Quantum signatures of chaos in a kicked top

Abstract

Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrödinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum-classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos-the quantum kicked top- and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos.

Observing chaos for quantum-dot microlasers with external feedback

“…The second source is the low number of QDs (~10) being effectively involved in the lasing operation 10 . The robustness of the chaotic lasing phenomenon, with respect to quantum noise where a description by rate equations 30 is inconsistent, is of great interest from the point of view of nonlinear dynamics 31,32 . Our results give first insight into the chaotic behaviour of microlasers with self-feedback and have high potential to stimulate further experimental and theoretical studies.…”

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

“…For example, the time evolution of coherent states of light in a Kerr medium is visualized by measuring Q ψ by cavity state tomography, observing quantum collapses and revivals, and confirming the nonclassical properties of the transient states [18]. Moreover, the zeros of this phase-space quasiprobability distribution have been used as an indicator of the regular or chaotic behavior in quantum maps for a variety of quantum problems: molecular [19] and atomic [20] systems, the kicked top [21], quantum billiards [22], or condensed matter systems [23] (see also [24,25] and references therein). They have also been considered as an indicator of metal insulator [26] and topological-band insulator [27] phase transitions, as well as of QPTs in Bose-Einstein condensates [10] and in the Dicke [28,29], vibron [17], and Lipkin-Meshkov-Glick (LMG) models [30].…”

Entanglement and its relationship to classical dynamics

“…It has been extensively studied both theoretically and experimentally for over two decades [1][2][3][4][5][6][7][8][9] and continues to be investigated today [10,11].…”