Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion---organized around the experimentally relevant limit of weak interactions---the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion---organized around the experimentally relevant limit of weak interactions---the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.
Due to the variety of tools available to control atomic, molecular, and optical (AMO) systems, they provide a versatile platform for studying many-body physics, quantum simulation, and quantum computation. Although extensive efforts are employed to reduce coupling between the system and the environment, the effects of the environment can never fully be avoided, so it is important to develop a comprehensive understanding of open quantum systems. The system-environment coupling often leads to loss via dissipation, which can be countered by a coherent drive. Open quantum systems subject to dissipation and drive are known as driven-dissipative systems, and they provide an excellent platform for studying many-body nonequilibrium physics. The first part of this dissertation will focus on driven-dissipative phase transitions. Despite the nonequilibrium nature of these systems, the corresponding phase transitions tend to exhibit emergent equilibrium behavior. However, we will show that in the vicinity of a multicritical point where multiple phase transitions intersect, genuinely nonequilibrium criticality can emerge, even though the individual phase transitions on their own exhibit equilibrium criticality. These nonequilibrium multicritical points can exhibit a variety of exotic phenomena not possible for their equilibrium counterparts, including the emergence of complex critical exponents, which lead to discrete scale invariance and spiraling phase boundaries. Furthermore, the Liouvillian gap can take on complex values, and the fluctuation-dissipation theorem is violated, corresponding to an effective temperature which gets "hotter" and "hotter" at longer and longer wavelengths. The second part of this dissertation will focus on Rydberg atoms. In particular, we study how the spontaneous generation of contaminant Rydberg states drastically modifies the behavior of a driven-dissipative Rydberg system due to the resultant dipole-dipole interactions. These interactions lead to a complicated competition of both blockade and anti-blockade effects, leading to strongly enhanced Rydberg populations for far-detuned drive and reduced Rydberg populations for resonant drive.
Recent progress in Cavity QED (CQED) has brought forth the possibility of wiring up individual CQED systems into lattices to investigate collective behavior and correlated phases of strongly coupled light and matter [1-9]. Such Lattice CQED systems operate on polaritonic quasi-particles that are hybrids of light and matter in a controllable proportion, combining long-range coherence of photons and strong interactions typically displayed by massive particles. In this talk, I will review recent work on proposed quantum simulation of Hubbard models with Lattice CQED systems, which are akin to the celebrated Bose-Hubbard model extensively studied with cold atomic gases in optical lattices and Josephson junction arrays. A crucial feature of Lattice CQED systems that I will focus on is their non-equilibrium nature. Unavoidable photon loss coupled with the ease of feeding in additional photons through continuous external driving renders such lattices open quantum systems. Under the influence of drive and dissipation, Lattice CQED systems typically display steady-state phases thereby providing a platform for realizing novel, non-equilibrium phases of light and matter that may be very dierent from those realized with condensed matter systems.
Ultracold atomic gases loaded into optical cavities constitute one of the most versatile platforms for the study of out-of-equilibrium dynamics and quantum simulation of many- body systems. In this thesis, we explore these two possibilities, motivated by current state-of-the-art atom-cavity experiments, uncovering novel phenomena and opening up new theoretical and experimental avenues into the intriguing world of quantum many- body physics. First, we study a gas of ultracold atoms coupled to three optical resonators. We show that the inherent Z2 symmetries, associated with each atom-cavity coupling, can be combined into a global SO(3) rotational symmetry which can be spontaneously broken. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We argue that by coupling the atoms equally to n different modes, it will in general be possible to generate a global SO(n) symmetry. Second, we investigate the dynamics of a spinor BEC inside an optical cavity. We focus on a two-component Dicke model with complex light-matter couplings, accounting for photon losses. We compute the steady-state phase diagram and find dynamical in- stabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Lastly, we explore the dynamics of a BEC inside an optical cavity in the presence of an optical lattice. We derive an effective master equation by adiabatically eliminating the cavity field. In the bad-cavity regime, we find an infinite-temperature steady state, but with relaxation dynamics that can be highly nontrivial. For small hopping, the interplay between dissipation and strong interactions leads to an algebraic relaxation of the system, whereas for large hopping, the approach to the steady state is exponential. In the good- cavity regime, we show that the system allows for optical pumping between momentum modes, enabling cavity cooling.
Light-matter interfaces have now entered a new stage marked by the ability to engineer quantum correlated states under driven-dissipative conditions. To propel this new generation of experiments, we are confronted with the need to model nonunitary many-body dynamics in strongly coupled regimes by transcending traditional approaches in quantum optics. In this work, we contribute to this program by adapting a functional-integral technique, conventionally employed in high-energy physics, in order to obtain nonequilibrium dynamics for interacting light-matter systems. Our approach is grounded in constructing “two-particle irreducible” (2PI) effective actions, which provide a nonperturbative and conserving framework for describing quantum evolution at a polynomial cost in time. We apply our method to complement the analysis of spin-glass formation in the context of frustrated multimode cavity quantum electrodynamics, initiated in our accompanying work [Hosseinabadi , ]. Finally, we outline the capability of the technique to describe other near-term platforms in many-body quantum optics, and its potential to make predictions for this new class of experiments. Published by the American Physical Society 2024
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to examine driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary locally reduce the entropy of the many-body system. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady state, precisely as with optical pumping. We characterize the dynamics of multipartite entanglement in an one-dimensional lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.