistry and photophysics. To introduce the field, the review starts with a general description of light-matter interactions, how to enhance these, and what characterizes the coupling strength. Then the photochemistry and photophysics of strongly coupled systems using Fabry-Perot and plasmonic cavities are described. This is followed by a description of room-temperature Bose-Einstein condensation/polariton lasing in polaritonic systems. The review ends with a discussion on the benefits, limitations, and future developments of strong exciton-photon coupling using organic molecules.
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Affiliation(s)
- Rahul Bhuyan
- Department
of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Göteborg, Sweden
| | - Jürgen Mony
- Department
of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Göteborg, Sweden
| | - Oleg Kotov
- Department
of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Gabriel W. Castellanos
- Department
of Applied Physics and Science Education, Eindhoven Hendrik Casimir
Institute and Institute for Complex Molecular Systems, Eindhoven University of Technology, 5612 AE Eindhoven, The Netherlands
| | - Jaime Gómez Rivas
- Department
of Applied Physics and Science Education, Eindhoven Hendrik Casimir
Institute and Institute for Complex Molecular Systems, Eindhoven University of Technology, 5612 AE Eindhoven, The Netherlands
| | - Timur O. Shegai
- Department
of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Karl Börjesson
- Department
of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Göteborg, Sweden
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27
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Schnappinger T, Sidler D, Ruggenthaler M, Rubio A, Kowalewski M. Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles. J Phys Chem Lett 2023; 14:8024-8033. [PMID: 37651603 PMCID: PMC10510432 DOI: 10.1021/acs.jpclett.3c01842] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 08/22/2023] [Indexed: 09/02/2023]
Abstract
Experimental studies indicate that optical cavities can affect chemical reactions through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models that take into account intermolecular interactions to describe ensembles are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a nonperturbative, self-consistent description of strongly coupled molecular ensembles, taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated intermolecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.
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Affiliation(s)
- Thomas Schnappinger
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
| | - Dominik Sidler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael Ruggenthaler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron
Institute, 162 Fifth
Avenue, New York, New York 10010, United States
- Nano-Bio
Spectroscopy Group, University of the Basque
Country (UPV/EHU), 20018 San Sebastián, Spain
| | - Markus Kowalewski
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
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28
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Mandal A, Taylor MA, Weight BM, Koessler ER, Li X, Huo P. Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics. Chem Rev 2023; 123:9786-9879. [PMID: 37552606 PMCID: PMC10450711 DOI: 10.1021/acs.chemrev.2c00855] [Citation(s) in RCA: 31] [Impact Index Per Article: 31.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Indexed: 08/10/2023]
Abstract
When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.
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Affiliation(s)
- Arkajit Mandal
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Michael A.D. Taylor
- The
Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, United States
| | - Braden M. Weight
- Department
of Physics and Astronomy, University of
Rochester, Rochester, New York 14627, United
States
| | - Eric R. Koessler
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Xinyang Li
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pengfei Huo
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
- The
Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, United States
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29
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Moiseyev N, Landau A. QED Theory for Controlling the Molecule-Cavity Interaction: From Solvable Analytical Models to Realistic Ones. J Chem Theory Comput 2023; 19:5465-5480. [PMID: 37494598 DOI: 10.1021/acs.jctc.3c00269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
The study of the interactions of chemical systems in a cavity and the ability to control the reactions inside the cavities become an evolving and hot field of research. Despite that, there is still a significant gap between experiment and theory. Herein, we aim to bridge this gap by starting with the analysis of solvable analytical models for reactions inside a cavity, then continuing to realistic models for many molecules inside a single mode and in a multimode cavity. In addition, we investigate different ways to control the strength of the molecule-cavity coupling term, which in turn allows controlling chemical reactions. Our analysis can benefit the development of ab initio computational methods to simulate molecular systems in polariton cavities; in addition, we show how to parameterize the model Hamiltonians in order to simulate a specific molecular system. Finally, we demonstrate the possibility of achieving isomerization, in case it is prohibited out of the cavity, by placing the reaction inside a cavity.
