Dynamics of disordered Tavis-Cummings and Holstein-Tavis-Cummings models

Finite temperature dynamics of the Holstein-Tavis-Cummings model

By employing the numerically accurate multiple Davydov Ansatz (mDA) formalism in combination with the thermo-field dynamics (TFD) representation of quantum mechanics, we systematically explore the influence of three parameters-temperature, photonic-mode detuning, and qubit-phonon coupling-on population dynamics and absorption spectra of the Holstein-Tavis-Cummings (HTC) model. It is found that elevated qubit-phonon couplings and/or temperatures have a similar impact on all dynamic observables: they suppress the amplitudes of Rabi oscillations in photonic populations as well as broaden the peaks and decrease their intensities in the absorption spectra. Our results unequivocally demonstrate that the HTC dynamics is very sensitive to the concerted variation of the three aforementioned parameters, and this finding can be used for fine-tuning polaritonic transport. The developed mDA-TFD methodology can be efficiently applied for modeling, predicting, optimizing, and comprehensively understanding dynamic and spectroscopic responses of actual molecular systems in microcavities.

Spontaneous Raman scattering from vibrational polaritons is obscured by reservoir states

Vibrational strong coupling results from the interaction between optically allowed molecular vibrational excitations and the resonant mode of an infrared cavity. Strong coupling leads to the formation of hybrid states, known as vibrational polaritons, which are readily observed in transmission measurements and a manifold of the reservoir states. In contrast, Raman spectroscopy of vibrational polaritons is elusive and has recently been the focus of both theoretical and experimental investigations. Because Raman measurements are frequently performed with high-numerical aperture excitation/collection optics, the angular dispersion of the strongly coupled system must be carefully considered. Herein, we experimentally investigated vibrational polaritons involving dispersive collective lattice resonances of infrared antenna arrays. Despite clear indications of the strong coupling to vibrational excitations in the transmission spectrum; we found that Raman spectra do not bear signatures of the polaritonic transitions. Detailed measurements indicate that the disappearance of the Raman signal is not due to the polariton dispersion in our samples. On the other hand, the Tavis-Cummings-Holstein model that we employed to interpret our results suggests that the ratio of the Raman transition strengths between the reservoir and the polariton states scales according to the number of strongly coupled molecules. Because the vibrational transitions are relatively weak, the number of molecules required to achieve strong coupling conditions is about 109 per unit cell of the array of infrared antennas. Therefore, the scaling predicted by the Tavis-Cummings-Holstein model can explain the absence of the polariton signatures in spontaneous Raman scattering experiments.

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

Vibrational Polaritons in Disordered Molecular Ensembles

Disorder is an intrinsic attribute of any realistic molecular system. It is known to lead to localization, which hampers efficient transport. It was recently proposed that in molecular ensembles strongly coupled to photonic cavities, moderate disorder leads to delocalization and increases of the transport and chemical reaction rates. Vibrational polaritons involve molecular vibrations hybridized with an infrared cavity. When the coupling strength largely exceeds the molecular inhomogeneity, polaritons are unaffected by disorder. However, in many experiments, such a homogeneous limit does not apply. We investigated vibrational polaritons involving molecular ensembles with systematically modified disorder. Counterintuitively, moderate disorder leads to an increase in Rabi splitting and the modification of the polariton bandwidths. Experimental spectroscopic data agree with a Tavis-Cummings-like model that suggests enhanced delocalization of the reservoir states occurs via the admixture of the cavity mode. Our results provide new insights into the paradigm of disorder-induced cavity-assisted delocalization in molecular polaritons.

Exact Results for the Tavis-Cummings and Hückel Hamiltonians with Diagonal Disorder

We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that in cases where the disorder has a Cauchy distribution, the disorder averaged one particle Green's function can be calculated directly, using a deterministic, complex (non-Hermitian) Hamiltonian. For this we use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solution for the case of N molecules with site disorder, confined to a microcavity, for any value of N. Our analysis shows that the width of the polaritonic states as a function of N depends on the nature of disorder, and hence it can be used to probe the way molecular energy levels are distributed. We also show how one can find exact results for Hückel type Hamiltonians with on-site Cauchy disorder and demonstrate its use.

