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Physical Review A

Squeezing and antisqueezing for a harmonic oscillator having a sudden change of mass

B. Baseia, A. L. De Brito, Vanderlei Salvador Bagnato

Published Apr 1, 1992• 19 citations
Publisher

Abstract

Following a recent paper by De Brito and Baseia [Phys. Rev. A 40, 4097 (1989)], the generation of squeezing is examined for a harmonic oscillator when a sudden change of mass takes place. The correspondence of such oscillators with the radiation field and some related results, such as modulation of squeezing, are also considered.
DOI
10.1103/physreva.45.5308

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Comment on ‘‘Squeezing and antisqueezing for a harmonic oscillator having a sudden change of mass’’

Петер Адам, József Janszky

It is shown that, contrary to the conclusions of a paper by Baseia, De Brito, and Bagnato [Phys. Rev. A 45, 5308 (1992)], a harmonic oscillator can be squeezed by consecutive sudden changes of its mass to and back.

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A Hilbert space of an harmonic oscillator is spanned into an over complete set of coherent states of another oscillator having different mass to show that a sudden change of mass of a quantum oscillator [e.g., due to mass emission in radiative processes] leads to squeezing. The correspondence of such oscillators with the radiation field is also considered. 12 refs.

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American Journal of Physics•Nov 1, 1995•5 citations
The Hilbert space of a harmonic oscillator with frequency ω can be spanned by the overcomplete set of coherent states of a second oscillator with frequency ω'. These states are squeezed states of the first oscillator. We examine the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency and explore the two limiting cases of an adiabatic and a sudden change. Only the latter results in squeezing, while in the former symmetrical uncertainities in coordinate and momentum turn out to be adiabatic invariants.
The theoretical basis of a mechanism for squeezing through a frequency jump of a harmonic oscillator is examined. It is found that a related squeezing transformation exists, but its interpretation in terms of a frequency change is not possible. A reinterpretation of the results in terms of a scaling transformation in coordinate or momentum variables is given. Moreover, a sudden jump is not essential, and squeezing can evolve continuously. The equations of motion for such a process are obtained and the interaction responsible for squeezing is obtained.