1
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Tsai HS, Shen CE, Hsu LY. Generalized Born-Huang expansion under macroscopic quantum electrodynamics framework. J Chem Phys 2024; 160:144112. [PMID: 38597310 DOI: 10.1063/5.0195087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2023] [Accepted: 03/19/2024] [Indexed: 04/11/2024] Open
Abstract
Born-Huang expansion is the cornerstone for studying potential energy surfaces and non-adiabatic couplings (NACs) in molecular systems. However, the traditional approach is insufficient to describe the molecular system, which strongly interacts with quantum light. Inspired by the work by Schäfer et al., we develop the generalized Born-Huang expansion theory within a macroscopic quantum electrodynamics (QED) framework. The theory we present allows us to describe electromagnetic vacuum fluctuations in dielectric media and incorporate the effects of dressed photons (or polaritons) into NACs. With the help of the generalized Born-Huang expansion, we clearly classify electronic nuclear NACs, polaritonic nuclear NACs, and polaritonic electronic NACs. Furthermore, to demonstrate the advantage of the macroscopic QED framework, we estimate polaritonic electronic NACs without any free parameter, such as the effective mode volume, and demonstrate the distance dependence of the polaritonic electronic NACs in a silver planar system. In addition, we take a hydrogen atom in free space as an example and derive spontaneous emission rates from photonic electronic NACs (polaritonic electronic NACs are reduced to photonic electronic NACs). We believe that this work not only provides an avenue for the theoretical exploration of NACs in a nucleus-electron-polariton coupled system but also offers a more comprehensive understanding for molecules coupled with quantum light.
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Affiliation(s)
- Hung-Sheng Tsai
- Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Chih-En Shen
- Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Liang-Yan Hsu
- Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
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2
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Chuang YT, Hsu LY. Microscopic theory of exciton-polariton model involving multiple molecules: Macroscopic quantum electrodynamics formulation and essence of direct intermolecular interactions. J Chem Phys 2024; 160:114105. [PMID: 38501476 DOI: 10.1063/5.0192704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 02/28/2024] [Indexed: 03/20/2024] Open
Abstract
Cavity quantum electrodynamics (CQED) and its extensions are widely used for the description of exciton-polariton systems. However, the exciton-polariton models based on CQED vary greatly within different contexts. One of the most significant discrepancies among these CQED models is whether one should include direct intermolecular interactions in the CQED Hamiltonian. To answer this question, in this article, we derive an effective dissipative CQED model including free-space dipole-dipole interactions (CQED-DDI) from a microscopic Hamiltonian based on macroscopic quantum electrodynamics. Dissipative CQED-DDI successfully captures the nature of vacuum fluctuations in dielectric media and separates them into free-space effects and dielectric-induced effects. The former include spontaneous emissions, dephasings, and dipole-dipole interactions in free space; the latter include exciton-polariton interactions and photonic losses due to dielectric media. We apply dissipative CQED-DDI to investigate the exciton-polariton dynamics (the population dynamics of molecules above a plasmonic surface) and compare the results with those based on the methods proposed by several previous studies. We find that direct intermolecular interactions are a crucial element when employing CQED-like models to study exciton-polariton systems involving multiple molecules.
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Affiliation(s)
- Yi-Ting Chuang
- Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Liang-Yan Hsu
- Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
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3
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Lednev M, García-Vidal FJ, Feist J. Lindblad Master Equation Capable of Describing Hybrid Quantum Systems in the Ultrastrong Coupling Regime. PHYSICAL REVIEW LETTERS 2024; 132:106902. [PMID: 38518335 DOI: 10.1103/physrevlett.132.106902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2023] [Accepted: 02/02/2024] [Indexed: 03/24/2024]
Abstract
Despite significant theoretical efforts devoted to studying the interaction between quantized light modes and matter, the so-called ultrastrong coupling regime still presents significant challenges for theoretical treatments and prevents the use of many common approximations. Here we demonstrate an approach that can describe the dynamics of hybrid quantum systems in any regime of interaction for an arbitrary electromagnetic (EM) environment. We extend a previous method developed for few-mode quantization of arbitrary systems to the case of ultrastrong light-matter coupling, and show that even such systems can be treated using a Lindblad master equation where decay operators act only on the photonic modes by ensuring that the effective spectral density of the EM environment is sufficiently suppressed at negative frequencies. We demonstrate the validity of our framework and show that it outperforms current state-of-the-art master equations for a simple model system, and then study a realistic nanoplasmonic setup where existing approaches cannot be applied.
