1
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Lai Y, Ying W, Huo P. Non-equilibrium rate theory for polariton relaxation dynamics. J Chem Phys 2024; 161:104109. [PMID: 39268826 DOI: 10.1063/5.0231396] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2024] [Accepted: 08/27/2024] [Indexed: 09/15/2024] Open
Abstract
We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein-Tavis-Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.
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Affiliation(s)
- Yifan Lai
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Wenxiang Ying
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
- The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA
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2
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Ying W, Mondal ME, Huo P. Theory and quantum dynamics simulations of exciton-polariton motional narrowing. J Chem Phys 2024; 161:064105. [PMID: 39120029 DOI: 10.1063/5.0225387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2024] [Accepted: 07/24/2024] [Indexed: 08/10/2024] Open
Abstract
The motional narrowing effect has been extensively studied for cavity exciton-polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior and (2) the asymmetric linewidths for the upper polariton and the lower polariton. However, a minimal theoretical model that is clear and adequate to address all these effects as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein-Tavis-Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion approach. The results reveal that under collective light-matter coupling between a cavity mode and N molecules, the polariton linewidth scales as 1/N under the slow limit, while scales as 1/N under the fast limit, due to the polaron decoupling effect. Furthermore, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions [Eqs. (34) and (35)] agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton-polariton motional narrowing based on the HTC model.
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Affiliation(s)
- Wenxiang Ying
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - M Elious Mondal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
- The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA
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3
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Amin M, Koessler ER, Morshed O, Awan F, Cogan NMB, Collison R, Tumiel TM, Girten W, Leiter C, Vamivakas AN, Huo P, Krauss TD. Cavity Controlled Upconversion in CdSe Nanoplatelet Polaritons. ACS NANO 2024; 18:21388-21398. [PMID: 39078943 PMCID: PMC11328175 DOI: 10.1021/acsnano.4c05871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/18/2024]
Abstract
Exciton-polaritons provide a versatile platform for investigating quantum electrodynamics effects in chemical systems, such as polariton-altered chemical reactivity. However, using polaritons in chemical contexts will require a better understanding of their photophysical properties under ambient conditions, where chemistry is typically performed. Here, we used cavity quality factor to control strong light-matter interactions and in particular the excited state dynamics of colloidal CdSe nanoplatelets (NPLs) coupled to a Fabry-Pérot optical cavity. With increasing cavity quality factor, we observe significant population of the upper polariton (UP) state, exemplified by the rare observation of substantial UP photoluminescence (PL). Excitation of the lower polariton (LP) states results in upconverted PL emission from the UP branch due to efficient exchange of population between the LP, UP and the reservoir of dark states present in collectively coupled polaritonic systems. In addition, we measure time scales for polariton dynamics ∼100 ps, implying great potential for NPL based polariton systems to affect photochemical reaction rates. State-of-the-art quantum dynamical simulations show outstanding quantitative agreement with experiments, and thus provide important insight into polariton photophysical dynamics of collectively coupled nanocrystal-based systems. These findings represent a significant step toward the development of practical polariton photochemistry platforms.
