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arXiv:2312.03073 · Reviews of Modern Physics

Universality in driven open quantum matter

Lukas M. Sieberer, Michael Buchhold, Jamir Marino, Sebastian Diehl

Published Jun 12, 2025• 75 citations
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Abstract

Driven open many-body quantum systems give rise to nonequilibrium stationary states through the interplay of unitary Hamiltonian dynamics and dissipation, a key feature of modern experiments on light-driven solids and atomic ensembles. This review explores the different types of universal behavior that emerge in these states and their theoretical classification within nonequilibrium quantum field theory, emphasizing the role of symmetry, topology, and quantum state purity.

DOI
10.1103/revmodphys.97.025004

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Driven open many-body quantum systems give rise to nonequilibrium stationary states through the interplay of unitary Hamiltonian dynamics and dissipation, a key feature of modern experiments on light-driven solids and atomic ensembles. This review explores the different types of universal behavior that emerge in these states and their theoretical classification within nonequilibrium quantum field theory, emphasizing the role of symmetry, topology, and quantum state purity.
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Driven-dissipative quantum many-body systems, i.e., many-particle systems where quantum coherent dynamics and dissipative effects occur on the same footing, can constitute a promising platform to initiate a systematic classification of quantum dynamical criticality. In this work, the authors show that both nonequilibrium and quantum features can be simultaneously present and persist in the low-frequency properties of a critical one-dimensional driven open Bose gas, and no effective equilibrium description is applicable for this novel type of nonequilibrium quantum criticality.
We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in that it is interaction driven, and of a classical phase transition, in that the ordered phase is continuously connected to a thermal state. We characterize the phase diagram and the critical behavior at the phase transition approached as a function of time. We find a novel fluctuation induced dynamical instability, which occurs at long wavelength as a consequence of a subtle dissipative renormalization effect on the speed of sound.
We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. The starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real-time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary nonequilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest nonequilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus, the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems---underlying particle number conservation and detailed balance, respectively---is identified as the root of this new nonequilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.
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.