Squeezed and Nonclassical States Due to Frequency Changes in Harmonic Oscillators

Zheng Li

I. A. Pedrosa

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.

J. Aliaga, G. Crespo, Araceli N. Proto

Coherent and squeezed states for the time-dependent-frequency harmonic oscillator are analyzed using maximum entropy principle techniques. The information-theoretic procedure leads to results equivalent to that of the Wigner-function formalism, although the former gives a physical interpretation of the involved parameters and allows for a nonzero-temperature density matrix.

Kazutaka G. Nakamura

Sumiyoshi Abe, Rudolf Ehrhardt

Harmonic oscillators with time-dependent frequencies describe physics of the Paul trap of ions, radiation fields in media of time-varying dielectric constants, and so on. Their ground states are generically squeezed states. Here the effects of small anharmonicity on such nonclassical states are discussed. A perturbative calculation is performed, in which the unperturbed states are prepared in terms of the Hermitian invariant of the time-dependent harmonic oscillator. A quartic potential perturbation is investigated in detail. It is found that the correction term as well as the unperturbed term in the ground-state persistence probability can be expressed by the moments of a number operator alone. The oscillatory behavior is found in that correction term, which shows a competition of excitation and deexcitation due to the time dependence of the frequency and the nonlinear interaction. This may be observed experimentally as the temporal fluctuation of the quasienergy levels. Some formulas are also presented for the variances and correlations of the quadratures in the perturbed states.