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Affiliation(s)
- Maksim Lednev
- 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 (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore 138632, Republic of Singapore
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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4
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Lorenzoni N, Cho N, Lim J, Tamascelli D, Huelga SF, Plenio MB. Systematic Coarse Graining of Environments for the Nonperturbative Simulation of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2024; 132:100403. [PMID: 38518302 DOI: 10.1103/physrevlett.132.100403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Revised: 01/22/2024] [Accepted: 02/13/2024] [Indexed: 03/24/2024]
Abstract
Conducting precise electronic-vibrational dynamics simulations of molecular systems poses significant challenges when dealing with realistic environments composed of numerous vibrational modes. Here, we introduce a technique for the construction of effective phonon spectral densities that capture accurately open-system dynamics over a finite time interval of interest. When combined with existing nonperturbative simulation tools, our approach can reduce significantly the computational costs associated with many-body open-system dynamics.
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Affiliation(s)
- Nicola Lorenzoni
- Institut für Theoretische Physik und IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
| | - Namgee Cho
- Institut für Theoretische Physik und IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
| | - James Lim
- Institut für Theoretische Physik und IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
| | - Dario Tamascelli
- Institut für Theoretische Physik und IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
| | - Susana F Huelga
- Institut für Theoretische Physik und IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
| | - Martin B Plenio
- Institut für Theoretische Physik und IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
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5
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Sokolovskii I, Groenhof G. Non-Hermitian molecular dynamics simulations of exciton-polaritons in lossy cavities. J Chem Phys 2024; 160:092501. [PMID: 38426514 DOI: 10.1063/5.0188613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 02/06/2024] [Indexed: 03/02/2024] Open
Abstract
The observation that materials can change their properties when placed inside or near an optical resonator has sparked a fervid interest in understanding the effects of strong light-matter coupling on molecular dynamics, and several approaches have been proposed to extend the methods of computational chemistry into this regime. Whereas the majority of these approaches have focused on modeling a single molecule coupled to a single cavity mode, changes to chemistry have so far only been observed experimentally when very many molecules are coupled collectively to multiple modes with short lifetimes. While atomistic simulations of many molecules coupled to multiple cavity modes have been performed with semi-classical molecular dynamics, an explicit description of cavity losses has so far been restricted to simulations in which only a very few molecular degrees of freedom were considered. Here, we have implemented an effective non-Hermitian Hamiltonian to explicitly treat cavity losses in large-scale semi-classical molecular dynamics simulations of organic polaritons and used it to perform both mean-field and surface hopping simulations of polariton relaxation, propagation, and energy transfer.
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Affiliation(s)
- Ilia Sokolovskii
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
| | - Gerrit Groenhof
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
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6
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Hoang TX, Leykam D, Kivshar Y. Photonic Flatband Resonances in Multiple Light Scattering. PHYSICAL REVIEW LETTERS 2024; 132:043803. [PMID: 38335352 DOI: 10.1103/physrevlett.132.043803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 12/07/2023] [Indexed: 02/12/2024]
Abstract
We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators' radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.
