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.
15 pages, 3 figures
References in corpus (11)
- A Straightforward Introduction to Continuous Quantum Measurement
- Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
- Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
- Quantum synchronization of two Van der Pol oscillators
- Mutual information as an order parameter for quantum synchronization
- Phase reduction of stochastic limit cycle oscillators
- Collective Atomic Recoil Laser as a synchronization transition
- A quantum heat engine with coupled superconducting resonators
- Quantum limit-cycles and the Rayleigh and van der Pol oscillators
- Observing Quantum Synchronization of a Single Trapped-Ion Qubit
- Secure and efficient synchronization scheme for quantum key distribution