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Affiliation(s)
- Mitesh Amin
- The Institute of Optics, University of Rochester, Rochester, New York 14627, United States
| | - Eric R Koessler
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Ovishek Morshed
- The Institute of Optics, University of Rochester, Rochester, New York 14627, United States
| | - Farwa Awan
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Nicole M B Cogan
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Robert Collison
- The Institute of Optics, University of Rochester, Rochester, New York 14627, United States
| | - Trevor M Tumiel
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - William Girten
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Christopher Leiter
- Department of Chemistry, Regis University, Denver, Colorado 80221, United States
| | - A Nickolas Vamivakas
- The Institute of Optics, University of Rochester, Rochester, New York 14627, United States
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, United States
| | - Pengfei Huo
- The Institute of Optics, University of Rochester, Rochester, New York 14627, United States
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Todd D Krauss
- The Institute of Optics, University of Rochester, Rochester, New York 14627, United States
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
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4
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Chang WJ, Zeng H, Terry Weatherly CK, Provazza J, Liu P, Weiss EA, Stern NP, Tempelaar R. Dark State Concentration Dependent Emission and Dynamics of CdSe Nanoplatelet Exciton-Polaritons. ACS NANO 2024. [PMID: 39042269 DOI: 10.1021/acsnano.4c03545] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
The recent surge of interest in polaritons has prompted fundamental questions about the role of dark states in strong light-matter coupling phenomena. Here, we systematically vary the relative number of dark states by controlling the number of stacked CdSe nanoplatelets confined in a Fabry-Pérot cavity. We find the emission spectrum to change significantly with an increasing number of nanoplatelets, with a gradual shift of the dominant emission intensity from the lower polariton branch to a manifold of dark states. Through accompanying calculations based on a kinetic model, this shift is rationalized by an entropic trapping of excitations by the dark state manifold, while a weak dark state dispersion due to local disorder explains their nonzero emission. Our results point toward the relevance of the dark state concentration to the optical and dynamical properties of cavity-embedded quantum emitters with ramifications for Bose-Einstein condensate formation, polariton lasing, polariton-based quantum transduction schemes, and polariton chemistry.
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Affiliation(s)
- Woo Je Chang
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Hongfei Zeng
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208-3113, United States
| | | | - Justin Provazza
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Pufan Liu
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Emily A Weiss
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Nathaniel P Stern
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Roel Tempelaar
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States
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5
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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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6
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Weight BM, Weix DJ, Tonzetich ZJ, Krauss TD, Huo P. Cavity Quantum Electrodynamics Enables para- and ortho-Selective Electrophilic Bromination of Nitrobenzene. J Am Chem Soc 2024; 146:16184-16193. [PMID: 38814893 PMCID: PMC11177318 DOI: 10.1021/jacs.4c04045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2024] [Revised: 05/15/2024] [Accepted: 05/17/2024] [Indexed: 06/01/2024]
Abstract
Coupling molecules to a quantized radiation field inside an optical cavity has shown great promise to modify chemical reactivity. In this work, we show that the ground-state selectivity of the electrophilic bromination of nitrobenzene can be fundamentally changed by strongly coupling the reaction to the cavity, generating ortho- or para-substituted products instead of the meta product. Importantly, these are products that are not obtained from the same reaction outside the cavity. A recently developed ab initio approach was used to theoretically compute the relative energies of the cationic Wheland intermediates, which indicate the kinetically preferred bromination site for all products. Performing an analysis of the ground-state electron density for the Wheland intermediates inside and outside the cavity, we demonstrate how strong coupling induces reorganization of the molecular charge distribution, which in turn leads to different bromination sites directly dependent on the cavity conditions. Overall, the results presented here can be used to understand cavity induced changes to ground-state chemical reactivity from a mechanistic perspective as well as to directly connect frontier theoretical simulations to state-of-the-art, but realistic, experimental cavity conditions.
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Affiliation(s)
- Braden M. Weight
- Department
of Physics and Astronomy, University of
Rochester, Rochester, New York 14627, United States
| | - Daniel J. Weix
- Department
of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Zachary J. Tonzetich
- Department
of Chemistry, University of Texas at San
Antonio, San Antonio, Texas 78249, United States
| | - Todd D. Krauss
- Department
of Chemistry, University of Rochester, Rochester, New York 14627, United States
- The
Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department
of Chemistry, University of Rochester, 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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7
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Freire-Fernández F, Sinai NG, Hui Tan MJ, Park SM, Koessler ER, Krauss T, Huo P, Odom TW. Room-Temperature Polariton Lasing from CdSe Core-Only Nanoplatelets. ACS NANO 2024; 18:15177-15184. [PMID: 38808728 DOI: 10.1021/acsnano.4c03164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
This paper reports how CdSe core-only nanoplatelets (NPLs) coupled with plasmonic Al nanoparticle lattices can exhibit exciton-polariton lasing. By improving a procedure to synthesize monodisperse 4-monolayer CdSe NPLs, we could resolve polariton decay dynamics and pathways. Experiment and theory confirmed that the system is in the strong coupling regime based on anticrossings in the dispersion diagrams and magnitude of the Rabi-splitting values. Notably, polariton lasing is observed only for cavity lattice periodicities that exhibit specific dispersive characteristics that enable polariton accumulation. The threshold of polariton lasing is 25-fold lower than the reported photon lasing values from CdSe NPLs in similar cavity designs. This open-cavity platform offers a simple approach to control exciton polaritons anticipated to benefit quantum information processing, optoelectronics, and chemical reactions.
