This work investigates the emergent thermalization regimes in a chaotic Tavis-Cummings (TC) model and their implications in quantum spectroscopy. While the TC model is a cornerstone of cavity quantum electrodynamics, traditional treatments often overlook many-body effects that arise in the thermodynamic limit. We utilize the Eigenstate Thermalization Hypothesis to demonstrate that a non-integrable excitonic Hamiltonian within the material manifold drives local thermalization. By tuning the polariton splitting $g$, we observe two dynamical regimes: a thermalizing regime at low interactions driven by quantum chaos and ergodicity, and a non-thermalizing regime at high interactions where strong coupling suppresses ergodicity. We further show that these regimes have direct implications on output photon statistics, specifically influencing the correlation times $τ_c$ of the cavity population and the second-order correlation function $g^{(2)}(t+τ)$. We propose that entangled-biphoton spectroscopy serves as an ideal experimental platform to probe these effects and to allow the characterization of the underlying many-body exciton-coupling disorder $σ$ through coincidence measurements of the output. Taken together, these results exploit a naturally occurring many-body phenomenon to bridge theoretical predictions with experimental observables.
This work investigates the emergent thermalization regimes in a chaotic Tavis-Cummings (TC) model and their implications in quantum spectroscopy. While the TC model is a cornerstone of cavity quantum electrodynamics, traditional treatments often overlook many-body effects that arise in the thermodynamic limit. We utilize the Eigenstate Thermalization Hypothesis to demonstrate that a non-integrable excitonic Hamiltonian within the material manifold drives local thermalization. By tuning the polariton splitting g, we observe two dynamical regimes: a thermalizing regime at low interactions driven by quantum chaos and ergodicity, and a non-thermalizing regime at high interactions where strong coupling suppresses ergodicity. We further show that these regimes have direct implications on output photon statistics, specifically influencing the correlation times τc of the cavity population and the second-order correlation function g(2)(t+τ). We propose that entangled-biphoton spectroscopy serves as an ideal experimental platform to probe these effects and to allow the characterization of the underlying many-body exciton-coupling disorder σ through coincidence measurements of the output. Taken together, these results exploit a naturally occurring many-body phenomenon to bridge theoretical predictions with experimental observables.
We consider a coupled atom-photon system described by the Tavis-Cummings dimer (two coupled cavities) in an open environment, to investigate the quantum signature of dissipative chaos. The appropriate classical limit of this model allows us to obtain a phase diagram identifying different dynamical phases, especially the onset of chaos. Both classically and quantum mechanically, we demonstrate the emergence of a steady state in the chaotic regime and analyze its properties. The interplay between quantum fluctuation and chaos leads to enhanced mixing dynamics and dephasing, resulting in the formation of an incoherent photonic fluid. The steady state exhibits an intriguing phenomenon of subsystem thermalization even outside the chaotic regime; however, the effective temperature increases with the degree of chaos. Moreover, the statistical properties of the steady state show a close connection with the random matrix theory, which, in contrast, is absent in the Liouvillian spectrum for this system. Finally, we discuss the experimental relevance of our findings, which can be tested in cavity and circuit quantum electrodynamics (QED) setups.
Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems. Thermalization in quantum many-body systems can unfold across space in surprising ways. The authors reveal nonequilibrium regimes in a driven-dissipative quantum chain, including a spatially emergent prethermal domain and a nonthermal condensate destabilized by quantum fluctuations, with broad implications for driven quantum platforms
The modern framework for quantum thermalization is grounded in the Eigenstate Thermalization Hypothesis (ETH), in which non-integrability and chaos are historically assumed as prerequisites. This work investigates this relationship in a three-species Bose-Josephson Junction (BJJ) with mutual interactions, experimentally achievable in current ultracold-atom platforms. After a thorough characterization of quantum chaos in this system, we examine the occurrence of thermal behavior expected when ETH holds. We identify three distinct regimes: chaotic, integrable, and separable. Remarkably, quantum thermalization occurs in both the chaotic and integrable regimes, while it breaks down in and near the separable limit — supporting that non-integrability is not a necessary condition for thermalization. Furthermore, since the system exhibits collective phenomena in the semiclassical limit, we identify ergodicity breaking phenomena such as athermal states in the chaotic regime classifiable as quantum scars, which show no signs of thermalization, consistently with a weak form of ETH.
