1
|
Fischer EW, Saalfrank P. Beyond Cavity Born-Oppenheimer: On Nonadiabatic Coupling and Effective Ground State Hamiltonians in Vibro-Polaritonic Chemistry. J Chem Theory Comput 2023; 19:7215-7229. [PMID: 37793029 DOI: 10.1021/acs.jctc.3c00708] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/06/2023]
Abstract
The emerging field of vibro-polaritonic chemistry studies the impact of light-matter hybrid states known as vibrational polaritons on chemical reactivity and molecular properties. Here, we discuss vibro-polaritonic chemistry from a quantum chemical perspective beyond the cavity Born-Oppenheimer (CBO) approximation and examine the role of electron-photon correlation in effective ground state Hamiltonians. We first quantitatively review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz Hamiltonian in dipole approximation and a vibrational strong coupling (VSC) Born-Huang expansion. We then derive nonadiabatic coupling elements arising from both "slow" nuclei and cavity modes compared to "fast" electrons via the generalized Hellmann-Feynman theorem, discuss their properties, and reevaluate the CBO approximation. In the second part, we introduce a crude VSC Born-Huang expansion based on adiabatic electronic states, which provides a foundation for widely employed effective Pauli-Fierz Hamiltonians in ground state vibro-polaritonic chemistry. Those do not strictly respect the CBO approximation but an alternative scheme, which we name crude CBO approximation. We argue that the crude CBO ground state misses electron-photon correlation relative to the CBO ground state due to neglected cavity-induced nonadiabatic transition dipole couplings to excited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as a first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model with a focus on nonadiabatic coupling under VSC and electron-photon correlation effects on classical activation barriers. We finally discuss the potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime.
Collapse
Affiliation(s)
- Eric W Fischer
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
| | - Peter Saalfrank
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
| |
Collapse
|
2
|
Finkelstein-Shapiro D, Mante PA, Balci S, Zigmantas D, Pullerits T. Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons. J Chem Phys 2023; 158:104104. [PMID: 36922135 DOI: 10.1063/5.0130287] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/18/2023] Open
Abstract
In polaritons, the properties of matter are modified by mixing the molecular transitions with light modes inside a cavity. Resultant hybrid light-matter states exhibit energy level shifts, are delocalized over many molecular units, and have a different excited-state potential energy landscape, which leads to modified exciton dynamics. Previously, non-Hermitian Hamiltonians have been derived to describe the excited states of molecules coupled to surface plasmons (i.e., plexcitons), and these operators have been successfully used in the description of linear and third order optical response. In this article, we rigorously derive non-Hermitian Hamiltonians in the response function formalism of nonlinear spectroscopy by means of Feshbach operators and apply them to explore spectroscopic signatures of plexcitons. In particular, we analyze the optical response below and above the exceptional point that arises for matching transition energies for plasmon and molecular components and study their decomposition using double-sided Feynman diagrams. We find a clear distinction between interference and Rabi splitting in linear spectroscopy and a qualitative change in the symmetry of the line shape of the nonlinear signal when crossing the exceptional point. This change corresponds to one in the symmetry of the eigenvalues of the Hamiltonian. Our work presents an approach for simulating the optical response of sublevels within an electronic system and opens new applications of nonlinear spectroscopy to examine the different regimes of the spectrum of non-Hermitian Hamiltonians.
Collapse
Affiliation(s)
| | - Pierre-Adrien Mante
- Division of Chemical Physics and Nanolund, Lund University, Box 124, 221 00 Lund, Sweden
| | - Sinan Balci
- Department of Photonics, Izmir Institute of Technology, 35430 Izmir, Türkiye
| | - Donatas Zigmantas
- Division of Chemical Physics and Nanolund, Lund University, Box 124, 221 00 Lund, Sweden
| | - Tõnu Pullerits
- Division of Chemical Physics and Nanolund, Lund University, Box 124, 221 00 Lund, Sweden
| |
Collapse
|
3
|
Zhang Z, Nie X, Lei D, Mukamel S. Multidimensional Coherent Spectroscopy of Molecular Polaritons: Langevin Approach. PHYSICAL REVIEW LETTERS 2023; 130:103001. [PMID: 36962020 DOI: 10.1103/physrevlett.130.103001] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
We present a microscopic theory for nonlinear optical spectroscopy of N molecules in an optical cavity. Using the Heisenberg-Langevin equation, an analytical expression is derived for the time- and frequency-resolved signals accounting for arbitrary numbers of vibrational excitations. We identify clear signatures of the polariton-polaron interaction from multidimensional projections of the signal, e.g., pathways and timescales. Cooperative dynamics of cavity polaritons against intramolecular vibrations is revealed, along with a crosstalk between long-range coherence and vibronic coupling that may lead to localization effects. Our results further characterize the polaritonic coherence and the population transfer that is slower.