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Affiliation(s)
| | - Nathan G Sinai
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Max Jin Hui Tan
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Sang-Min Park
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Eric Rodolfo Koessler
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Todd Krauss
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
- Institute of Optics, University of Rochester, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
- Institute of Optics, University of Rochester, Rochester, New York 14627, United States
| | - Teri W Odom
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
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8
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Odewale E, Wanasinghe ST, Rury AS. Assessing the Determinants of Cavity Polariton Relaxation Using Angle-Resolved Photoluminescence Excitation Spectroscopy. J Phys Chem Lett 2024; 15:5705-5713. [PMID: 38768370 PMCID: PMC11146005 DOI: 10.1021/acs.jpclett.4c01120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2024] [Revised: 05/09/2024] [Accepted: 05/13/2024] [Indexed: 05/22/2024]
Abstract
The strong coupling of light and matter within electromagnetic resonators leads to the formation of cavity polaritons whose hybrid nature may help certain ground and excited state chemical processes. To help enable the development of polariton chemistry, we have developed and applied a spectroscopic technique to leverage the relatively larger spatial coherence of polaritons to assess the determinants of relaxation in hybrid light-matter states. By exciting the lower polariton (LP) state in cavity samples filled with different metalloporphyrin chromophores, we measured and modeled angle-resolved photoluminescence excitation spectra. Our results suggest that the shortest lived constituent of the LP state characterized by specific Hopfield coefficients limits the light absorption of the intracavity molecules, which we equate with the effective polariton lifetime. Our results suggest that researchers need to consider the lifetimes of both photons and excitons participating in strong light-matter coupling when designing polaritonic systems and the methods they can use to assess the relaxation of polaritonic states.
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Affiliation(s)
- Elizabeth
O. Odewale
- Department
of Chemistry, Wayne State University, Detroit, Michigan 48202, United States
- Materials
Structural Dynamics Laboratory, Wayne State
University, Detroit, Michigan 48202, United States
| | - Sachithra T. Wanasinghe
- Department
of Chemistry, Wayne State University, Detroit, Michigan 48202, United States
- Materials
Structural Dynamics Laboratory, Wayne State
University, Detroit, Michigan 48202, United States
| | - Aaron S. Rury
- Department
of Chemistry, Wayne State University, Detroit, Michigan 48202, United States
- Materials
Structural Dynamics Laboratory, Wayne State
University, Detroit, Michigan 48202, United States
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9
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Yu Q, Bowman JM. Fully Quantum Simulation of Polaritonic Vibrational Spectra of Large Cavity-Molecule System. J Chem Theory Comput 2024; 20:4278-4287. [PMID: 38717309 DOI: 10.1021/acs.jctc.4c00129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
The formation of molecular vibrational polaritons, arising from the interplay between molecular vibrations and infrared cavity modes, is a quantum phenomenon necessitating accurate quantum dynamical simulations. Here, we introduce the cavity vibrational self-consistent field/virtual state configuration interaction method, enabling quantum simulation of the vibrational spectra of many-molecule systems within the optical cavity. Focusing on the representative (H2O)21 system, we showcase this parameter-free quantum approach's ability to capture both linear and nonlinear vibrational spectral features. Our findings highlight the growing prominence of molecular couplings among OH stretches and bending excited bands with increased light-matter interaction, revealing distinctive nonlinear spectral features induced by vibrational strong coupling.
