Lie Algebraic Quantum Phase Reduction
arXiv:2208.12006 · doi:10.1103/PhysRevLett.132.093602
Abstract
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schrödinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves. The observable clusters capture the phase dynamics of individual quantum oscillators, unlike indirect indicators obtained from density operators. Furthermore, our method can be applied to finite-level systems that lack classical counterparts.
arXiv comment15 pages, 3 figures
References in corpus (45)
- A Straightforward Introduction to Continuous Quantum Measurement
- Observing single quantum trajectories of a superconducting qubit
- Real-time optimal quantum control of mechanical motion at room temperature
- Quantum synchronization of quantum van der Pol oscillators with trapped ions
- Irreversible Performance of a Quantum Harmonic Heat Engine
- Quantum synchronization of a driven self-sustained oscillator
- Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
- Observation of a continuous time crystal
- Feedback cooling of a single trapped ion
- Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
- Entanglement tongue and quantum synchronization of disordered oscillators
- Quantum synchronization of two Van der Pol oscillators
- Quantum synchronization and entanglement generation
- Mutual information as an order parameter for quantum synchronization
- Quantum correlations and mutual synchronization
- Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine
- Synchronizing the Smallest Possible System
- Stochastic phase reduction for a general class of noisy limit cycle oscillators
- Phase reduction of stochastic limit cycle oscillators
- Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
- Observing quantum state diffusion by heterodyne detection of fluorescence
- Noise-Induced Transitions in Optomechanical Synchronization
- Observation of quantum phase synchronization in spin-1 atoms
- Synchronization of Interacting Quantum Dipoles
- Observing and Verifying the Quantum Trajectory of a Mechanical Resonator
- Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime
- Quantum Synchronization on the IBM Q System
- Critical Response of a Quantum van der Pol Oscillator
- Collective Atomic Recoil Laser as a synchronization transition
- From a continuous to a discrete time crystal in a dissipative atom-cavity system
- Universal simulation of Markovian open quantum systems
- A quantum heat engine with coupled superconducting resonators
- Quantum limit-cycles and the Rayleigh and van der Pol oscillators
- Quantum Synchronisation in Nanoscale Heat Engines
- Heat and work along individual trajectories of a quantum bit
- Phase Synchronization between Two Superradiant Lasers
- Semiclassical Phase Reduction Theory for Quantum Synchronization
- Synchronization in two-level quantum systems
- Observing Quantum Synchronization of a Single Trapped-Ion Qubit
- Role of Coherence and Degeneracies in Quantum Synchronisation
- Implementation of quantum synchronization over a 20-km fiber distance based on frequency-correlated photon pairs and HOM interference
- Enhancement of quantum synchronization via continuous measurement and feedback control
- Secure and efficient synchronization scheme for quantum key distribution
- Perfect quantum-state synchronization
- Quantum-phase synchronization