Relaxation oscillations and frequency entrainment in quantum mechanics
arXiv:1711.07376 · doi:10.1103/PhysRevE.102.042213
Abstract
Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown to emerge as a special case. Most importantly, the hallmark of strong nonlinearity--relaxation oscillations--is shown in quantum mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations are found to occur via two distinct mechanisms in phase space.
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References in corpus (28)
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- QuTiP: An open-source Python framework for the dynamics of open quantum systems
- Introduction to Quantum Noise, Measurement and Amplification
- Quantum synchronization of quantum van der Pol oscillators with trapped ions
- Multiphoton Quantum Optics and Quantum State Engineering
- Quantum synchronization of a driven self-sustained oscillator
- Entanglement tongue and quantum synchronization of disordered oscillators
- Quantum synchronization of two Van der Pol oscillators
- Deterministic quantum nonlinear optics with single atoms and virtual photons
- Quantum synchronization and entanglement generation
- Mutual information as an order parameter for quantum synchronization
- Observation of Three-Photon Spontaneous Parametric Downconversion in a Superconducting Parametric Cavity
- Squeezing Enhances Quantum Synchronization
- Continuous Quantum Measurement and the Emergence of Classical Chaos
- Quantum limits on phase-preserving linear amplifiers
- Van der Pol and the history of relaxation oscillations: toward the emergence of a concept
- Genuine quantum signatures in synchronization of anharmonic self-oscillators
- Critical Response of a Quantum van der Pol Oscillator
- Quantum nonlinear dynamics of continuously measured systems
- Oscillation collapse in coupled quantum van der Pol oscillators
- Generalized squeezed states
- Conservative perturbation theory for nonconservative systems
- Tuning quantum measurements to control chaos
- The Quantum Theory of MIMO Markovian Feedback with Diffusive Measurements
- Complete Parameterizations of Diffusive Quantum Monitorings
- Phase-preserving linear amplifiers not simulable by the parametric amplifier
- Finding Hannay angle in dissipative oscillatory systems via conservative perturbation theory
- Phase diffusion and the small-noise approximation in linear amplifiers: Limitations and beyond
Cited by in corpus (4)
- Quantum Coherence Resonance
- Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation
- Phase-preserving linear amplifiers not simulable by the parametric amplifier
- Quantum asymptotic phase reveals signatures of quantum synchronization