Decoherence in chaotic and integrable systems: A random matrix approach

– In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find at intermediate times a weak effect of spectral correlations that is reminiscent of the correlation hole. New experimental techniques in atomic and quantum optics and more recently in solid state physics have made measurements of decoherence of entangled states possible. The perspective of quantum computing makes this subject also relevant to applications. In this context the question arises how the integrability or chaoticity of the corresponding classical systems i.e. “quantum chaos” affects the process of decoherence [1–3]. Such properties manifest themselves both in the spectrum and the wave functions. While the former is invariant the latter are basis dependent. Yet that does not mean that the latter are irrelevant in a semi-classical context; indeed any wave packet localized in phase space will feel special features of the dynamics such as KAM tori or short periodic orbits much more strongly, than their influence on the spectrum. Such effects will be more pronounced in integrable or near integrable systems, than in chaotic ones, because KAM tori are felt everywhere. If we think of the possible configuration of systems this can refer both to the initial wave packet and to the Hamiltonian. For the former we can e.g. think of successive laser excitations in Rydberg systems, and for the latter of appropriate external fields in atoms or of designed mesoscopic systems. It is therefore relevant to ask which properties are due to the nature of the system, and which are due to the preparation of the packet. Studying decoherence we can never do entirely without a packet, but to reduce the influence of preparation to a minimum, random matrix theory (RMT) is ideally suited, and we will develop such models for a wide range of situations. To construct our RMT model we start from the standard assumption, that the classical ensembles [4] (such as the Gaussian orthogonal ensemble (GOE) for time reversal invariant systems) describe the universal features induced by classical chaos in quantum systems [5]. For the classically integrable situation we expect a random spectrum if we exclude harmonic oscillators [6]. For the description of a random wave packet the orthogonal invariance of