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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Time evolution of two coupled general driven time-dependent oscillators

Chi‐Fai Lo

Published Sep 1, 1995• 7 citations
Publisher
DOI
10.1007/bf02726150

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In this paper we generalize Wang's approach [J. Phys. A 20, 5041 (1987)] and investigate the algebraic structure of the Schr\"odinger equation associated with a general driven time-dependent oscillator. Using the Lie-algebraic technique we obtain an exact form of the time-evolution operator which, in turn, enables us to derive the propagator of the system readily. Since the propagator is for the most general time-dependent oscillator, results for any special case can be easily deduced from it. These results will be useful for future studies in quantum optics as well as in atomic and molecular physics.
In this paper we examine the possibility of generating displaced and squeezed number states out of number states by the general driven time-dependent oscillator. Using the evolution-operator method developed by Cheng and Fung [J. Phys. A 21, 4115 (1988)], we investigate the evolution of a number state of a general driven time-dependent oscillator as well as its squeezing property. Our analyses indicate that the wave function of the time-dependent oscillator starts as a number state at t=0 and evolves as a displaced and squeezed number state at a later time.