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Affiliation(s)
- Thanh Xuan Hoang
- Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Republic of Singapore
| | - Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Yuri Kivshar
- Nonlinear Physics Center, Research School of Physics, Australian National University, Canberra ACT 2601, Australia
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7
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Svendsen MK, Thygesen KS, Rubio A, Flick J. Ab Initio Calculations of Quantum Light-Matter Interactions in General Electromagnetic Environments. J Chem Theory Comput 2024; 20:926-936. [PMID: 38189259 PMCID: PMC10809713 DOI: 10.1021/acs.jctc.3c00967] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Revised: 11/17/2023] [Accepted: 12/12/2023] [Indexed: 01/09/2024]
Abstract
The emerging field of strongly coupled light-matter systems has drawn significant attention in recent years because of the prospect of altering both the physical and chemical properties of molecules and materials. Because this emerging field draws on ideas from both condensed-matter physics and quantum optics, it has attracted the attention of theoreticians from both fields. While the former often employ accurate descriptions of the electronic structure of the matter, the description of the electromagnetic environment is often oversimplified. In contrast, the latter often employs sophisticated descriptions of the electromagnetic environment while using oversimplified few-level approximations of the electronic structure. Both approaches are problematic because the oversimplified descriptions of the electronic system are incapable of describing effects such as light-induced structural changes in the electronic system, while the oversimplified descriptions of the electromagnetic environments can lead to unphysical predictions because the light-matter interactions strengths are misrepresented. In this work, we overcome these shortcomings and present the first method which can quantitatively describe both the electronic system and general electromagnetic environments from first principles. We realize this by combining macroscopic QED (MQED) with Quantum Electrodynamical Density-Functional Theory. To exemplify this approach, we consider the example of an absorbing spherical cavity and study the impact of different parameters of both the environment and the electronic system on the transition from weak-to-strong coupling for different aromatic molecules. As part of this work, we also provide an easy-to-use tool to calculate the cavity coupling strengths for simple cavity setups. Our work is a significant step toward parameter-free ab initio calculations for strongly coupled quantum light-matter systems and will help bridge the gap between theoretical methods and experiments in the field.
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Affiliation(s)
- Mark Kamper Svendsen
- 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
- Computational
Atomic scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- Center
for Computational Quantum Physics, Flatiron
Institute, 10010 New York, New York, United States
| | - Kristian Sommer Thygesen
- Computational
Atomic scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Angel Rubio
- 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
- Center
for Computational Quantum Physics, Flatiron
Institute, 10010 New York, New York, United States
- Nano-Bio
Spectroscopy Group and European Theoretical Spectroscopy Facility
(ETSF), Universidad del País Vasco
(UPV/EHU), Av. Tolosa
72, 20018 San Sebastian, Spain
| | - Johannes Flick
- Center
for Computational Quantum Physics, Flatiron
Institute, 10010 New York, New York, United States
- Department
of Physics, City College of New York, 10031 New York, New York, United States
- Department
of Physics, The Graduate Center, City University
of New York, 10016 New York, New York, United States
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8
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Ruggenthaler M, Sidler D, Rubio A. Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics. Chem Rev 2023; 123:11191-11229. [PMID: 37729114 PMCID: PMC10571044 DOI: 10.1021/acs.chemrev.2c00788] [Citation(s) in RCA: 21] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Indexed: 09/22/2023]
Abstract
In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.
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Affiliation(s)
- Michael Ruggenthaler
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Dominik Sidler
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max-Planck-Institut
für Struktur und Dynamik der Materie, 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
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9
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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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10
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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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11
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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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12
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Ben-Asher A, Fernández-Domínguez AI, Feist J. Non-Hermitian Anharmonicity Induces Single-Photon Emission. PHYSICAL REVIEW LETTERS 2023; 130:243601. [PMID: 37390444 DOI: 10.1103/physrevlett.130.243601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2022] [Accepted: 05/22/2023] [Indexed: 07/02/2023]
Abstract
Single-photon sources are in high demand for quantum information applications. A paradigmatic way to achieve single-photon emission is through anharmonicity in the energy levels, such that the absorption of a single photon from a coherent drive shifts the system out of resonance and prevents absorption of a second one. We identify a novel mechanism for single-photon emission through non-Hermitian anharmonicity, i.e., anharmonicity in the losses instead of in the energy levels. We demonstrate the mechanism in two types of systems, including a feasible setup consisting of a hybrid metallodielectric cavity weakly coupled to a two-level emitter, and show that it induces high-purity single-photon emission at high repetition rates.
