Periodically modulated quantum nonlinear oscillators

M. I. Dykman

in Fluctuating Nonlinear Oscillators

Published in print July 2012 | ISBN: 9780199691388
Published online September 2012 | e-ISBN: 9780191742255 | DOI:
Periodically modulated quantum nonlinear oscillators

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This 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 a relaxation of the oscillator is accompanied by quantum noise. This leads to a finite-width distribution over quantum states even for T = 0. It also leads to switching between coexisting vibrational states via transitions over the barrier in phase space. The switching mechanism, quantum activation, has no analogue 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 studied in optomechanics is analyzed.

Keywords: bistability; switching; switching rate scaling; bifurcation; power spectra; fine structure; cooling; quantum activation; parametric modulation; resonant modulation

Chapter.  19687 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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