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Physical Review A

Comment on ‘‘Squeezing and frequency jump of a harmonic oscillator’’

József Janszky, Yu. Ya. Yushin

Published May 1, 1989• 24 citations
Publisher

Abstract

The relevance of the conclusions of a paper by Fan and Zaidi [Phys. Rev. A 37, 2985 (1988)] concerning the possibility of generating squeezed states of a harmonic oscillator by sudden change of its frequency is analyzed.
DOI
10.1103/physreva.39.5445

Related papers

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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Reply to ‘‘Comment on ‘Squeezing and frequency jump of a harmonic oscillator’ ’’

Haider R. Zaidi, Fan Hong-Yi

We disagree with the conclusions of the preceding Comment [Janszky and Yushin, Phys. Rev. A 39, 5437 (1989)]. It is shown in this Reply that a squeeze operator can also serve as the time evolution operator for a Franck-Condon transition, and that our previous interpretation is correct. It is also pointed out that the model Hamiltonian used in the preceding Comment is not appropriate for a Franck-Condon transition.

Physical Review A•May 1, 1989•10 citations

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Squeezing and Frequency Changes in Harmonic Oscillations

R. Graham

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.

Journal of Modern Optics•Jun 1, 1987•81 citations
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.
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.
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.