||November 15 (Wed), 2017
||National University of Singapore
||Quantum nonlinear dynamics: Noise-induced amplification and relaxation oscillations
||We propose a noisy quantum analogue of the well known Stuart-Landau equation for a weakly nonlinear oscillator using a single bosonic mode interacting with a gain medium and a nonlinear absorber, each taken to be a collection of two-level atoms. We show that broadband quantum noise amplifies the bosonic mode. We call this effect quantum noise-induced amplification, a process not captured in previous models of quantum nonlinear oscillators. Our model contains two interesting limits: 1) When the nonlinear absorber is operated in the low-temperature regime. This recovers the phenomenological weakly nonlinear van der Pol model often considered in quantum synchronisation. 2) When the nonlinear absorber is operated in the high-temperature limit. This turns the nonlinear oscillator into a quasilinear amplifier with multiplicative noise. Such models of amplifiers have not been considered in amplifier theory. We also go beyond the weakly nonlinear regime by using an appropriate Hamiltonian from classical dissipative systems and show how quantum analogues of relaxation oscillators which van der Pol proposed in his famous 1926 paper can arise.