Periodically modulated quantum nonlinear oscillators

Abstract

This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric, with frequency close to twice the eigenfrequency. It is shown that relaxation of the oscillator is accompanied by quantum noise, which leads to a finite-width distribution over quantum states even for T=0. The quantum noise also leads to switching between coexisting vibrational states via transitions over the barrier in phase space. The switching mechanism, quantum activation, has no analog in thermal equilibrium systems. The switching rates display characteristic scaling near bifurcation points. The power and absorption/amplification spectra of modulated oscillators are studied, including their fine structure. Nonresonant modulation can lead to cooling, heating, or self-sustained vibrations of an oscillator. The relation between the previously discussed direct nonresonant excitation of the oscillator and the excitation mechanism studied in optomechanics is analyzed.

arXiv commentA chapter for the book "Fluctuating Nonlinear Oscillators. From nanomechanics to quantum superconducting circuits", ed. M. I. Dykman, to be published by Oxford University Press, 2012

Cited by in corpus (4)

• Dynamic Relaxation of a Levitated Nanoparticle from a Non-Equilibrium Steady State
• Spectral Evidence of Squeezing of a Weakly Damped Driven Nanomechanical Mode
• Amplification and spectral evidence of squeezing in the response of a strongly driven nanoresonator to a probe field
• Quantum statistics in time-modulated exciton-photon system