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Affiliation(s)
- Qi Yu
- Department of Chemistry, Fudan University, Shanghai 200438, P. R. China
| | - Joel M Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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10
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Zeng H, Pérez-Sánchez JB, Eckdahl CT, Liu P, Chang WJ, Weiss EA, Kalow JA, Yuen-Zhou J, Stern NP. Control of Photoswitching Kinetics with Strong Light-Matter Coupling in a Cavity. J Am Chem Soc 2023; 145:19655-19661. [PMID: 37643086 DOI: 10.1021/jacs.3c04254] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Most photochemistry occurs in the regime of weak light-matter coupling, in which a molecule absorbs a photon and then performs photochemistry from its excited state. In the strong coupling regime, enhanced light-matter interactions between an optical field and multiple molecules lead to collective hybrid light-matter states called polaritons. This strong coupling leads to fundamental changes in the nature of the excited states including multi-molecule delocalized excitations, modified potential energy surfaces, and dramatically altered energy levels relative to non-coupled molecules. The effect of strong light-matter coupling on covalent photochemistry has not been well explored. Photoswitches undergo reversible intramolecular photoreactions that can be readily monitored spectroscopically. In this work, we study the effect of strong light-matter coupling on the kinetics of photoswitching within optical cavities. Reproducing prior experiments, photoswitching of spiropyran/merocyanine photoswitches is decelerated in a cavity. Fulgide photoswitches, however, show the opposite effect, with strong coupling accelerating photoswitching. While modified merocyanine switching can be explained by changes in radiative decay rates or the amount of light in the cavity, modified fulgide switching kinetics suggest direct changes to excited-state reaction kinetics.
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Affiliation(s)
- Hongfei Zeng
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, United States
| | - Juan B Pérez-Sánchez
- Department of Chemistry and Biochemistry, University of California-San Diego, La Jolla, California 92093, United States
| | - Christopher T Eckdahl
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Pufan Liu
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Woo Je Chang
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Emily A Weiss
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Julia A Kalow
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Joel Yuen-Zhou
- Department of Chemistry and Biochemistry, University of California-San Diego, La Jolla, California 92093, United States
| | - Nathaniel P Stern
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, United States
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11
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Mondal ME, Koessler ER, Provazza J, Vamivakas AN, Cundiff ST, Krauss TD, Huo P. Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons. J Chem Phys 2023; 159:094102. [PMID: 37655761 DOI: 10.1063/5.0166188] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 08/10/2023] [Indexed: 09/02/2023] Open
Abstract
We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton-polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light-matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton-phonon coupling among polariton states due to the strong light-matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.
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Affiliation(s)
- M Elious Mondal
- 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
| | - Justin Provazza
- Quantum Simulation Technologies, Inc., Boston, Massachusetts 02135, USA
| | - A Nickolas Vamivakas
- The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Steven T Cundiff
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Todd D Krauss
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
- The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
- The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA
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12
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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: 45] [Impact Index Per Article: 45.0] [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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13
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Diroll BT, Guzelturk B, Po H, Dabard C, Fu N, Makke L, Lhuillier E, Ithurria S. 2D II-VI Semiconductor Nanoplatelets: From Material Synthesis to Optoelectronic Integration. Chem Rev 2023; 123:3543-3624. [PMID: 36724544 DOI: 10.1021/acs.chemrev.2c00436] [Citation(s) in RCA: 32] [Impact Index Per Article: 32.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The field of colloidal synthesis of semiconductors emerged 40 years ago and has reached a certain level of maturity thanks to the use of nanocrystals as phosphors in commercial displays. In particular, II-VI semiconductors based on cadmium, zinc, or mercury chalcogenides can now be synthesized with tailored shapes, composition by alloying, and even as nanocrystal heterostructures. Fifteen years ago, II-VI semiconductor nanoplatelets injected new ideas into this field. Indeed, despite the emergence of other promising semiconductors such as halide perovskites or 2D transition metal dichalcogenides, colloidal II-VI semiconductor nanoplatelets remain among the narrowest room-temperature emitters that can be synthesized over a wide spectral range, and they exhibit good material stability over time. Such nanoplatelets are scientifically and technologically interesting because they exhibit optical features and production advantages at the intersection of those expected from colloidal quantum dots and epitaxial quantum wells. In organic solvents, gram-scale syntheses can produce nanoparticles with the same thicknesses and optical properties without inhomogeneous broadening. In such nanoplatelets, quantum confinement is limited to one dimension, defined at the atomic scale, which allows them to be treated as quantum wells. In this review, we discuss the synthetic developments, spectroscopic properties, and applications of such nanoplatelets. Covering growth mechanisms, we explain how a thorough understanding of nanoplatelet growth has enabled the development of nanoplatelets and heterostructured nanoplatelets with multiple emission colors, spatially localized excitations, narrow emission, and high quantum yields over a wide spectral range. Moreover, nanoplatelets, with their large lateral extension and their thin short axis and low dielectric surroundings, can support one or several electron-hole pairs with large exciton binding energies. Thus, we also discuss how the relaxation processes and lifetime of the carriers and excitons are modified in nanoplatelets compared to both spherical quantum dots and epitaxial quantum wells. Finally, we explore how nanoplatelets, with their strong and narrow emission, can be considered as ideal candidates for pure-color light emitting diodes (LEDs), strong gain media for lasers, or for use in luminescent light concentrators.
