Recoherence in the entanglement dynamics and classical orbits in theN-atom Jaynes-Cummings model

Abstract

The rise in linear entropy of a subsystem in the N -atom JaynesCummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation J z . Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase space projection associated to the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase space borderline produces a maximum rate of entanglement. The consequence of this fact for initial conditions centered at periodic orbits in regular regions is a clear periodic recoherence. For chaotic situations the same phenomenon (proximity of the atomic phase space borderline) is in general responsible for oscillations in the entanglement properties. PACS numbers: 05.45.Mt, 32.80.Qk 1 I INTRODUCTIONThe importance of studying in detail the decoherence process is twofold. Firstly it may be viewed as a key to the understanding of some of the striking differences between the quantum and classical description of the world such as "the non existence at the classical level of the majority of states allowed by quantum mechanics" [1]. The decoherence process is believed to be the agent which eliminates interference between two or more macroscopically separated localized states [2]. Secondly, given the impressive technological advances in several experimental areas (Quantum Optics, Condensed Matter and Atomic Physics, etc.), it is nowadays possible to realize a system of two interacting degrees of freedom and watch the time evolution of the corresponding entanglement process [3]. It is therefore also of importance to understand the entanglement process in simple Hamiltonian systems. Two degrees of freedom Hamiltonian systems often present a very rich dynamics which in many cases is not yet completely understood from a general point of view. In particular, if the interaction is nonlinear the system may present chaotic behavior in the classical limit. The consequences of this fact to the quantum dynamics is yet an unsettled issue. A step in this direction was taken a few years ago, as it was conjectured that "the rate of entropy production can be used as an intrinsically quantum test of the chaotic versus regular nature of the evolution" [4]. The idea has been tested in some models [5,6]. More specifically, in the context of the N-atom Jaynes-Cummings model, the reduced density linear entropy (or idempotency defect) has been used as a measure of the entanglement of the quantum subsystems. For a given classical energy, initial conditions for the quantum states are prepared as coherent wave packets centered at regular and chaotic regions of the classical phase space. For short times, a fast increase in decoherence for chaotic initial conditions is found when compared to regular ones. Typically the linear entropy in this model rises from zero to...

Semiclassical limit of the entanglement in closed pure systems

“…These remarkably different time scales and the extensivity of the entropy have already been mentioned in slightly different contexts in [33] and [37] respectively. Also, other time scales have been established in [35].…”

Quantum Integrable Multiatom Matter-Radiation Models With and Without the Rotating-Wave Approximation

“…which in contrast to the popular belief [11] is exactly solvable through Bethe ansatz, as we see below. To make the model more physical we should add a field term ω f b † b to the Hamiltonian (19).…”

“…Identifying the models in real systems and experimental verification of the related results presented here, especially in many-atom microlasers [25] or in trapped ions away from resonance point [11] would be an important application.…”

“…However this approximation, which is justified only near the resonance point ω f ≈ ω a , should be avoided in the general case [11], when additional counter rotating wave (CRW) terms must appear:…”

The Critical Point Entanglement and Chaos in the Dicke Model

“…To date, many aspects of the model have been studied, such as the dynamical properties of quantum entanglement and decoherence [3][4][5][6][7][8], quantum phase transitions (QPT) [2,[9][10][11] and chaotic properties [3,5,9,10,[12][13][14][15]. Furuya et al [3] did the initial work on the entanglement process in a varied version of the model and concluded that for short times, there is a faster increase in decoherence for chaotic initial conditions as compared to regular ones, which have an oscillatory increase.…”