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30
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Davidsson E, Kowalewski M. The role of dephasing for dark state coupling in a molecular Tavis-Cummings model. J Chem Phys 2023; 159:044306. [PMID: 37493131 PMCID: PMC7615654 DOI: 10.1063/5.0155302] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 07/07/2023] [Indexed: 07/27/2023] Open
Abstract
The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.
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Affiliation(s)
- Eric Davidsson
- Department of Physics, Stockholm University, Albanova University Center, SE-106 91 Stockholm, Sweden
| | - Markus Kowalewski
- Department of Physics, Stockholm University, Albanova University Center, SE-106 91 Stockholm, Sweden
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31
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Kuttruff J, Romanelli M, Pedrueza-Villalmanzo E, Allerbeck J, Fregoni J, Saavedra-Becerril V, Andréasson J, Brida D, Dmitriev A, Corni S, Maccaferri N. Sub-picosecond collapse of molecular polaritons to pure molecular transition in plasmonic photoswitch-nanoantennas. Nat Commun 2023; 14:3875. [PMID: 37414750 DOI: 10.1038/s41467-023-39413-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 06/09/2023] [Indexed: 07/08/2023] Open
Abstract
Molecular polaritons are hybrid light-matter states that emerge when a molecular transition strongly interacts with photons in a resonator. At optical frequencies, this interaction unlocks a way to explore and control new chemical phenomena at the nanoscale. Achieving such control at ultrafast timescales, however, is an outstanding challenge, as it requires a deep understanding of the dynamics of the collectively coupled molecular excitation and the light modes. Here, we investigate the dynamics of collective polariton states, realized by coupling molecular photoswitches to optically anisotropic plasmonic nanoantennas. Pump-probe experiments reveal an ultrafast collapse of polaritons to pure molecular transition triggered by femtosecond-pulse excitation at room temperature. Through a synergistic combination of experiments and quantum mechanical modelling, we show that the response of the system is governed by intramolecular dynamics, occurring one order of magnitude faster with respect to the uncoupled excited molecule relaxation to the ground state.
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Affiliation(s)
- Joel Kuttruff
- Department of Physics, University of Konstanz, Universitätsstraße 10, 78464, Konstanz, Germany
| | - Marco Romanelli
- Department of Chemical Sciences, University of Padova, via Marzolo 1, 35131, Padova, Italy
| | - Esteban Pedrueza-Villalmanzo
- Department of Physics, University of Gothenburg, Origovägen 6B, 412 96, Gothenburg, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Kemigården 4, 412 96, Göteborg, Sweden
| | - Jonas Allerbeck
- Department of Physics, University of Konstanz, Universitätsstraße 10, 78464, Konstanz, Germany
- nanotech@surfaces Laboratory, Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland
| | - Jacopo Fregoni
- Department of Physics, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049, Madrid, Spain
| | - Valeria Saavedra-Becerril
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Kemigården 4, 412 96, Göteborg, Sweden
| | - Joakim Andréasson
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Kemigården 4, 412 96, Göteborg, Sweden
| | - Daniele Brida
- Department of Physics and Materials Science, University of Luxembourg, 162a avenue de la Faïencerie, L-1511, Luxembourg, Luxembourg
| | - Alexandre Dmitriev
- Department of Physics, University of Gothenburg, Origovägen 6B, 412 96, Gothenburg, Sweden.
| | - Stefano Corni
- Department of Chemical Sciences, University of Padova, via Marzolo 1, 35131, Padova, Italy.
- CNR Institute of Nanoscience, via Campi 213/A, 41125, Modena, Italy.
| | - Nicolò Maccaferri
- Department of Physics and Materials Science, University of Luxembourg, 162a avenue de la Faïencerie, L-1511, Luxembourg, Luxembourg.
- Department of Physics, Umeå University, Linnaeus väg 24, 901 87, Umeå, Sweden.
- Umeå Centre for Microbial Research, Umeå University, 901 87, Umeå, Sweden.
