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Physical Review A

Generating displaced and squeezed number states by a general driven time-dependent oscillator

Chi‐Fai Lo

Published Jan 1, 1991• 87 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.43.404

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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.
The author examines the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency. Using the evolution operator method developed by Cheng and Fung, he investigates the evolution of a coherent state of a time-dependent harmonic oscillator as well as its squeezing and coherence property. Two specific models of frequency variation are explored; namely, one whose frequency is exponentially decreasing in time and the other with a periodic frequency. His analyses indicates that the wavefunction of the time-dependent oscillator starts as a coherent state at t=O and evolves as a squeezed state at a later time. It is also shown that squeezing cannot be generated by an adiabatic change of the oscillator frequency because the variances of q and p turn out to be adiabatic invariants, whereas a sudden change can produce squeezing.
Time evolution of squeezed coherent states for a quantum parametric oscillator with the most general self-adjoint quadratic Hamiltonian is found explicitly. For this, we use the unitary displacement and squeeze operators in coordinate representation and the evolution operator obtained by the Wei-Norman Lie algebraic approach. Then, we analyze squeezing properties of the wave packets according to the complex parameter of the squeeze operator and the time-variable parameters of the Hamiltonian. As an application, we construct all exactly solvable generalized quantum oscillator models classically corresponding to a driven simple harmonic oscillator. For each model, defined according to the frequency modification in position space, we describe explicitly the squeezing and displacement properties of the wave packets. This allows us to see the exact influence of all parameters and make a basic comparison between the different models.