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The Journal of Physical Chemistry A

Emergence of Collective Coherent States from Strong-Light Coupling of Disordered Systems

Gregory D. Scholes

Published Jul 29, 2021• 18 citations
Publisher

Abstract

An empirical framework for studying the way vacuum fluctuations in a Fabry–Perot cavity produce collective light–matter hybrid states (polariton states) is reported. The reason that the Tavis–Cummings model, where a single mode of the radiation field couples to all the molecules, succeeds is discussed in terms of the strong phase correlation of the vacuum fluctuations in the cavity, which produces a single effective cavity mode (ECM). The model is used to study the onset of the collective state, or “superradiant phase”, for ensembles of molecules with significant disorder in their transition energies, as a function of cavity strength factor, from low Q cavities to high Q cavities. A key result is the quantification of the coherence of the ensemble of the lowest energy eigenstate. This is assessed, primarily, using an entropy distance measure. The statistical model provides a physical intuition for the formation of coherence of polariton states when the collective coupling is strong enough that they dominate over the tail of the dark-state density-of-states.

DOI
10.1021/acs.jpca.1c05400

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An empirical framework for studying the way vacuum fluctuations in a Fabry–Perot cavity produce collective light–matter hybrid states (polariton states) is reported. The reason that the Tavis–Cummings model, where a single mode of the radiation field couples to all the molecules, succeeds is discussed in terms of the strong phase correlation of the vacuum fluctuations in the cavity, which produces a single effective cavity mode (ECM). The model is used to study the onset of the collective state, or “superradiant phase”, for ensembles of molecules with significant disorder in their transition energies, as a function of cavity strength factor, from low Q cavities to high Q cavities. A key result is the quantification of the coherence of the ensemble of the lowest energy eigenstate. This is assessed, primarily, using an entropy distance measure. The statistical model provides a physical intuition for the formation of coherence of polariton states when the collective coupling is strong enough that they dominate over the tail of the dark-state density-of-states.
We analyze equilibrium properties of coupled-doped cavities described by the Jaynes–Cummings–Hubbard Hamiltonian. In particular, we characterize the entanglement of the system in relation to the insulating–superfluid phase transition. We point out the existence of a crossover inside the superfluid phase of the system when the excitations change from polaritonic to purely photonic. Using an ensemble statistical approach for small systems and stochastic mean-field theory for large systems, we analyze static disorder of the characteristic parameters of the system and explore the ground state-induced statistics. We report on a variety of glassy phases deriving from the hybrid statistics of the system. On-site strong disorder induces insulating behavior through two different mechanisms. For disorder in the light–matter detuning, low-energy cavities dominate the statistics, allowing the excitations to localize and bunch in such cavities. In the case of disorder in the light–matter coupling, sites with strong coupling between light and matter become very significant, which enhances the Mott-like insulating behavior. Inter-site (hopping) disorder induces fluidity and the dominant sites are strongly coupled to each other.
Collective light-matter phenomena such as Dicke superradiance are often described as a collection of effective spins coupled homogeneously to a bosonic mode, giving rise to a collective bright mode with enhanced light-matter coupling. In fermionic systems, Pauli exclusion and Fermi-surface structure can significantly modify this picture, while randomness in the atom-light couplings raises the question of whether disorder promotes or suppresses collective behavior. Here, we study a cavity model in which fermionic particles couple to a photonic mode through a random all-to-all interaction matrix with tunable mean and variance. Combining numerical mean-field methods, analytic stability analysis and random-matrix predictions, and benchmarks against exact diagonalization, we characterize both the onset and structure of the superradiant phase. While mean coupling and disorder variance contribute in the same way to the onset, they lead to drastically different behavior within the condensed phase. Uniform coupling supports a single bright collective fermionic mode with conventional Dicke-like scaling of the cavity field. Disorder, instead, gives rise to a qualitatively different collective regime in which many grey fermionic states participate coherently, producing a parametrically enhanced scaling of the condensate with system size. Our results reveal a mechanism through which disorder can, perhaps counterintuitively, promote collective light-matter phenomena.
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light–matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis–Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.
The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.
Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.
The field of Polaritonic Chemistry studies molecules strongly coupled to the light field of optical cavities. The resulting modification of the potential energy landscape has been demonstrated to enable control over the chemical and physical properties of materials and molecular ensembles. This thesis extends the Tavis–Cummings model to describe molecules under strong light–matter coupling, incorporating static dipole moments and dipole self-energy contributions derived from the Pauli–Fierz Hamiltonian. These additional terms are shown to be essential for reproducing cavity-modified molecular dynamics and spectra. Simulations on the nuclear wavefunction propagation of MgH+ molecules demonstrate the impact of these terms, while an effective two-level system model accurately captures the behavior of large ensembles. Beyond single excitations, the thesis also explores the higher excitation manifolds of the Tavis-Cummings model, which reveals that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable. Open-system simulations highlight how the coherence of the system's initial state governs decay pathways and enables long-lived energy storage. Finally, a multilevel vibrational model coupled to a two-mode cavity is introduced, where a Raman scheme enables selective mixing of vibrational states. The simulation results show that continuous pumping can drive molecules into specific vibrational states while suppressing electronic excitation, both for single molecules and small ensembles. Together, these results provide new theoretical insights into the mechanisms by which optical cavities reshape molecular energy landscapes. The results suggest approaches for controlling photonic, electronic, and vibrational dynamics in strongly coupled systems, contributing to the theoretical foundation of polariton chemistry.