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Affiliation(s)
- Benjamin T Diroll
- Center for Nanoscale Materials, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, United States
| | - Burak Guzelturk
- X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, United States
| | - Hong Po
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI-Paris, PSL Research University, Sorbonne Université Univ Paris 06, CNRS UMR 8213, 10 rue Vauquelin 75005 Paris, France
| | - Corentin Dabard
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI-Paris, PSL Research University, Sorbonne Université Univ Paris 06, CNRS UMR 8213, 10 rue Vauquelin 75005 Paris, France
| | - Ningyuan Fu
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI-Paris, PSL Research University, Sorbonne Université Univ Paris 06, CNRS UMR 8213, 10 rue Vauquelin 75005 Paris, France
| | - Lina Makke
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI-Paris, PSL Research University, Sorbonne Université Univ Paris 06, CNRS UMR 8213, 10 rue Vauquelin 75005 Paris, France
| | - Emmanuel Lhuillier
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 75005 Paris, France
| | - Sandrine Ithurria
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI-Paris, PSL Research University, Sorbonne Université Univ Paris 06, CNRS UMR 8213, 10 rue Vauquelin 75005 Paris, France
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14
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Koessler ER, Mandal A, Huo P. Incorporating Lindblad Decay Dynamics into Mixed Quantum-Classical Simulations. J Chem Phys 2022; 157:064101. [DOI: 10.1063/5.0099922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We derive the $\mathcal{L}$-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the $\mathcal{L}$-MFE method that satisfies this exact mapping. This establishes a method that uses independent trajectories which exactly reproduces Lindblad decay dynamics using a wavefunction description, with deterministic changes of the magnitudes of the quantum expansion coefficients, while only adding on a stochastic phase. We further demonstrate that when including nuclei in the Ehrenfest dynamics, the $\mathcal{L}$-MFE method gives semi-quantitatively accurate results, with the accuracy limited by the accuracy of the approximations present in the semiclassical MFE approach. This work provides a general framework to incorporate Lindblad dynamics into semiclassical or mixed quantum-classical simulations.
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Affiliation(s)
- Eric R Koessler
- Chemistry, University of Rochester, United States of America
| | | | - Pengfei Huo
- Department of Chemsitry, University of Rochester Department of Chemistry, United States of America
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15
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Lüttgens JM, Kuang Z, Zorn NF, Buckup T, Zaumseil J. Evidence for a Polariton-Mediated Biexciton Transition in Single-Walled Carbon Nanotubes. ACS PHOTONICS 2022; 9:1567-1576. [PMID: 35607642 PMCID: PMC9121424 DOI: 10.1021/acsphotonics.1c01590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Indexed: 06/15/2023]
Abstract
Strong coupling of excitonic resonances with a cavity gives rise to exciton-polaritons which possess a modified energy landscape compared to the uncoupled emitter. However, due to the femtosecond lifetime of the so-called bright polariton states and transient changes of the cavity reflectivity under excitation, it is challenging to directly measure the polariton excited state dynamics. Here, near-infrared pump-probe spectroscopy is used to investigate the ultrafast dynamics of exciton-polaritons based on strongly coupled (6,5) single-walled carbon nanotubes in metal-clad microcavities. We present a protocol for fitting the reflectivity-associated response of the cavity using genetic algorithm-assisted transfer-matrix simulations. With this approach, we are able to identify an absorptive exciton-polariton feature in the transient transmission data. This feature appears instantaneously under resonant excitation of the upper polariton but is delayed for off-resonant excitation. The observed transition energy and detuning dependence point toward a direct upper polariton-to-biexciton transition. Our results provide direct evidence for exciton-polariton intrinsic transitions beyond the bright polariton lifetime in strongly coupled microcavities.