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Affiliation(s)
- Anael Ben-Asher
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E28049 Madrid, Spain
| | - Antonio I Fernández-Domínguez
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E28049 Madrid, Spain
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E28049 Madrid, Spain
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13
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Mandal A, Xu D, Mahajan A, Lee J, Delor M, Reichman DR. Microscopic Theory of Multimode Polariton Dispersion in Multilayered Materials. NANO LETTERS 2023; 23:4082-4089. [PMID: 37103998 DOI: 10.1021/acs.nanolett.3c01017] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multilayered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multilayered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.
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Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Ding Xu
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Ankit Mahajan
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Milan Delor
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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14
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Wei YC, Hsu LY. Polaritonic Huang-Rhys Factor: Basic Concepts and Quantifying Light-Matter Interactions in Media. J Phys Chem Lett 2023; 14:2395-2401. [PMID: 36856331 DOI: 10.1021/acs.jpclett.3c00065] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The Huang-Rhys (HR) factor, a dimensionless factor that characterizes electron-phonon (vibronic) coupling, has been extensively employed to investigate a variety of material properties. In the same spirit, we propose a quantity called the polaritonic HR factor to quantitatively describe the effects of (i) light-matter coupling induced by permanent dipoles and (ii) dipole self-energy. The former leads to polaritonic displacements, while the latter is associated with the electronic coupling shift named reorganization dipole self-coupling. In the framework of macroscopic quantum electrodynamics, our theory can evaluate the polaritonic HR factor, reorganization dipole self-coupling, and modified light-matter coupling strength in an arbitrary dielectric environment without free parameters, whose magnitudes are in good agreement with the previous experimental results. We believe that this study provides a useful perspective on understanding and quantifying light-matter interactions in media.
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Affiliation(s)
- Yu-Chen Wei
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan
- Department of Chemistry, National Taiwan University, Taipei 106, Taiwan
| | - Liang-Yan Hsu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan
- Department of Chemistry, National Taiwan University, Taipei 106, Taiwan
- National Center for Theoretical Sciences, Taipei 106, Taiwan
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15
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Sukharev M, Subotnik J, Nitzan A. Dissociation slowdown by collective optical response under strong coupling conditions. J Chem Phys 2023; 158:084104. [PMID: 36859100 DOI: 10.1063/5.0133972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled Maxwell-Schrödinger equations with molecular rovibrational degrees of freedom explicitly taken into account. It is shown that the dissociation is significantly affected (slowed down) when the system is driven at its polaritonic frequencies. The observed effect is demonstrated to be of transient nature and has no classical analog. An intuitive explanation of the dissociation slowdown at polaritonic frequencies is proposed.
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Affiliation(s)
- Maxim Sukharev
- College of Integrative Sciences and Arts, Arizona State University, Mesa, Arizona 85212, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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16
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Shlesinger I, Palstra IM, Koenderink AF. Integrated Sideband-Resolved SERS with a Dimer on a Nanobeam Hybrid. PHYSICAL REVIEW LETTERS 2023; 130:016901. [PMID: 36669214 DOI: 10.1103/physrevlett.130.016901] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 12/14/2022] [Indexed: 06/17/2023]
Abstract
In analogy to cavity optomechanics, enhancing specific sidebands of a Raman process with narrowband optical resonators would allow for parametric amplification, entanglement of light and molecular vibrations, and reduced transduction noise. We report on the demonstration of waveguide-addressable sideband-resolved surface-enhanced Raman scattering (SERS). We realized a hybrid plasmonic-photonic resonator consisting of a 1D photonic crystal cavity decorated with a sub-20 nm gap dimer nanoantenna. Hybrid resonances in the near-IR provide designer Q factors of 1000, and Q/V=(λ^{3}/10^{6})^{-1}, with SERS signal strength on par with levels found in state-of-the-art purely plasmonic systems. We evidence Fano line shapes in the SERS enhancement of organic molecules, and quantitatively separate out the pump enhancement and optical reservoir contributions.
