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Relaxation oscillations and frequency entrainment in quantum mechanics
1Centre for Quantum Technologies, National University of Singapore, Singapore.
Physical Review. E
|November 20, 2020
Summary
Frequency entrainment for quantum oscillators now extends beyond weak nonlinearities. This study reveals relaxation oscillations in quantum mechanics, a key feature of strong nonlinearity, occurring through two distinct phase-space mechanisms.
Area of Science:
- Quantum physics
- Nonlinear dynamics
- Quantum optics
Background:
- Frequency entrainment in continuous-variable oscillators was limited to weakly nonlinear systems.
- Previous models primarily described the Stuart-Landau oscillator in the weakly nonlinear regime.
Purpose of the Study:
- To extend frequency entrainment to quantum continuous-variable oscillators with arbitrary nonlinearities.
- To investigate the emergence of strong nonlinearity phenomena in quantum oscillators.
Main Methods:
- Theoretical analysis of quantum continuous-variable oscillators.
- Phase-space analysis to identify oscillation mechanisms.
Main Results:
- Frequency entrainment is achieved for quantum oscillators with arbitrary nonlinearities.
- The previously known steady state of weakly nonlinear oscillators (Stuart-Landau) is recovered as a special case.
- Relaxation oscillations, a hallmark of strong nonlinearity, are demonstrated in quantum mechanics.
Conclusions:
- This work removes the weak nonlinearity restriction for frequency entrainment in quantum oscillators.
- Two distinct mechanisms for relaxation oscillations in quantum phase space are identified based on oscillator nonlinearity.
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