Decoherence, relaxation, and chaos in a kicked-spin ensemble

Abstract

We study the dynamics of a quantum spin ensemble controlled by trains of ultrashort pulses. To model disturbances of the kicks, we consider that the spins are submitted to different kick trains which follow regular, random, stochastic or chaotic dynamical processes. These are described by dynamical systems on a torus. We study the quantum decoherence and the population relaxation of the spin ensemble induced by these classical dynamical processes disturbing the kick trains. For chaotic kick trains we show that the decoherence and the relaxation processes exhibit a signature of chaos directly related to the Lyapunov exponents of the dynamical system. This signature is a horizon of coherence, i.e. a preliminary duration without decoherence followed by a rapid decoherence process.

Analyses of the transmission of the disorder from a disturbed environment to a spin chain

“…In the present paper, we want to consider irregular trains of kicks (the strengths and the delays of the different kicks are modified with respect to the time) which can potentially induce richer dynamical behaviors of the spin chain. Indeed in a previous paper [17], we have observed several interesting behaviors. In this previous study we have considered only irregular kicked spin ensembles without any coupling between the spins.…”

“…We see in [17] that the disorder induces into the classical kick bath by the disturbance is transmitted to the spin chain by the kicks. In this paper we will see that this effect is also present when the spins into the chain are coupled.…”

“…The first part of the evolution will only depend on the initial dispersion d 0 and the kick bath chosen (see [17]). …”

“…7) with respect to an increase of the initial dispersion. We take a large number of spins in the ensemble because we know that from this number all spin ensembles have the same behaviors (see [17]). The graphics show that, when there is a coupling, largest is the dispersion with a large coupling, more the population and the coherence of one spin and of an average spin of the chain go to the maximal lost of information : the microcanonic distribution.…”

“…Largest is the initial dispersion, more the coherence falls to 0, what is not the case for the spin ensemble. The coherence goes to a value ρ min ≥ 0 (for more information, see [17]). Fig.…”