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American Journal of Physics

Sudden expansion or squeezing of a harmonic oscillator

Claude Aslangul

Published Nov 1, 1995• 5 citations
Publisher

Abstract

I consider the dynamics of a harmonic oscillator when its (circular) frequency ω is suddenly changed by a given factor λ. This exactly solvable time-dependent system can be analyzed by using the basic tools of quantum mechanics and provides a simple illustration of their mutual relations and usefulness.
DOI
10.1119/1.18049

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It is shown that squeezing will inevitably be generated in a harmonic oscillator with time-dependent frequency for any nonvanishing rate of frequency change, sudden or smooth. The general form of the time-dependent transition probabilities among the eigenstates of the initial Hamiltonian is obtained with an exact operator approach. Results for the case of a sudden frequency jump are explicitly given as an illustration. It is also pointed out that to generate squeezing in a harmonic oscillator, the Hamiltonian does not have to be a unitary squeeze transformation of the free Hamiltonian.