Echoes of a squeezed oscillator

Abstract

Parametric coupling is commonly used to prepare oscillators in a time-varying squeezed state in which the variance of the coordinate or momentum may dip below that of the equilibrium thermal or quantum ground state during a fraction of the period. We show here that pulses applied to drive parametrically an inhomogeneously broadened set of harmonic oscillators result in a spontaneous recovery of coherence, manifesting itself as an echo, similar to those exhibited by an ensemble of spins aligned by a magnetic field, when excited by properly designed electromagnetic pulses. Such echoes, of classical or quantum nature, are expected to arise in the squeezing of linear systems of various sorts and, in particular, light and vibrational modes. Unlike existing methods for the generation of spin echoes, squeezed echoes do not require the use of resonant excitation.