Collapse
Affiliation(s)
- Zhedong Zhang
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong SAR
- City University of Hong Kong, Shenzhen Research Institute, Shenzhen, Guangdong 518057, China
| | - Xiaoyu Nie
- School of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
| | - Dangyuan Lei
- Department of Materials Science and Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR
| | - Shaul Mukamel
- Department of Chemistry, Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, USA
| |
Collapse
|
4
|
Fischer EW, Saalfrank P. Cavity-induced non-adiabatic dynamics and spectroscopy of molecular rovibrational polaritons studied by multi-mode quantum models. J Chem Phys 2022; 157:034305. [DOI: 10.1063/5.0098006] [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
We study theoretically the quantum dynamics and spectroscopy of rovibrational polaritons formed in a model system composed of a single rovibrating diatomic molecule, which interacts with two degenerate, orthogonally polarized modes of an optical Fabry–Pérot cavity. We employ an effective rovibrational Pauli–Fierz Hamiltonian in length gauge representation and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly excited vibro-polaritonic states in a two-dimensional angular coordinate branching space. The lower and upper vibrational polaritons are of mixed light–matter hybrid character, whereas the intermediate state is purely photonic in nature. The VPCIs provide effective population transfer channels between singly excited vibrational polaritons, which manifest in rich interference patterns in rotational densities. Spectroscopically, three bright singly excited states are identified when an external infrared laser field couples to both a molecular and a cavity mode. The non-trivial VPCI topology manifests as pronounced multi-peak progression in the spectral region of the upper vibrational polariton, which is traced back to the emergence of rovibro-polaritonic light–matter hybrid states. Experimentally, ubiquitous spontaneous emission from cavity modes induces a dissipative reduction of intensity and peak broadening, which mainly influences the purely photonic intermediate state peak as well as the rovibro-polaritonic progression.
Collapse
Affiliation(s)
- Eric W. Fischer
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
| | - Peter Saalfrank
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
| |
Collapse
|
5
|
Wu J, Guo M, Zhou H, Liu J, Li J, Zhang J. Experimental realization of efficient nondegenerate four-wave mixing in cesium atoms. OPTICS EXPRESS 2022; 30:12576-12585. [PMID: 35472891 DOI: 10.1364/oe.452790] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 03/23/2022] [Indexed: 06/14/2023]
Abstract
Nondegenerate four-wave mixing (FWM) in diamond-type atomic systems has important applications in a wide range of fields, including quantum entanglement generation, frequency conversion, and optical information processing. Although the efficient self-seeded nondegenerate FWM with amplified spontaneous emission (ASE) has been realized extensively, the seeded nondegenerate FWM without ASE is inefficient in reported experiments so far. Here we present the experimental realization of the seeded nondegenerate FWM in cesium atoms with a significantly improved efficiency. Specifically, with two pump lasers at 852 and 921 nm and a seed laser at 895 nm, a continuous-wave laser at 876 nm is efficiently generated via FWM in a cesium vapor cell with a power up to 1.2 mW, three orders of magnitude larger than what has been achieved in previous experiments. The improvement of the efficiency benefits from the exact satisfaction of the phase-matching condition realized by an elaborately designed setup. Our results may find applications in the generation of squeezing and entanglement of light via nondegenerate FWM.
Collapse
|
6
|
Li TE, Nitzan A, Subotnik JE. Polariton relaxation under vibrational strong coupling: Comparing cavity molecular dynamics simulations against Fermi's golden rule rate. J Chem Phys 2022; 156:134106. [PMID: 35395873 DOI: 10.1063/5.0079784] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Under vibrational strong coupling (VSC), the formation of molecular polaritons may significantly modify the photo-induced or thermal properties of molecules. In an effort to understand these intriguing modifications, both experimental and theoretical studies have focused on the ultrafast dynamics of vibrational polaritons. Here, following our recent work [Li et al., J. Chem. Phys. 154, 094124 (2021)], we systematically study the mechanism of polariton relaxation for liquid CO2 under a weak external pumping. Classical cavity molecular dynamics (CavMD) simulations confirm that polariton relaxation results from the combined effects of (i) cavity loss through the photonic component and (ii) dephasing of the bright-mode component to vibrational dark modes as mediated by intermolecular interactions. The latter polaritonic dephasing rate is proportional to the product of the weight of the bright mode in the polariton wave function and the spectral overlap between the polariton and dark modes. Both these factors are sensitive to parameters such as the Rabi splitting and cavity mode detuning. Compared to a Fermi's golden rule calculation based on a tight-binding harmonic model, CavMD yields a similar parameter dependence for the upper polariton relaxation lifetime but sometimes a modest disagreement for the lower polariton. We suggest that this disagreement results from polariton-enhanced molecular nonlinear absorption due to molecular anharmonicity, which is not included in our analytical model. We also summarize recent progress on probing nonreactive VSC dynamics with CavMD.