The Tavis-Cummings (TC) model has been widely used to investigate the collective coupling effect in hybrid light-matter systems; however, the TC model neglects the effect of a dielectric environment (the spectral structure of photonic bath), and it remains unclear whether the TC model can adequately depict the light-matter interaction in a non-homogeneous, dispersive, and absorbing medium. To clarify the ambiguity, in this work, we first connect the macroscopic quantum electrodynamics and the TC model with dissipation. Based on the relationship between these two theoretical frameworks, we develop a guideline that allows us to examine the applicability of the TC model with dissipation. The guideline states that if 1) the generalized spectral densities are independent of the positions of molecules and 2) the generalized spectral densities resemble a Lorentzian function, then the hybrid light-matter system can be properly described by the TC model with dissipation. In order to demonstrate how to use the guideline, we examine the position dependence and the lineshape of the generalized spectral densities in three representative systems, including a silver Fabry-Pérot cavity, a silver surface, and an aluminum spherical cavity. We find that only the aluminum spherical cavity meets the two conditions, i.e., position independence and Lorentzian lineshape, required for the utilization of the dissipative TC model. Our results indicate that the use of the TC model with dissipation to study the collective coupling effect should be done with care, providing an important perspective on resonance energy transfer and polariton chemistry.
Classical statistical mechanics relies on the ergodic hypothesis, which states that a system explores the entire allowed phase space during its time evolution. Pure quantum states are at odds with this concept as they remain in a single quantum state even if the system's parameters are suddenly altered. However, in a generic many-body system, coherent dynamics drive local thermalization of its subsystems. In this case, any local observable appears thermal and can be described by a statistical ensemble even though the full state remains pure. The key to understanding the phenomenon of quantum thermalization lies in the entanglement properties of the system: The presence of entanglement creates local entropy that validates the use of statistical physics.\nIn this thesis, we experimentally study the emergence of statistical mechanics in a quantum state and observe the fundamental role of quantum entanglement in facilitating this emergence. We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale while we measure that the full quantum state remains pure.\nThe only known robust exception from the paradigm of quantum thermalization is provided by disordered systems. In this case, the particle transport ceases through the system, preventing the formation of a sufficient amount of entanglement required for thermalization. However, if the many-body system is interacting, the state develops non-local quantum correlations that are inaccessible to any local observable. These correlations spread exponentially slowly in time throughout the entire system and are considered a hallmark feature of many-body-localized states.\nIn order to study the interplay between thermalization and localization in our system, we develop novel methods for high fidelity state preparation and readout. We achieved an exquisite isolation of our system from the environment, which allows us to monitor coherent many-body dynamics over multiple decades of time evolution.\nWe experimentally realize such a many-body localized system and observe the formation of non-local quantum correlations, while the particle transport is frozen in the system. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.
Isolated, many-body quantum systems, evolving under their intrinsic dynamics, exhibit a multitude of exotic phenomena and raise foundational questions about statistical mechanics. A flurry of theoretical work has been devoted to understanding how these systems reach thermal equilibrium in the absence of coupling to an external bath and, when thermalization does not occur, investigating the emergent non-equilibrium phases of matter. With the advent of synthetic quantum systems, such as ultra-cold atoms in optical lattices or trapped ions, these questions are no longer academic and can be directly studied in the laboratory. This dissertation explores the non-equilibrium phenomena that stem from the interplay between interactions, disorder, symmetry, topology, and external driving. First, we study how strong disorder, leading to many-body localization, can arrest the heating of a Floquet system and stabilize symmetry-protected topological order that does not have a static analogue. We analyze its dynamical and entanglement properties, highlight its duality to a discrete time crystal, and propose an experimental implementation in a cold-atom setting.Quenched disorder and the many-body localized state are crucial ingredients in protecting macroscopic quantum coherence. We explore the stability of many-body localization in two and higher dimensions and analyze its robustness to rare regions of weak disorder.We then study a second example of non-thermal behavior, namely integrability. We show that a class of random spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram, which includes regions of integrability, classical chaos, and of a novel integrable structure whose conservation laws are reminiscent of the integrals of motion found in a many-body localized phase.The third group of disordered, non-ergodic systems we consider, spin glasses, have fascinating connections to complexity theory and the hardness of constraint satisfaction. We define a statistical ensemble that interpolates between the classical and quantum limits of such a problem and show that there exists a sharp boundary separating satisfiable and unsatisfiable phases.