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Acta Physica Sinica

SQUEEZED STATES AND SQUEEZED-COHERENTSTATES OF THE GENERALIZED QUADRATICTIME-DEPENDENT HARMONICOSCILLATOR

U Yl

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

The problem of time evolution and squeezed states of the generalized quadratic time-dependent harmonic oscillator is studied by making use of the time-evolution operator approach. Then, the squeezed states and high-n squeezed states of the driven harmonic oscillator with strongly pulsating mass are constructed. Finally, we show how the squeezed-coherent states and high-n squeezed-coherent states, which preserve the minimum uncertainty codition, can be generated.

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The problem of time evolution and squeezed states of the generalized quadratic time-dependent harmonic oscillator is studied by making use of the time-evolution operator approach. Then, the squeezed states and high-n squeezed states of the driven harmonic oscillator with strongly pulsating mass are constructed. Finally, we show how the squeezed-coherent states and high-n squeezed-coherent states, which preserve the minimum uncertainty codition, can be generated.
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.
The authors study the evolution of SU(1,1) coherent states, which may represent squeezed vacuum states, in harmonic oscillators with time-dependent masses. Such oscillators may model a quantised electromagnetic field in a cavity where the field changes with time under the action of some reservoir. They consider three types of variable mass: a decaying mass, a pulsating mass, and a mass with damping and pulsation. They have found that in the most interesting cases involving pulsation, a high degree of squeezing (enhanced squeezing) may be obtained in the vicinity of the resonance where the pulsation frequency is twice the natural oscillator frequency.
In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.
Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known concepts, I propose a method for obtaining generalized minimum-uncertainty squeezed states, give examples, and relate it to known concepts. I comment on the remaining concept, that of general displacement-operator squeezed states.