Effects of disorder on polaritonic and dark states in a cavity using the disordered Tavis-Cummings model

We consider molecules confined to a microcavity of dimensions such that an excitation of the molecule is nearly resonant with a cavity mode. The molecular excitation energies are assumed to be Gaussianly distributed with mean ϵ_a and variance σ. We find an asymptotically exact solution for large number density N. Conditions for the existence of the polaritonic states and expressions for their energies are obtained. Polaritonic states are found to be quite stable against disorder. Our results are verified by comparison with simulations. When ϵ_a is equal to energy of the cavity state ϵ_c, the Rabi splitting is found to increase by 2σ²N|Ṽ|, where Ṽ is the coupling of a molecular excitation to the cavity state. An analytic expression is found for the disorder-induced width of the polaritonic peak. Results for various densities of states and the absorption spectrum are presented. The dark states turn "gray" in the presence of disorder with their contribution to the absorption increasing with σ. Lifetimes of the cavity and molecular states are found to be important, and for sufficiently large Rabi splitting, the width of the polaritonic peaks is dominated by them. We also give analytical results for the case where the molecular levels follow a uniform distribution. We conclude that the study of the width of the polaritonic peaks as a function of the Rabi splitting can give information on the distribution of molecular energy levels. Finally, the effects of (a) orientational disorder and (b) spatial variation on the cavity field are presented.

Accurate Simulation of Spectroscopic Signatures of Cavity-Assisted, Conical-Intersection-Controlled Singlet Fission Processes

A numerically accurate, fully quantum methodology has been developed for the simulation of the dynamics and nonlinear spectroscopic signals of cavity-assisted, conical-intersection-controlled singlet fission systems. The methodology is capable of handling several molecular systems strongly coupled to the photonic mode of the cavity and treats the intrinsic conical intersection and cavity-induced polaritonic conical intersections in a numerically exact manner. Contributions of higher-lying molecular electronic states are accounted for comprehensively. The intriguing process of cavity-modified fission dynamics, including all of its electronic, vibrational, and photonic degrees of freedom, together with its two-dimensional spectroscopic manifestation, is simulated for two rubrene dimers strongly coupled to the cavity mode.

Engineering Cavity Singlet Fission in Rubrene

By employing the numerically exact multiple Davydov D₂ ansatz, we study cavity-manipulated singlet fission that is mediated by polaritonic conical intersections for both one- and two-molecule systems. The population evolution of the TT state and the cavity photons is carefully examined in search for a high fission efficiency via cavity engineering. Several interesting mechanisms have been uncovered, such as photon-assisted singlet fission, system localization via a displaced photon state, and collective enhancement of the fission efficiency for the two-molecule system. It is also found that the system localization process in the two-molecule system differs substantially from that in the one-molecule system because of the appearance of a novel central polaritonic conical intersection in the two-molecule system. It has been demonstrated that the cavity-controlled singlet fission process can be switched on and off by controlling the average pumping photon number.

Simulation of Emission Spectra of Transition Metal Dichalcogenide Monolayers with the Multimode Brownian Oscillator Model

The multimode Brownian oscillator model is employed to simulate the emission spectra of transition metal dichalcogenide (TMD) monolayers. Good agreement is obtained between measured and simulated photoluminescence spectra of WSe₂, WS₂, MoSe₂, and MoS₂ at various temperatures. The Huang-Rhys factor extracted from the model can be associated with that from the modified semiempirical Varshni equation at high temperatures. Individual mechanisms leading to the unique temperature-dependent emission spectra of those TMDs are validated by the multimode Brownian oscillator (MBO) fitting, while it is, in turn, confirmed that the MBO analysis is an effective method for studying the optical properties of TMD monolayers. Parameters extracted from the MBO fitting can be used to explore exciton-photon-phonon dynamics of TMDs in a more comprehensive model.

Modeling Molecular J and H Aggregates using Multiple-Davydov D2 Ansatz

The linear absorption spectrum of J and H molecular aggregates is studied using the time-dependent Dirac-Frenkel variational principle (TDVP) with the multi-Davydov D2 (mD2) trial wavefunction (Ansatz). Both the electronic...