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Affiliation(s)
- Jan M. Lüttgens
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Zhuoran Kuang
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
- Centre
for Advanced Materials, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Nicolas F. Zorn
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Tiago Buckup
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
- Centre
for Advanced Materials, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Jana Zaumseil
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
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16
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He Z, Xu C, He W, He J, Zhou Y, Li F. Principle and Applications of Multimode Strong Coupling Based on Surface Plasmons. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:1242. [PMID: 35457950 PMCID: PMC9024653 DOI: 10.3390/nano12081242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 03/27/2022] [Accepted: 04/03/2022] [Indexed: 11/16/2022]
Abstract
In the past decade, strong coupling between light and matter has transitioned from a theoretical idea to an experimental reality. This represents a new field of quantum light-matter interaction, which makes the coupling strength comparable to the transition frequencies in the system. In addition, the achievement of multimode strong coupling has led to such applications as quantum information processing, lasers, and quantum sensors. This paper introduces the theoretical principle of multimode strong coupling based on surface plasmons and reviews the research related to the multimode interactions between light and matter. Perspectives on the future development of plasmonic multimode coupling are also discussed.
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Affiliation(s)
- Zhicong He
- School of Mechanical and Electrical Engineering, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430073, China; (Z.H.); (C.X.); (W.H.); (J.H.); (Y.Z.)
- School of Mechanical and Electrical Engineering, Hubei Polytechnic University, Huangshi 435003, China
- Hubei Key Laboratory of Intelligent Transportation Technology and Device, Hubei Polytechnic University, Huangshi 435003, China
| | - Cheng Xu
- School of Mechanical and Electrical Engineering, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430073, China; (Z.H.); (C.X.); (W.H.); (J.H.); (Y.Z.)
| | - Wenhao He
- School of Mechanical and Electrical Engineering, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430073, China; (Z.H.); (C.X.); (W.H.); (J.H.); (Y.Z.)
| | - Jinhu He
- School of Mechanical and Electrical Engineering, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430073, China; (Z.H.); (C.X.); (W.H.); (J.H.); (Y.Z.)
| | - Yunpeng Zhou
- School of Mechanical and Electrical Engineering, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430073, China; (Z.H.); (C.X.); (W.H.); (J.H.); (Y.Z.)
| | - Fang Li
- School of Mechanical and Electrical Engineering, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430073, China; (Z.H.); (C.X.); (W.H.); (J.H.); (Y.Z.)
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17
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Sun K, Dou C, Gelin MF, Zhao Y. Dynamics of disordered Tavis-Cummings and Holstein-Tavis-Cummings models. J Chem Phys 2022; 156:024102. [PMID: 35032972 DOI: 10.1063/5.0076485] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
By employing the time-dependent variational principle and the versatile multi-D2 Davydov trial states, in combination with the Green's function method, we study the dynamics of the Tavis-Cummings model and the Holstein-Tavis-Cummings model in the presence of diagonal disorder and cavity-qubit coupling disorder. For the Tavis-Cummings model, time evolution of the photon population, the optical absorption spectra, and the hetero-entanglement between the qubits and the cavity mode are calculated by using the Green's function method to corroborate numerically exact results of Davydov's Ansätze. For the Holstein-Tavis-Cummings model, only the latter is utilized to simulate effects of disorder on the photon population dynamics and the absorption spectra. We have demonstrated that the complementary employment of analytical and numerical methods permits uncovering a fairly comprehensive picture of a variety of complex behaviors in disordered multidimensional polaritonic cavity quantum electrodynamics systems.