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32
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Abstract
The coherent exchange of energy between materials and optical fields leads to strong light-matter interactions and so-called polaritonic states with intriguing properties, halfway between light and matter. Two decades ago, research on these strong light-matter interactions, using optical cavity (vacuum) fields, remained for the most part the province of the physicist, with a focus on inorganic materials requiring cryogenic temperatures and carefully fabricated, high-quality optical cavities for their study. This review explores the history and recent acceleration of interest in the application of polaritonic states to molecular properties and processes. The enormous collective oscillator strength of dense films of organic molecules, aggregates, and materials allows cavity vacuum field strong coupling to be achieved at room temperature, even in rapidly fabricated, highly lossy metallic optical cavities. This has put polaritonic states and their associated coherent phenomena at the fingertips of laboratory chemists, materials scientists, and even biochemists as a potentially new tool to control molecular chemistry. The exciting phenomena that have emerged suggest that polaritonic states are of genuine relevance within the molecular and material energy landscape.
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Affiliation(s)
- Kenji Hirai
- Division of Photonics and Optical Science, Research Institute for Electronic Science (RIES), Hokkaido University, North 20 West 10, Kita ward, Sapporo, Hokkaido 001-0020, Japan
| | - James A Hutchison
- School of Chemistry and ARC Centre of Excellence in Exciton Science, The University of Melbourne, Masson Road, Parkville, Victoria 3052 Australia
| | - Hiroshi Uji-I
- Division of Photonics and Optical Science, Research Institute for Electronic Science (RIES), Hokkaido University, North 20 West 10, Kita ward, Sapporo, Hokkaido 001-0020, Japan
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, 3001 Heverlee Leuven Belgium
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33
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Lentrodt D, Diekmann O, Keitel CH, Rotter S, Evers J. Certifying Multimode Light-Matter Interaction in Lossy Resonators. PHYSICAL REVIEW LETTERS 2023; 130:263602. [PMID: 37450811 DOI: 10.1103/physrevlett.130.263602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Revised: 07/21/2022] [Accepted: 05/19/2023] [Indexed: 07/18/2023]
Abstract
Quantum models based on few-mode master equations have been a central tool in the study of resonator quantum electrodynamics, extending the seminal single-mode Jaynes-Cummings model to include loss and multiple modes. Despite their broad application range, previous approaches within this framework have either relied on a Markov approximation or a fitting procedure. By combining ideas from pseudomode and quasinormal mode theory, we develop a certification criterion for multi-mode effects in lossy resonators. It is based on a witness observable, and neither requires a fitting procedure nor a Markov approximation. Using the resulting criterion, we demonstrate that such multi-mode effects are important for understanding previous experiments in x-ray cavity QED with Mössbauer nuclei and that they allow one to tune the nuclear ensemble properties.
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Affiliation(s)
- Dominik Lentrodt
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - Oliver Diekmann
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
- Institute for Theoretical Physics, Vienna University of Technology (TU Wien), 1040 Vienna, Austria
| | - Christoph H Keitel
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - Stefan Rotter
- Institute for Theoretical Physics, Vienna University of Technology (TU Wien), 1040 Vienna, Austria
| | - Jörg Evers
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
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34
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Cederbaum LS, Fedyk J. Activating cavity by electrons. COMMUNICATIONS PHYSICS 2023; 6:111. [PMID: 38665403 PMCID: PMC11041782 DOI: 10.1038/s42005-023-01227-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 04/27/2023] [Indexed: 04/28/2024]
Abstract
The interaction of atoms and molecules with quantum light as realized in cavities has become a highly topical and fast growing research field. This interaction leads to hybrid light-matter states giving rise to new phenomena and opening up pathways to control and manipulate properties of the matter. Here, we substantially extend the scope of the interaction by allowing free electrons to enter the cavity and merge and unify the two active fields of electron scattering and quantum-light-matter interaction. In the presence of matter, hybrid metastable states are formed at electron energies of choice. The properties of these states depend strongly on the frequency and on the light-matter coupling of the cavity. The incoming electrons can be captured by the matter inside the cavity solely due to the presence of the cavity. The findings are substantiated by an explicit example and general consequences are discussed.
