All-to-all interacting and disordered many-body systems are notoriously hard to simulate on quantum platforms, as interactions are commonly mediated by auxiliary degrees of freedom that lower the amount of disorder, introducing undesired correlations. In this work, we show how a Trotterization scheme can be effectively utilized to densify the disorder of the model. In particular, we study the statistical properties of the resulting model, as well as Trotterization errors in the simulation that affect the time evolution and dynamical observables. As a concrete example, we propose an implementation via a single-mode cavity QED platform of the complex Sachdev-Ye-Kitaev model. We analyze several features of the effective model, such as the distribution of the effective couplings, the number of interacting sites, state preparation, and the behavior of quantum chaos probes. We conclude this work with a detailed investigation of the robustness of our findings against dissipation, both analytically and numerically.
All-to-all interacting and disordered many-body systems are notoriously hard to simulate on quantum platforms, as interactions are commonly mediated by auxiliary degrees of freedom that lower the amount of disorder, introducing undesired correlations. In this work, we show how a Trotterization scheme can be effectively utilized to densify the disorder of the model. In particular, we study the statistical properties of the resulting model, as well as Trotterization errors in the simulation that affect the time evolution and dynamical observables. As a concrete example, we propose an implementation via a single-mode cavity QED platform of the complex Sachdev-Ye-Kitaev model. We analyze several features of the effective model, such as the distribution of the effective couplings, the number of interacting sites, state preparation, and the behavior of quantum chaos probes. We conclude this work with a detailed investigation of the robustness of our findings against dissipation, both analytically and numerically.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.
We show that cavity quantum electrodynamics (QED) devices can realize dissipative Sachdev-Ye-Kitaev (SYK) universality, a paradigmatic setting for quantum chaos in open many-body systems. Ultracold fermions with disordered, all-to-all cavity-mediated interactions provide two complementary routes: atomic spontaneous emission in a single-mode cavity and photon leakage from a multimode cavity. Strikingly, both converge to the same non-Hermitian random-matrix universality despite originating from integrable and chaotic closed-system limits, respectively. In the single-mode cavity, dissipation creates quantum chaos from an integrable Hamiltonian. We trace this convergence to a tunable growth in dissipative rank, controlled, respectively, by the Lamb-Dicke parameter and the cavity-mode spacing. The integrability-to-chaos crossover is accompanied by a dynamical crossover from long-lived prethermal memory to rapid thermalization, visible in single-atom-resolved densities.
Understanding how quantum systems transition from integrable to fully chaotic behavior remains a central open problem in physics. The Sachdev--Ye--Kitaev (SYK) model provides a paradigmatic framework for studying many-body chaos and holography, yet it captures only the strongly correlated limit, leaving intermediate regimes unexplored. Here, we investigate the Yukawa--SYK (YSYK) model, where bosonic fields mediate random fermionic interactions, and demonstrate that it naturally bridges single-particle and many-body chaos. Using spectral and dynamical chaos markers, we perform a comprehensive finite-size characterization of the YSYK model. We show that the interaction strength acts as a tunable control parameter interpolating between the SYK2 and SYK4 limits, and introduce a framework enabling direct and quantitative comparison with these benchmark models. In the intermediate regimes, we uncover distinct dynamical regimes marked by partial ergodicity breaking, prethermalization plateaus, and incomplete scrambling. Finally, we propose a feasible optical-cavity implementation of the YSYK model using ultra-cold atoms. Our results establish the YSYK model as a unifying platform connecting single-particle and many-body chaos, paving the way for experimental observation of these phenomena.
Recent advances in theoretical physics have increasingly focused on the dynamics of quantum systems with many interacting degrees of freedom, while ultracold atom platforms now enable the realization of diverse theoretical models with precise control over system parameters and advanced monitoring techniques. A prominent example is cavity quantum electrodynamics (CQED), where large atomic or molecular ensembles are coupled to high-finesse optical cavities, enabling strong interaction with confined electromagnetic modes and leading to phenomena such as the superradiant phase transition, in which atoms and photons form a coherent state. Most theoretical studies of CQED have concentrated on regimes of spatially uniform atom–cavity coupling, where collective behavior allows a description in terms of the classical dynamics of a few macroscopic variables. However, experimental capabilities now permit exploration beyond this limit, though theoretical progress is hindered by the exponential computational complexity of simulating large quantum systems, particularly when environmental coupling is included. This thesis addresses such challenges by developing efficient approaches, within the Keldysh formalism of non-equilibrium quantum field theory, to study systems with strongly disordered interactions coupled to external reservoirs. Two representative models are considered: a disordered spin–boson model describing light–matter interactions with quenched disorder, relevant to recent CQED experiments in confocal cavities, and a fermion–phonon system governed by the Yukawa–Sachdev–Ye–Kitaev (Yukawa-SYK) model. Both systems are quantum critical, exhibiting a continuum of low-energy modes above their stationary states, yet disorder produces qualitatively distinct dynamical behaviors: in the spin–boson system it induces slow, glassy relaxation, whereas in the Yukawa-SYK model it leads to rapid thermalization. These contrasting outcomes reveal the non-trivial role of disorder in quantum many-body systems and motivate further investigation into its effects on non-equilibrium quantum dynamics.
Cavity quantum electrodynamics (QED) with ultracold fermions provides a promising platform for realizing many-body quantum chaos through disordered, photon-mediated long-range interactions. Such setups are inherently open and are therefore subject to dissipation arising from cavity photon loss and atomic spontaneous emission. In this article, we study the driven-dissipative dynamics of a typical cavity QED setting including controllable disorder and long-range interactions. We find that the two dissipation sources have qualitatively different structures. Cavity loss reduces to a single dephasing channel, whereas spontaneous emission in the experimentally relevant regime generates a collection of nonlocal dephasing channels. Cavity-induced dephasing preserves signatures distinguishing integrable from chaotic Hamiltonian dynamics in observables that depend linearly on the density matrix, while spontaneous emission suppresses these signatures. By contrast, quantities that probe the structure of the many-body state, such as the entanglement entropy, are strongly affected by both dissipation mechanisms. Assuming experimentally realistic parameters, we derive quantitative constraints for the observation and control of many-body quantum chaos in cavity-QED platforms.
Abstract As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The second is that small fluctuations of the parameters of optical elements do not affect the first conclusion. This implies that the method is robust against the certain type of errors as we considered. Last but not least, we present an example of implementation of the simulation on a photonic chip as well as an optimized scheme. By such examples, we show a reduction of the costs compared to its classical counterpart and the potential for further improvement, which promotes a more general application.