Scattering-induced dynamical entanglement and the quantum-classical correspondence

Abstract

Abstract. -The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition quantum effects also come into play: for example partial revivals, which are expected to persist in the semiclassical limit, affect the long time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos.Entanglement, i.e. the nonseparability intrinsic to composite systems, is one of the most peculiar features of the quantum world. In its most popular form, found for example in the original EPR proposal [1], the entanglement is of geometrical nature. However any usual potential interaction between two particles can generically lead to entanglement, provided several quantum states are accessible to both particles. The study of such dynamical entanglement is particularly interesting for systems which possess a classical counterpart. Indeed as is well-known [2], such systems can be investigated with semiclassical tools, allowing to interpret the quantum dynamics in terms of classical properties. Recent investigations have been focusing on the relation between the generation of entanglement and the underlying classical dynamics. Initial work in spin-boson systems [3] and in coupled kicked tops [4] suggested that chaotic dynamics generate more and faster entanglement. This claim was subsequently revised [5,6] and efforts are now being made to derive universal relations ruling the generation of entanglement irrespective of system specifics. Different approaches based on perturbation expansions [5,7,8], Random Matrix theory [9,10] and semiclassical methods [11,12] have been proposed. In particular it was shown and verified [11,13] that entanglement generated from initial Gaussian states averaged over configuration space depends on the global classical dynamical regime. However contrarily to the well established quantum-classical correspondence for spectral statistics and large scale fluctuations [14], it is still not clear to what extent an analog universal correspondence exists for dynamical entanglement production; for example c EDP Sciences

Entanglement and chaos in the kicked top

“…It was initially suggested that underlying chaotic dynamics was correlated with higher and faster entanglement. However it was later realized that integrable dynamics could lead to equivalent or even more efficient entanglement In earlier works [5,9], we have shown that the entanglement dynamics did depend on classical phase-space features, but in a specific and system-dependent way rather than in a generic manner. Our results were obtained in a modified two-particle kicked top, i.e.…”

Dynamical Entanglement in Non-Relativistic Elastic Scattering

“…In this case, rotational symmetry means that the S-matrix must have the highly-restricted form (6). From (8), we see that the phase shift difference ∆δ determines whether the dynamics can be entangling. In particular, we see that only for ∆δ = ±π/4 can the S-operator lead to maximal entanglement.…”

Entanglement in the classical limit: Quantum correlations from classical probabilities

“…Somewhat more modestly, several recent works [4][5][6][7][8][9][10] have studied in semiclassical systems the link between the generation of entanglement and the dynamics of the corresponding classical system, including in experimental realizations [11]. The numerical and analytical results obtained so far indicate that the entanglement dynamics in quantum systems having a classically chaotic counterpart sharply differs from those whose classical counterpart is regular, though this difference is dependent on the specificities of the considered systems (types and strengths of the coupling, choice of initial states, etc.).…”