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Physical Review A

Squeezed states and quantum-mechanical parametric amplification

Lowell S. Brown

Published Sep 1, 1987• 15 citations
Publisher

Abstract

The relation of a previous paper on the parametric amplification of a quantum oscillator to squeezed states is described. In particular, we show that in general the amplification factor is also the ``squeezing factor'' of the final state.
DOI
10.1103/physreva.36.2463

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Advanced Quantum Technologies•Nov 29, 2025•2 citations
Parametric amplification may be obtained in a harmonic oscillator if its spring constant is replaced by a time-dependent function. It is shown that the quantum transition probabilities may be expressed in a simple closed analytic form which involves only the classical amplification factor of the oscillator. The authors also compute the time evolution of the density matrix which initially describes a thermodynamic ensemble at temperature TTT and show that this matrix can similarly be expressed in such a closed form.
Using only elementary quantum-mechanical concepts, the statistical properties of various harmonic oscillator states that are linear superpositions of its energy eigenfunctions are described. These superpositions include coherent states and squeezed (or two-photon coherent) states. The resulting Gaussian, minimum-uncertainty wave packets are shown to oscillate back and forth for both coherent and squeezed states, but with an oscillating ‘‘width’’ for the squeezed states. Also examined are the principles underlying the production of squeezed electromagnetic waves via parametric amplification or four-wave mixing, their measurement by homodyne detection, and the connection between squeezing and non-Poissonian counting statistics.
ABSTRACT Previous investigations of mechanical squeezing have primarily been concentrated on a single manipulation method. We propose an innovative scheme to address the research gap by leveraging the synergy of an optical Kerr media and mechanical parametric amplification (MPA) in an optomechanical system to efficiently generate strong mechanical squeezing. By reasonably choosing the system parameters, this scheme has the following outstanding advantages: the squeezing effect of the cavity field induced by the optical Kerr medium can be transferred to the mechanical oscillator, which has been squeezed by the mechanical parametric amplifiers. The squeezing of the mechanical oscillator is higher than that of either state alone, and through this joint effect the squeezing can be significantly increased, ultimately realizing a strong mechanical squeezing. The scheme also exhibits notable robustness against both thermal noise and decay of the mechanical oscillator. The presented scheme provides an efficient and experimentally feasible platform for achieving strong mechanical squeezing, paving the way for generating other quantum effects.