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arXiv:quant-ph/0208013 · Physical Review A

Decoherence from chaotic internal dynamics in two coupled δ -function-kicked rotors

Hwa-Kyun Park, Sanguk Kim

Published Jun 26, 2003• 27 citations
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Abstract

We show that classical-quantum correspondence of center-of-mass motion in two coupled $\ensuremath{\delta}$-kicked rotors is enhanced by the entanglement of the center of-mass motion to the internal degree of freedom. The observed correspondence can be attributed to the decoherence generated from chaotic internal dynamics with a few degrees of freedom.

DOI
10.1103/physreva.67.060102

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We show that classical-quantum correspondence of center-of-mass motion in two coupled \ensuremathδ\ensuremath{\delta}\ensuremathδ-kicked rotors is enhanced by the entanglement of the center of-mass motion to the internal degree of freedom. The observed correspondence can be attributed to the decoherence generated from chaotic internal dynamics with a few degrees of freedom.
We investigate the quantum-classical transition of a kicked rotor (KR) under perturbation by a second one. The influence of such a chaotic KR makes decoherence of the first one, resulting in the emergence of classical diffusion from its quantum dynamics. Such quantum-classical transition persists by decreasing the effective Planck's constant ℏ, and at the same time, decreasing the mass of the second KR and the interaction strength proportionally. In the limit of ħ → 0, due to vanishing small mass and interaction, the second KR has almost no effect on the classical dynamics of the first one. We demonstrate this via two different coupling potentials.
The relation between the degree of entanglement and time scale of time-irreversible behavior is investigated for classically chaotic quantum coupled kicked rotors by comparing the entanglement entropy (EE) and the lifetime of correspondence with classical decay of correlation, which was recently introduced. Both increase on average drastically with a strong correlation when the strength of coupling between the kicked rotors exceeds a certain threshold. The EE shows an anomalously large fluctuation resembling a critical fluctuation around the threshold value of coupling strength where the entanglement sharply increases toward full entanglement. In this regime it can be shown that, although the correlation is hidden, EE and the lifetime of individual eigenfunctions also have a positive correlation that can be seen via another measure.
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.