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Acta Physica Sinica

Decoherence by a classically small influence

Wen-Lei Zhao, Jianzhong Wang, Dou Fu-Quan

Published Jan 1, 2012• 3 citations
Publisher

Abstract

Via a system of two kicked particles that are coupled in an infinite square well, we numerically show that the interaction with a particle of very small mass is able to lead to a quantum-to-classical transition on condition that the corresponding classical dynamics is almost unaffected. With the decrease of the mass of one of the particles, its effect on the classical dynamics of the other one decreases. Such an effect is even negligible if the mass of the particle is small enough. The classically chaotic dynamics of this small particle is effective for promoting the decoherence of the heavy particle. Therefore its quantum behavior exhibits the transition from the dynamical localization to the classically chaotic diffusion with the decrease of the effective Planck's constant ħ. Under the perturbation from the small particle, the linear entropy is rapidly saturated as time passes by. With the decrease of ħ, the time-averaged linear entropy exponentially increases from zero to almost unity.

DOI
10.7498/aps.61.240302

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We investigate the quantum to classical transition induced by two-particle interaction via a system of periodically kicked particles. The classical dynamics of particle 1 is almost unaffected in condition that its mass is much larger than that of particle 2. Interestingly, such classically weak influence leads to the quantum to classical transition of the dynamical behavior of particle 1. Namely, the quantum diffusion of this particle undergoes the transition from dynamical localization to the classically chaotic diffusion with the decrease of the effective Planck constant ℏ eff. The behind physics is due to the growth of entanglement in the system. The classically very weak interaction leads to the exponential decay of purity in condition that the classical dynamics of external degrees freedom is strongly chaotic.
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.
We investigate numerically the tunneling effect under influence of another particle in a double well system. Such influence from only one degree of freedom makes decoherence and quantum-classical transition, i.e., suppression of the tunneling effect. The decoherence happens even for cases that the influence is from a particle of very small mass, and it has virtually no effect in the corresponding classical dynamics. There are cases similar to dynamical localization that the suppressed tunneling rate is several times smaller than the classical counterpart. This result is relevant for understanding quantitatively the dynamical process of decoherence and quantum to classical transition.
We discuss the emergence of the classical description from quantum mechanics for chaotic systems. We consider a specific model, which corresponds to an ion trapped in a harmonic potential and submitted to a sequence of laser pulses: the kicked harmonic oscillator, under conditions that lead to chaotic behavior for the classical system. We show that noise plays an essential role in the transition from quantum to classical behavior. This transition is described in terms of the separation between the classical phase space distribution and the Wigner function corresponding to the quantum system, obtained by integrating over the whole phase space the magnitude of the difference between the two distributions. It is shown that, in the semiclassical limit, this separation is governed by a single parameter, which depends on the diffusion coefficient, the Lamb-Dicke parameter, and the kick strength. The Lamb-Dicke parameter plays the role of a dimensioneless Planck constant. As this parameter goes to zero, we show that both distributions remain close together for all times.
We study how decoherence rules the quantum-classical transition of the kicked harmonic oscillator. The system presents classical dynamics that ranges from regular to strong chaotic behavior depending on the amplitude of the kicks. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and quantum phase space distributions is proportional to a single parameter chi identical to K Planck's (eff)(2)/4D(3/2) , which relates the effective Planck constant, Planck's (eff), to the kicking strength, K, and the diffusion constant, D. This relation between classical and quantum distributions is valid when chi<1 , a case that is always attainable in the semiclassical regime, independent of the value of the strength of noise given by D. Our results extend a recent study performed in the chaotic regime.
We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model. For a wide range of parameters, the distance between the corresponding phase-space distributions depends on a single parameter $\ensuremath{\chi}$ that relates an effective Planck constant ${\ensuremath{\hbar}}_{\mathrm{eff}}$, the Lyapunov coefficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on ${\ensuremath{\hbar}}_{\mathrm{eff}}$, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for $\ensuremath{\chi}\ensuremath{\lesssim}1$, the separation remains small, going down with ${\ensuremath{\hbar}}_{\mathrm{eff}}^{2}$, so the concept of separation time loses its meaning.