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Communications in Theoretical Physics

Density Matrix for Generalized Degenerate Parametric Amplifier in New Squeezed Coherent State Representation

Fan Hong‐Yi, Wang YiHua

Published Sep 15, 1999• 0 citations
Publisher

Abstract

Based on the new type of single-mode squeezed coherent state , which differs from the conventional squeezed state in that its displacement parameter depends on its squeezing parameter, we calculate the partition functioa, free energy and density matrix for a generalized degenerate parametric amplifier.
DOI
10.1088/0253-6102/32/2/309

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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.
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