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Affiliation(s)
- Kewei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Cunzhi Dou
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yang Zhao
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
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18
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Mandal A, Li X, Huo P. Theory of vibrational polariton chemistry in the collective coupling regime. J Chem Phys 2022; 156:014101. [PMID: 34998324 DOI: 10.1063/5.0074106] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
We theoretically demonstrate that the chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.
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Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Xinyang Li
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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19
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Phillips C, Lai YF, Walker GC. Fabry-Pérot Phonon Polaritons in Boron Nitride Nanotube Resonators. J Phys Chem Lett 2021; 12:11683-11687. [PMID: 34843252 DOI: 10.1021/acs.jpclett.1c03274] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Phonon polaritons (PhPs) offer extreme confinement of optical fields and strong dispersion in the mid-infrared spectral region. To study the propagation and interference of PhPs in a 1-D system, we employ scattering scanning near-field optical microscopy (s-SNOM), analytical, and computational techniques to describe the resonance behavior observed in boron nitride nanotubes (BNNTs). In BNNTs of a sufficiently small length, the reflected standing waves from both terminals strongly interfere with one another, leading to large constructive enhancement at select wavelengths through the Fabry-Pérot interference. This 1-D nanoresonant behavior illustrates methods to increase and localize field strength at positions on a BNNT nanotube.
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Affiliation(s)
- Cassandra Phillips
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
| | - Yi-Fang Lai
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
| | - Gilbert C Walker
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
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20
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DelPo CA, Khan SUZ, Park KH, Kudisch B, Rand BP, Scholes GD. Polariton Decay in Donor-Acceptor Cavity Systems. J Phys Chem Lett 2021; 12:9774-9782. [PMID: 34595929 DOI: 10.1021/acs.jpclett.1c02644] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Enhanced delocalization is beneficial for absorbing molecules in organic solar cells, and in particular bilayer devices, where excitons face small diffusion lengths as a barrier to reaching the charge-generating donor-acceptor interface. As hybrid light-matter states, polaritons offer exceptional delocalization which could be used to improve the efficiency of bilayer organic photovoltaics. Polariton delocalization can aid in delivering excitons to the donor-acceptor interface, but the subsequent charge transfer event must compete with the fast decay of the polariton. To evaluate the viability of polaritons as tools to improve bilayer organic solar cells, we studied the decay of the lower polariton in three cavity systems: a donor only, a donor-acceptor bilayer, and a donor-acceptor blend. Using several spectroscopic techniques, we identified an additional decay pathway through charge transfer for the polariton in the bilayer cavity, demonstrating charge transfer from the polariton is fast enough to outcompete the decay to the ground state.
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Affiliation(s)
- Courtney A DelPo
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Saeed-Uz-Zaman Khan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, United States
| | - Kyu Hyung Park
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Bryan Kudisch
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Barry P Rand
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, United States
- Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544, United States
| | - Gregory D Scholes
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
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21
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Li X, Mandal A, Huo P. Theory of Mode-Selective Chemistry through Polaritonic Vibrational Strong Coupling. J Phys Chem Lett 2021; 12:6974-6982. [PMID: 34283619 DOI: 10.1021/acs.jpclett.1c01847] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Recent experiments have demonstrated remarkable mode-selective reactivities by coupling molecular vibrations with a quantized radiation field inside an optical cavity. The fundamental mechanism behind such effects, on the other hand, remains elusive. In this work, we provide a theoretical explanation of the basic principle of how cavity frequency can be tuned to achieve mode-selective reactivities. We find that the dynamics of the radiation mode leads to a cavity frequency-dependent dynamical caging effect of a reaction coordinate, resulting in suppression of the rate constant. In the presence of competitive reactions, it is possible to preferentially cage a reaction coordinate when the barrier frequencies of competing reactions are different, resulting in a selective slow down of a given reaction. Our theoretical results illustrate the cavity-induced mode-selective chemistry through polaritonic vibrational strong couplings, revealing the fundamental mechanism for changing chemical selectivities through cavity quantum electrodynamics.
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Affiliation(s)
- Xinyang Li
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Arkajit Mandal
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, United States
- Institute of Optics, University of Rochester, Rochester, New York 14627, United States
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