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Affiliation(s)
- Lorenz S. Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - Jacqueline Fedyk
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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35
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Toldo JM, do Casal MT, Ventura E, do Monte SA, Barbatti M. Surface hopping modeling of charge and energy transfer in active environments. Phys Chem Chem Phys 2023; 25:8293-8316. [PMID: 36916738 PMCID: PMC10034598 DOI: 10.1039/d3cp00247k] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/05/2023]
Abstract
An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.
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Affiliation(s)
| | | | - Elizete Ventura
- Departamento de Química, CCEN, Universidade Federal da Paraíba, 58059-900, João Pessoa, Brazil.
| | - Silmar A do Monte
- Departamento de Química, CCEN, Universidade Federal da Paraíba, 58059-900, João Pessoa, Brazil.
| | - Mario Barbatti
- Aix-Marseille University, CNRS, ICR, Marseille, France.
- Institut Universitaire de France, 75231, Paris, France
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36
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Li TE, Hammes-Schiffer S. Electronic Born-Oppenheimer approximation in nuclear-electronic orbital dynamics. J Chem Phys 2023; 158:114118. [PMID: 36948810 DOI: 10.1063/5.0142007] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/24/2023] Open
Abstract
Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born-Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications.
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Affiliation(s)
- Tao E Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
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37
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Mukherjee A, Feist J, Börjesson K. Quantitative Investigation of the Rate of Intersystem Crossing in the Strong Exciton-Photon Coupling Regime. J Am Chem Soc 2023; 145:5155-5162. [PMID: 36813757 PMCID: PMC9999416 DOI: 10.1021/jacs.2c11531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Abstract
Strong interactions between excitons and photons lead to the formation of exciton-polaritons, which possess completely different properties compared to their constituents. The polaritons are created by incorporating a material in an optical cavity where the electromagnetic field is tightly confined. Over the last few years, the relaxation of polaritonic states has been shown to enable a new kind of energy transfer event, which is efficient at length scales substantially larger than the typical Förster radius. However, the importance of such energy transfer depends on the ability of the short-lived polaritonic states to efficiently decay to molecular localized states that can perform a photochemical process, such as charge transfer or triplet states. Here, we investigate quantitatively the interaction between polaritons and triplet states of erythrosine B in the strong coupling regime. We analyze the experimental data, collected mainly employing angle-resolved reflectivity and excitation measurements, using a rate equation model. We show that the rate of intersystem crossing from the polariton to the triplet states depends on the energy alignment of the excited polaritonic states. Furthermore, it is demonstrated that the rate of intersystem crossing can be substantially enhanced in the strong coupling regime to the point where it approaches the rate of the radiative decay of the polariton. In light of the opportunities that transitions from polaritonic to molecular localized states offer within molecular photophysics/chemistry and organic electronics, we hope that the quantitative understanding of such interactions gained from this study will aid in the development of polariton-empowered devices.
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Affiliation(s)
- Arpita Mukherjee
- Department of Chemistry and Molecular Biology, University of Gothenburg, Kemivägen 10, 412 96 Gothenburg, Sweden
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid E-28049, Spain
| | - Karl Börjesson
- Department of Chemistry and Molecular Biology, University of Gothenburg, Kemivägen 10, 412 96 Gothenburg, Sweden
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38
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Hsieh MH, Krotz A, Tempelaar R. A Mean-Field Treatment of Vacuum Fluctuations in Strong Light-Matter Coupling. J Phys Chem Lett 2023; 14:1253-1258. [PMID: 36719108 DOI: 10.1021/acs.jpclett.2c03724] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Mean-field mixed quantum-classical dynamics could provide a much-needed means to inexpensively model quantum electrodynamical phenomena by describing the optical field and its vacuum fluctuations classically. However, this approach is known to suffer from an unphysical transfer of energy out of the vacuum fluctuations when the light-matter coupling becomes strong. We highlight this issue for the case of an atom in an optical cavity and resolve it by introducing an additional set of classical coordinates to specifically represent vacuum fluctuations whose light-matter interaction is scaled by the instantaneous ground-state population of the atom. This not only rigorously prevents the aforementioned unphysical energy transfer but is also shown to yield a radically improved accuracy in terms of the atomic population and the optical field dynamics, generating results in excellent agreement with full quantum calculations. As such, the resulting method emerges as an attractive solution for the affordable modeling of strong light-matter coupling phenomena involving macroscopic numbers of optical modes.
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Affiliation(s)
- Ming-Hsiu Hsieh
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois60208, United States
| | - Alex Krotz
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois60208, United States
| | - Roel Tempelaar
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois60208, United States
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39
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Li TE, Hammes-Schiffer S. QM/MM Modeling of Vibrational Polariton Induced Energy Transfer and Chemical Dynamics. J Am Chem Soc 2023; 145:377-384. [PMID: 36574620 DOI: 10.1021/jacs.2c10170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Vibrational strong coupling (VSC) provides a novel means to modify chemical reactions and energy transfer pathways. To efficiently model chemical dynamics under VSC in the collective regime, herein a hybrid quantum mechanical/molecular mechanical (QM/MM) cavity molecular dynamics (CavMD) scheme is developed and applied to an experimentally studied chemical system. This approach can achieve linear scaling with respect to the number of molecules for a dilute solution under VSC by assuming that each QM solute molecule is surrounded by an independent MM solvent bath. Application of this approach to a dilute solution of Fe(CO)5 in n-dodecane under VSC demonstrates polariton dephasing to the dark modes and polariton-enhanced molecular nonlinear absorption. These simulations predict that strongly exciting the lower polariton may provide an energy transfer pathway that selectively excites the equatorial CO vibrations rather than the axial CO vibrations. Moreover, these simulations also directly probe the cavity effect on the dynamics of the Fe(CO)5 Berry pseudorotation reaction for comparison to recent two-dimensional infrared spectroscopy experiments. This theoretical approach is applicable to a wide range of other polaritonic systems and provides a tool for exploring the use of VSC for selective infrared photochemistry.
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Affiliation(s)
- Tao E Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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40
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Cheng CY, Krainova N, Brigeman AN, Khanna A, Shedge S, Isborn C, Yuen-Zhou J, Giebink NC. Molecular polariton electroabsorption. Nat Commun 2022; 13:7937. [PMID: 36566224 DOI: 10.1038/s41467-022-35589-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 12/09/2022] [Indexed: 12/25/2022] Open
Abstract
We investigate electroabsorption (EA) in organic semiconductor microcavities to understand whether strong light-matter coupling non-trivially alters their nonlinear optical [[Formula: see text]] response. Focusing on strongly-absorbing squaraine (SQ) molecules dispersed in a wide-gap host matrix, we find that classical transfer matrix modeling accurately captures the EA response of low concentration SQ microcavities with a vacuum Rabi splitting of [Formula: see text] meV, but fails for high concentration cavities with [Formula: see text] meV. Rather than new physics in the ultrastrong coupling regime, however, we attribute the discrepancy at high SQ concentration to a nearly dark H-aggregate state below the SQ exciton transition, which goes undetected in the optical constant dispersion on which the transfer matrix model is based, but nonetheless interacts with and enhances the EA response of the lower polariton mode. These results indicate that strong coupling can be used to manipulate EA (and presumably other optical nonlinearities) from organic microcavities by controlling the energy of polariton modes relative to other states in the system, but it does not alter the intrinsic optical nonlinearity of the organic semiconductor inside the cavity.
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Affiliation(s)
- Chiao-Yu Cheng
- Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Nina Krainova
- Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Alyssa N Brigeman
- Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Ajay Khanna
- Department of Chemistry and Biochemistry, University of California Merced, Merced, CA, 95343, USA
| | - Sapana Shedge
- Department of Chemistry and Biochemistry, University of California Merced, Merced, CA, 95343, USA
| | - Christine Isborn
- Department of Chemistry and Biochemistry, University of California Merced, Merced, CA, 95343, USA
| | - Joel Yuen-Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, CA, 92093, USA
| | - Noel C Giebink
- Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, 16802, USA.
