Exact steady state of quantum van der Pol oscillator: critical phenomena and enhanced metrology
arXiv:2412.03354 · doi:10.1103/zybb-vxfz
Abstract
Quantum criticality of open many-body systems has attracted lots of interest for emergent phenomena and universality. Here we present the exact steady state of the quantum van der Pol oscillator using the complex -representation. We show the threshold corresponds to a dissipative phase transition with abrupt changes of steady-state properties and enhanced metrology. The critical behaviors and finite-size effects are investigated through the analytical steady state. Moreover, we obtain divergent quantum Fisher information (QFI) in the thermodynamic limit both at the critical point and in the time crystal phase, but only the QFI at the critical point approaches the Heisenberg limit. We further prove that the steady-state photon number is the optimized estimated observable with the largest signal-to-noise ratio. We show that the Heisenberg-limited metrology originates from the larger enhancement of the susceptibility than the standard deviation of the photon number. Our work reveals the underlying relation between the time crystal, dissipative phase transition, and enhanced metrology.
17 pages, 5 figures
References in corpus (39)
- Dissipative Phase Transition in Central Spin Systems
- Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
- Quantum criticality as a resource for quantum estimation
- Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
- Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
- Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion
- Enhanced metrology at the critical point of a many-body Rydberg atomic system
- Critical dynamical properties of a first-order dissipative phase transition
- Universal non-equilibrium properties of dissipative Rydberg gases
- Signatures of a dissipative phase transition in photon correlation measurements
- Dissipative Phase Transition in the Open Quantum Rabi Model
- Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
- Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
- Critical parametric quantum sensing
- A non-equilibrium superradiant phase transition in free space
- Quantum entanglement in the spatial symmetry breaking phase transition of a driven-dissipative Bose-Hubbard dimer
- Quantum limit-cycles and the Rayleigh and van der Pol oscillators
- Observation of a superradiant phase transition with emergent cat states
- Nonreciprocal Superradiant Phase Transitions and Multicriticality in a Cavity QED System
- Biasing the quantum vacuum to control macroscopic probability distributions
- Floquet time-crystals as sensors of AC fields
- Topological synchronization of quantum van der Pol oscillators
- Microwave photon detection at parametric criticality
- Continuous Dissipative Phase Transitions without Symmetry Breaking
- General linearized theory of quantum fluctuations around arbitrary limit cycles
- Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator
- Dissipative phase transitions in -photon driven quantum nonlinear resonators
- Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model
- Liouvillian spectral collapse in the Scully-Lamb laser model
- Driven-dissipative time crystalline phases in a two-mode bosonic system with Kerr nonlinearity
- Exact solution of the infinite-range dissipative transverse-field Ising model
- Prethermal Floquet time crystals in chiral multiferroic chains and applications as quantum sensors of AC fields
- Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model
- Dissipative phase transitions in optomechanical systems
- Probing a dissipative phase transition with a trapped ion through reservoir engineering
- Time Crystal in a Single-mode Nonlinear Cavity
- Lee-Yang theory of the superradiant phase transition in the open Dicke model
- Driven-Dissipative Bose-Einstein Condensation and the Upper Critical Dimension
- Decoding the drive-bath interplay: A guideline to enhance superconductivity