Collapse
Affiliation(s)
- Tao E Li
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
7
|
Multimode polariton effects on molecular energy transport and spectral fluctuations. Commun Chem 2022; 5:48. [PMID: 36697846 PMCID: PMC9814737 DOI: 10.1038/s42004-022-00660-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 03/04/2022] [Indexed: 01/28/2023] Open
Abstract
Despite the potential paradigm breaking capability of microcavities to control chemical processes, the extent to which photonic devices change properties of molecular materials is still unclear, in part due to challenges in modeling hybrid light-matter excitations delocalized over many length scales. We overcome these challenges for a photonic wire under strong coupling with a molecular ensemble. Our simulations provide a detailed picture of the effect of photonic wires on spectral and transport properties of a disordered molecular material. We find stronger changes to the probed molecular observables when the cavity is redshifted relative to the molecules and energetic disorder is weak. These trends are expected to hold also in higher-dimensional cavities, but are not captured with theories that only include a single cavity-mode. Therefore, our results raise important issues for future experiments and model building focused on unraveling new ways to manipulate chemistry with optical cavities.
Collapse
|
8
|
Chen YY, Ye C, Li Y. Enantio-detection via cavity-assisted three-photon processes. OPTICS EXPRESS 2021; 29:36132-36144. [PMID: 34809032 DOI: 10.1364/oe.436211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
We propose a method for enantio-detection of chiral molecules based on a cavity-molecule system, where the left- and right-handed molecules are coupled with a cavity and two classical light fields to form cyclic three-level models. Via the cavity-assisted three-photon processes based on the cyclic three-level model, photons are generated continuously in the cavity even in the absence of external driving to the cavity. However, the photonic fields generated from the three-photon processes of left- and right-handed molecules differ with the phase difference π according to the inherent properties of electric-dipole transition moments of enantiomers. This provides a potential way to detect the enantiomeric excess of chiral mixture by monitoring the output field of the cavity.
Collapse
|
9
|
Gu B, Cavaletto SM, Nascimento DR, Khalil M, Govind N, Mukamel S. Manipulating valence and core electronic excitations of a transition-metal complex using UV/Vis and X-ray cavities. Chem Sci 2021; 12:8088-8095. [PMID: 34194698 PMCID: PMC8208133 DOI: 10.1039/d1sc01774h] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 05/02/2021] [Indexed: 11/21/2022] Open
Abstract
We demonstrate how optical cavities can be exploited to control both valence- and core-excitations in a prototypical model transition metal complex, ferricyanide ([Fe(iii)(CN)6]3-), in an aqueous environment. The spectroscopic signatures of hybrid light-matter polariton states are revealed in UV/Vis and X-ray absorption, and stimulated X-ray Raman signals. In an UV/Vis cavity, the absorption spectrum exhibits the single-polariton states arising from the cavity photon mode coupling to both resonant and off-resonant valence-excited states. We further show that nonlinear stimulated X-ray Raman signals can selectively probe the bipolariton states via cavity-modified Fe core-excited states. This unveils the correlation between valence polaritons and dressed core-excitations. In an X-ray cavity, core-polaritons are generated and their correlations with the bare valence-excitations appear in the linear and nonlinear X-ray spectra.
Collapse
Affiliation(s)
- Bing Gu
- Department of Chemistry and Department of Physics & Astronomy, University of California Irvine CA 92697 USA
| | - Stefano M Cavaletto
- Department of Chemistry and Department of Physics & Astronomy, University of California Irvine CA 92697 USA
| | - Daniel R Nascimento
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory Richland WA 99352 USA
| | - Munira Khalil
- Department of Chemistry, University of Washington Seattle WA USA
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory Richland WA 99352 USA
| | - Shaul Mukamel
- Department of Chemistry and Department of Physics & Astronomy, University of California Irvine CA 92697 USA
| |
Collapse
|
10
|
Finkelstein-Shapiro D, Mante PA, Sarisozen S, Wittenbecher L, Minda I, Balci S, Pullerits T, Zigmantas D. Understanding radiative transitions and relaxation pathways in plexcitons. Chem 2021. [DOI: 10.1016/j.chempr.2021.02.028] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
11
|
Lineshape analysis of concentrated perchlorate anion aqueous solution with coherence exchange model incorporating multiple bath modes. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2020.138274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
12
|
Affiliation(s)
| | - Gregory D Scholes
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| |
Collapse
|