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41
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Della Sala F, Pachter R, Sukharev M. Advances in modeling plasmonic systems. J Chem Phys 2022; 157:190401. [DOI: 10.1063/5.0130790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Affiliation(s)
- Fabio Della Sala
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano, LE, Italy
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
| | - Ruth Pachter
- Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Ohio 45433, USA
| | - Maxim Sukharev
- College of Integrative Sciences and Arts, Arizona State University, Mesa, Arizona 85212, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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42
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Stemo G, Yamada H, Katsuki H, Yanagi H. Influence of Vibrational Strong Coupling on an Ordered Liquid Crystal. J Phys Chem B 2022; 126:9399-9407. [DOI: 10.1021/acs.jpcb.2c04004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Garrek Stemo
- Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma 630-0192 Japan
| | - Hayata Yamada
- Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma 630-0192 Japan
| | - Hiroyuki Katsuki
- Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma 630-0192 Japan
| | - Hisao Yanagi
- Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma 630-0192 Japan
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43
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Pavosevic F, Rubio A. Wavefunction embedding for molecular polaritons. J Chem Phys 2022; 157:094101. [DOI: 10.1063/5.0095552] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Polaritonic chemistry relies on the strong light-matter interaction phenomena for altering the chemical reaction rates inside optical cavities. To explain and to understand these processes, the development of reliable theoretical models is essential. While computationally efficient quantum electrodynamics self-consistent field (QED-SCF) methods, such as quantum electrodynamics density functional theory (QEDFT) needs accurate functionals, quantum electrodynamics coupled cluster (QED-CC) methods provide a systematic increase in accuracy but at much greater cost. To overcome this computational bottleneck, herein we introduce and develop the QED-CC-in-QED-SCF projection-based embedding method that inherits all the favorable properties from the two worlds, computational efficiency and accuracy. The performance of the embedding method is assessed by studying some prototypical but relevant reactions, such as methyl transfer reaction, proton transfer reaction, as well as protonation reaction in a complex environment. The results obtained with the new embedding method are in excellent agreement with more expensive QED-CC results. The analysis performed on these reactions indicate that the electron-photon correlation effects are local in nature and that only a small region should be treated at the QED-CC level for capturing important effects due to cavity. This work sets the stage for future developments of polaritonic quantum chemistry methods and it will serve as a guideline for development of other polaritonic embedding models.
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Affiliation(s)
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Germany
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44
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Sánchez-Barquilla M, Fernández-Domínguez AI, Feist J, García-Vidal FJ. A Theoretical Perspective on Molecular Polaritonics. ACS PHOTONICS 2022; 9:1830-1841. [PMID: 35726239 PMCID: PMC9204811 DOI: 10.1021/acsphotonics.2c00048] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2022] [Revised: 05/20/2022] [Accepted: 05/20/2022] [Indexed: 06/15/2023]
Abstract
In the past decade, much theoretical research has focused on studying the strong coupling between organic molecules (or quantum emitters, in general) and light modes. The description and prediction of polaritonic phenomena emerging in this light-matter interaction regime have proven to be difficult tasks. The challenge originates from the enormous number of degrees of freedom that need to be taken into account, both in the organic molecules and in their photonic environment. On one hand, the accurate treatment of the vibrational spectrum of the former is key, and simplified quantum models are not valid in many cases. On the other hand, most photonic setups have complex geometric and material characteristics, with the result that photon fields corresponding to more than just a single electromagnetic mode contribute to the light-matter interaction in these platforms. Moreover, loss and dissipation, in the form of absorption or radiation, must also be included in the theoretical description of polaritons. Here, we review and offer our own perspective on some of the work recently done in the modeling of interacting molecular and optical states with increasing complexity.
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Affiliation(s)
- Mónica Sánchez-Barquilla
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Antonio I. Fernández-Domínguez
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Johannes Feist
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Francisco J. García-Vidal
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Institute
of High Performance Computing, Agency for
Science, Technology, and Research (A*STAR), Connexis, Singapore, 138632 Singapore
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