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Physical Review Letters

Suppression of Decoherence in a Wave Packet via Nonlinear Resonance

E. A. Shapiro, Ian A. Walmsley, Misha Ivanov

Published Jan 29, 2007• 22 citations
Publisher

Abstract

We propose a simple approach for suppressing decoherence of a wave packet excited in an anharmonic oscillator. We show that when a resonant external field forces the oscillator to follow the driving force, motion around the resonant trajectory inside a stable resonant island can be made almost completely immune to the environment. As an example, we study suppression of decoherence due to coupling to thermally populated rotations in vibrational wave packets in a Na2 molecule.

DOI
10.1103/physrevlett.98.050501

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We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of harmonically-bound particles moving in an external potential, we show that the coupling between the center-of-mass and internal degrees of freedom takes the form of parametric driving of the vibrational degrees of freedom, and that nontrivial coupling depends on the second derivative of the external potential. We find a solution to this parametric driving problem in one dimension for a fixed center-of-mass trajectory. We also propose a measure of compositeness, which quantifies the extent to which such a composite system cannot be approximated as a single, indivisible particle. We perform numerical simulations for a simple interference experiment, consisting of two wave packets scattering off of a square well, and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom, which depends on the initial state of the internal mode. We also calculate the measure of compositeness for this system.
Abstract The time evolution of wave packets in the Morse potential is investigated under the influence of the environment consisting of harmonic oscillators. We obtain a Markovian master equation that incorporates the fact that due to the nonequidistant spectrum, the relaxation rate of each energy eigenstate is different. The nonunitary time evolution is visualized by the aid of the Wigner function related to the reduced density operator of the Morse system. The time scale of decoherence is much shorter than that of dissipation, and gives rise to states which are mixtures of localized states along the phase space orbit of the corresponding classical particle. This behaviour is to a large extent independent of the coupling strength, the temperature of the environment and also of the initial state.