Keldysh Field Theory for Driven Open Quantum Systems

Abstract

Recent experimental developments in diverse areas - ranging from cold atomic gases over 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 condensed matter. This concerns both their non-thermal flux equilibrium states, as well as 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.

73 pages, 13 figures

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• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Colloquium: Graphene spectroscopy
• Atomic three-body loss as a dynamical three-body interaction
• An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate
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• Many-body phenomena in QED-cavity arrays
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• Dissipative preparation of Chern insulators
• Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies
• Bose-glass phases of ultracold atoms due to cavity backaction
• Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Induced self-stabilization in fractional quantum Hall states of light
• Functional renormalisation group approach to far-from-equilibrium quantum field dynamics
• A pumped atom laser
• Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
• Non-perturbative fixed point in a non-equilibrium phase transition
• Mean field theory and fluctuation spectrum of a pumped, decaying Bose-Fermi system across the quantum condensation transition
• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions
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• Facilitated spin models of dissipative quantum glasses
• Ultracold atoms and the Functional Renormalization Group
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• Numerical study of the Kardar-Parisi-Zhang equation
• Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities
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• Universal post-quench prethermalization at a quantum critical point
• Quantum kinetics of ultracold fermions coupled to an optical resonator
• Temporal coherence of one-dimensional non-equilibrium quantum fluids
• Photon transport in a dissipative chain of nonlinear cavities
• A quantum Langevin model for non-equilibrium condensation
• Heating dynamics of bosonic atoms in a noisy optical lattice
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Out-of-equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics
• Dynamical and Steady State Properties of a Bose-Hubbard Chain with Bond-Dissipation: A Study based on Matrix Product Operators
• Transient fluctuation relations for time-dependent particle transport
• Quench dynamics of one-dimensional interacting bosons in a disordered potential: Elastic dephasing and critical speeding-up of thermalization
• Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators
• Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
• Open quantum reaction-diffusion dynamics: absorbing states and relaxation
• Dissipative quantum dynamics of fermions in optical lattices: a slave-spin approach
• Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance
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• A solvable family of driven-dissipative many-body systems
• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Electrodynamic duality and vortex unbinding in driven-dissipative condensates
• Orthogonality catastrophe in dissipative quantum many body systems
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations
• Linked cluster expansions for open quantum systems on a lattice
• Distinctive class of dissipation-induced phase transitions and their universal characteristics
• Exact solutions of interacting dissipative systems via weak symmetries
• Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Entanglement structure of current-driven diffusive fermion systems
• Dicke phase transition without total spin conservation
• Exact description of quantum stochastic models as quantum resistors
• Nonlinear Langevin dynamics via holography
• Field Theory of Many-Body Lindbladian Dynamics
• Generic transport formula for a system driven by Markovian reservoirs
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• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
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• Kibble-Zurek mechanism in driven-dissipative systems crossing a non-equilibrium phase transition
• Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator
• Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems
• Quantum metamaterial for nondestructive microwave photon counting
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• Long-range photon fluctuations enhance photon-mediated electron pairing and superconductivity
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• Superfluid signatures in a dissipative quantum point contact
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• Wide-Mass-Scanning-Range Setup and Phase-Resolved Protocol for Axion Dark Matter Detection
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Control of Overfitting with Physics
• Steady-states and response functions of the periodically driven O(N) scalar field theory
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Phases of translation-invariant systems out of equilibrium: Iterative Green's function techniques and renormalization group approaches
• Path Integral Approach to Input-Output Theory
• Diffusion and Thermalization in a Boundary-Driven Dephasing Model
• Work Statistics and Adiabatic Assumption in Nonequilibrium Many-Body Theory
• Optimized Sampling of Mixed-State Observables
• Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy
• Non-Hermitian Dirac theory from Lindbladian dynamics
• The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation
• Quantum speed limit and nonclassicality in open quantum system models using the Wigner function
• Stability of Fractional Quantum Hall States in Disordered Photonic Systems
• Coulomb drag by motion of a monolayer polar crystal through graphene nanoconstriction
• Singularities in nearly-uniform 1D condensates due to quantum diffusion
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Shape effects of localized losses in quantum wires: dissipative resonances and nonequilibrium universality
• Keldysh field theory approach to direct electric and thermoelectric currents in quantum dots coupled to superconducting leads
• Unifying quantum stochastic methods using Wick's theorem on the Keldysh contour
• Statistical physics of flux-carrying Brownian particles
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Non-equilibrium charge-vortex duality
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism
• Quantum Point Contact with Local Two-body Loss
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Resolving mean-field solutions of dissipative phase transitions using permutational symmetry
• Decoding the drive-bath interplay: A guideline to enhance superconductivity
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Exploring excited eigenstates of many-body systems using the functional renormalization group
• Polaritonic linear dynamic in Keldysh formalism
• Steady-State Quantum Zeno Effect of Driven-Dissipative Bosons with Dynamical Mean-Field Theory
• Noise-induced transition from superfluid to vortex state in two-dimensional nonequilibrium polariton condensates -- semi-analytical treatment
• Quench Dynamics of Anyon Tonks-Girardeau Gases
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Quantum regression theorem in the Unruh-DeWitt battery
• Generalized stochastic spin-wave theory for open quantum spin systems
• Tuning Density and Spin Ordering of Degenerate Fermi Gases in an Optical Cavity
• Condensation in hybrid superconducting cavity-microscopic spins systems with finite-bandwidth drive
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system
• Archimedean Screw in Driven Chiral Magnets
• Coherent pair injection as a route towards the enhancement of supersolid order in many-body bosonic models
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Nanomechanically-induced nonequilibrium quantum phase transition to a self-organized density wave of a Bose-Einstein condensate
• Lattice Lindblad simulation
• Non-Markovian dynamics in nonstationary Gaussian baths: a hierarchy of pure states approach
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Lindblad master equations for quantum systems coupled to dissipative bosonic modes
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains
• Emergent structures in open EFTs
• Topological signatures in a weakly dissipative Kitaev chain of finite length
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Experimental observation of multimode quantum phase transitions in a superconducting Bose-Hubbard simulator
• Physical constraints on effective non-Hermitian systems
• Time correlations from steady-state expectation values
• Switching of the information backflow between a helical spin system and non-Markovian bath
• Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits
• Path-Integral Approach to Quantum Acoustics
• Interaction effects on electronic Floquet spectra: Excitonic effects
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach
• Transition between vacuum and finite-density states in the infinite-dimensional Bose-Hubbard model with spatially inhomogeneous dissipation
• Non-thermal pairing glue of electrons in the steady state
• Markovian Embeddings of Non-Markovian Open System Dynamics