Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations

Abstract

We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z_2$ symmetry breaking, $\mathcal{P}\mathcal{T}$ symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.

arXiv commentpublished version, 12 pages

References in corpus (42)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum many-body systems out of equilibrium
• Keldysh Field Theory for Driven Open Quantum Systems
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Spectral theory of Liouvillians for dissipative phase transitions
• Dissipative Phase Transition in Central Spin Systems
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Probing a dissipative phase transition via dynamical optical hysteresis
• Steady-state phases and tunneling-induced instabilities in the driven-dissipative Bose-Hubbard model
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Nonequilibrium quantum criticality in open electronic systems
• Critical dynamical properties of a first-order dissipative phase transition
• Signatures of a dissipative phase transition in photon correlation measurements
• Observation of the photon-blockade breakdown phase transition
• Dissipative Phase Transition in the Open Quantum Rabi Model
• Emergent equilibrium in many-body optical bistability
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• Symmetry breaking and error correction in open quantum systems
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Squeezed light induced symmetry breaking superradiant phase transition
• Non-Hermitian dynamics without dissipation in quantum systems
• Power-laws in the dynamic hysteresis of quantum nonlinear photonic resonators
• A quantum transducer using a parametric driven-dissipative phase transition
• Driven-dissipative quantum Kerr resonators: new exact solutions, photon blockade and quantum bistability
• PT-symmetric quantum Liouvillian dynamics
• Emergence of PT-symmetry breaking in open quantum systems
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Universal power law decay in the dynamic hysteresis of an optical cavity with non-instantaneous photon-photon interactions
• Non-equilibrium magnetic phases in spin lattices with gain and loss
• Gaussian trajectory approach to dissipative phase transitions: the case of quadratically driven photonic lattices
• Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator
• Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement
• Dissipation-driven phase transition in 2D Josephson arrays
• Few-mode geometric description of a driven-dissipative phase transition in an open quantum system
• Critical Theory for the Breakdown of Photon Blockade
• Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition
• Classical critical dynamics in quadratically driven Kerr resonators
• Diffusive-Gutzwiller approach to the quadratically driven photonic lattice

Cited by in corpus (32)

• Quantum squeezing and sensing with pseudo anti-parity-time symmetry
• Parity-symmetry-breaking quantum phase transition via parametric drive in a cavity magnonic system
• Microwave photon detection at parametric criticality
• Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators
• Dissipative phase transitions in $n$-photon driven quantum nonlinear resonators
• Many-Body Open Quantum Systems
• Variational waveguide QED simulators
• Critical Theory for the Breakdown of Photon Blockade
• Diverging current fluctuations in critical Kerr resonators
• Anti-parity-time symmetry hidden in a damping linear resonator
• Dissipative phase transitions in optomechanical systems
• Parametrically driving a quantum oscillator into exceptionality
• Nonreciprocal quantum phase transition in cavity magnonics
• Super-operator structures and no-go theorems for dissipative quantum phase transitions
• Dissipative phase transition in systems with two-photon drive and nonlinear dissipation near the critical point
• High-performance Kerr quantum battery
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators
• Dissipative quantum phase transitions monitored by current fluctuations
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator
• Path Integral Approach to Input-Output Theory
• Nonreciprocal superradiant quantum phase transition induced by the magnon Kerr effect
• Driven-Dissipative Bose-Einstein Condensation and the Upper Critical Dimension
• Finite-time and Finite-size scalings of coercivity in dynamic hysteresis
• Fokker-Planck treatment of nonlinearities in the dispersive coupling of an ion and an optical cavity
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Numerical simulation methods for quantum sensing at parametric criticality
• Time correlations from steady-state expectation values
• Superquantization rule for multistability in driven-dissipative quantum systems
• Experimental observation of multimode quantum phase transitions in a superconducting Bose-Hubbard simulator