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Chinese Physics Letters

Unraveling a Driven Damped Harmonic Oscillator through Entangled State Representation

Seyed Mahmoud Ashrafi, M. R. Bazrafkan

Published Nov 1, 2013• 2 citations
Publisher

Abstract

Employing the thermo-entangled state representation, the common eigenstates of relative position and the total momentum of a two-mode system, we solve the master equation of a damped harmonic oscillator driven by a time-dependent uniform force field.
DOI
10.1088/0256-307x/30/11/110304

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Time evolution of a harmonic oscillator linearly coupled to a heat bath is compared for three classes of initial states for the bath modes-grand canonical ensemble, number states, and coherent states. It is shown that for a wide class of number states the behavior of the oscillator is similar to the case of the equilibrium bath. If the bath modes are initially in coherent states, then the variances of the oscillator coordinate and momentum, as well as its entanglement to the bath, asymptotically approach the same values as for the oscillator at zero temperature and the average coordinate and momentum show a Brownian-like behavior. We derive an exact master equation for the characteristic function of the oscillator valid for arbitrary factorized initial conditions. In the case of the equilibrium bath this equation reduces to an equation of the Hu-Paz-Zhang type, while for the coherent states bath it leads to an exact stochastic master equation with a multiplicative noise.