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Affiliation(s)
- Ilan Shlesinger
- Department of Physics of Information in Matter and Center for Nanophotonics, NWO-I Institute AMOLF, Science Park 104, NL1098XH Amsterdam, Netherlands
| | - Isabelle M Palstra
- Department of Physics of Information in Matter and Center for Nanophotonics, NWO-I Institute AMOLF, Science Park 104, NL1098XH Amsterdam, Netherlands
- Institute of Physics, University of Amsterdam, NL1098XH Amsterdam, Netherlands
| | - A Femius Koenderink
- Department of Physics of Information in Matter and Center for Nanophotonics, NWO-I Institute AMOLF, Science Park 104, NL1098XH Amsterdam, Netherlands
- Institute of Physics, University of Amsterdam, NL1098XH Amsterdam, Netherlands
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17
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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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18
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Lu Y, Zhao Y, Li R, Liu J. Anomalous spontaneous emission dynamics at chiral exceptional points. OPTICS EXPRESS 2022; 30:41784-41803. [PMID: 36366646 DOI: 10.1364/oe.473824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Here, we present an analytical description of local density of states (LDOS) for microcavity featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics from a quantum emitter (QE) due to the non-Lorentzian response of EPs. Specifically, we reveal that a squared Lorentzian term of LDOS contributed by chiral EPs can destructively interfere with the linear Lorentzian profile, resulting in the null Purcell enhancement to a QE with special transition frequency, which we call EP induced transparency. While for the case of constructive interference, the squared Lorentzian term can narrow the linewidth of Rabi splitting even below that of bare components, and thus significantly suppresses the decay of Rabi oscillation. Interestingly, we further find that an open microcavity with chiral EPs supports atom-photon bound states for population trapping and decay suppression in long-time dynamics. As applications, we demonstrate the advantages of microcavity operated at chiral EPs in achieving high-fidelity entanglement generation and high-efficiency single-photon generation. Our work unveils the exotic cavity quantum electrodynamics unique to chiral EPs, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.
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19
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Sánchez-Barquilla M, García-Vidal FJ, Fernández-Domínguez AI, Feist J. Few-mode field quantization for multiple emitters. NANOPHOTONICS 2022; 11:4363-4374. [PMID: 36147197 PMCID: PMC9455278 DOI: 10.1515/nanoph-2021-0795] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 08/08/2022] [Indexed: 06/16/2023]
Abstract
The control of the interaction between quantum emitters using nanophotonic structures holds great promise for quantum technology applications, while its theoretical description for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes form a high-dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a small number of discrete modes. This extends the previous work in ref. (I. Medina, F. J. García-Vidal, A. I. Fernández-Domínguez, and J. Feist, "Few-mode field quantization of arbitrary electromagnetic spectral densities," Phys. Rev. Lett., vol. 126, p. 093601, 2021) to the case of an arbitrary number of emitters, without any restrictions on the emitter level structure or dipole operators. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We illustrate the power of our approach for a system of three emitters placed within a hybrid metallodielectric photonic structure and show that excitation transfer is highly sensitive to the properties of the hybrid photonic-plasmonic modes.
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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-28049Madrid, Spain
| | - Francisco J. García-Vidal
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049Madrid, Spain
- Institute of High Performance Computing, Agency for Science, Technology, and Research (A*STAR), Connexis, 138632Singapore, Singapore
| | - Antonio I. Fernández-Domínguez
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049Madrid, Spain
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049Madrid, Spain
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20
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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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21
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Fregoni J, Garcia-Vidal FJ, Feist J. Theoretical Challenges in Polaritonic Chemistry. ACS PHOTONICS 2022; 9:1096-1107. [PMID: 35480492 PMCID: PMC9026242 DOI: 10.1021/acsphotonics.1c01749] [Citation(s) in RCA: 42] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 02/01/2022] [Accepted: 02/02/2022] [Indexed: 06/14/2023]
Abstract
Polaritonic chemistry exploits strong light-matter coupling between molecules and confined electromagnetic field modes to enable new chemical reactivities. In systems displaying this functionality, the choice of the cavity determines both the confinement of the electromagnetic field and the number of molecules that are involved in the process. While in wavelength-scale optical cavities the light-matter interaction is ruled by collective effects, plasmonic subwavelength nanocavities allow even single molecules to reach strong coupling. Due to these very distinct situations, a multiscale theoretical toolbox is then required to explore the rich phenomenology of polaritonic chemistry. Within this framework, each component of the system (molecules and electromagnetic modes) needs to be treated in sufficient detail to obtain reliable results. Starting from the very general aspects of light-molecule interactions in typical experimental setups, we underline the basic concepts that should be taken into account when operating in this new area of research. Building on these considerations, we then provide a map of the theoretical tools already available to tackle chemical applications of molecular polaritons at different scales. Throughout the discussion, we draw attention to both the successes and the challenges still ahead in the theoretical description of polaritonic chemistry.
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22
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Sáez-Blázquez R, Cuartero-González Á, Feist J, García-Vidal FJ, Fernández-Domínguez AI. Plexcitonic Quantum Light Emission from Nanoparticle-on-Mirror Cavities. NANO LETTERS 2022; 22:2365-2373. [PMID: 35285655 PMCID: PMC8949753 DOI: 10.1021/acs.nanolett.1c04872] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
We investigate the quantum-optical properties of the light emitted by a nanoparticle-on-mirror cavity filled with a single quantum emitter. Inspired by recent experiments, we model a dark-field setup and explore the photon statistics of the scattered light under grazing laser illumination. Exploiting analytical solutions to Maxwell's equations, we quantize the nanophotonic cavity fields and describe the formation of plasmon-exciton polaritons (or plexcitons) in the system. This way, we reveal that the rich plasmonic spectrum of the nanocavity offers unexplored mechanisms for nonclassical light generation that are more efficient than the resonant interaction between the emitter natural transition and the brightest optical mode. Specifically, we find three different sample configurations in which strongly antibunched light is produced. Finally, we illustrate the power of our approach by showing that the introduction of a second emitter in the platform can enhance photon correlations further.
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Affiliation(s)
- Rocío Sáez-Blázquez
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, 28049 Madrid, Spain
- Vienna
Center for Quantum Science and Technology, Atominstitut, TU Wien, 1040 Vienna, Austria
| | - Álvaro Cuartero-González
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, 28049 Madrid, Spain
- Mechanical
Engineering Department, ICAI, Universidad
Pontificia Comillas, 28015 Madrid, Spain
| | - Johannes Feist
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, 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, 28049 Madrid, Spain
- Institute
of High Performance Computing, Agency for
Science, Technology, and Research (A*STAR), Singapore 138632, Singapore
| | - Antonio I. Fernández-Domínguez
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, 28049 Madrid, Spain
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23
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Wang S, Chuang YT, Hsu LY. Simple but accurate estimation of light-matter coupling strength and optical loss for a molecular emitter coupled with photonic modes. J Chem Phys 2021; 155:134117. [PMID: 34624977 DOI: 10.1063/5.0060171] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Light-matter coupling strength and optical loss are two key physical quantities in cavity quantum electrodynamics (CQED), and their interplay determines whether light-matter hybrid states can be formed or not in chemical systems. In this study, by using macroscopic quantum electrodynamics (MQED) combined with a pseudomode approach, we present a simple but accurate method, which allows us to quickly estimate the light-matter coupling strength and optical loss without free parameters. Moreover, for a molecular emitter coupled with photonic modes (including cavity modes and plasmon polariton modes), we analytically and numerically prove that the dynamics derived from the MQED-based wavefunction approach is mathematically equivalent to the dynamics governed by the CQED-based Lindblad master equation when the Purcell factor behaves like Lorentzian functions.
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Affiliation(s)
- Siwei Wang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Yi-Ting Chuang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Liang-Yan Hsu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
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24
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Accurate Truncations of Chain Mapping Models for Open Quantum Systems. NANOMATERIALS 2021; 11:nano11082104. [PMID: 34443934 PMCID: PMC8398816 DOI: 10.3390/nano11082104] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Revised: 08/16/2021] [Accepted: 08/17/2021] [Indexed: 01/25/2023]
Abstract
The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.
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