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Chinese Science Bulletin

Damped harmonic oscillator and squeezed state

王晓光

Published Feb 28, 1995• 0 citations
Publisher

Abstract

Study of the two-photon coherent state or squeezed state has made great progress both in theory and in experiment for the generalization of usual coherent state of the electromagnetic field. The squeezed state can be produced by some nonlinear process and the Hamiltonian which governs the dynamics of squeezed state usually has a quatratic form. The time-dependent Bateman Hamiltonian of damped harmonic oscillator just has this

DOI
10.1360/sb1995-40-4-291

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Study of the two-photon coherent state or squeezed state has made great progress both in theory and in experiment for the generalization of usual coherent state of the electromagnetic field. The squeezed state can be produced by some nonlinear process and the Hamiltonian which governs the dynamics of squeezed state usually has a quatratic form. The time-dependent Bateman Hamiltonian of damped harmonic oscillator just has this
The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.
We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd