Laboratoire de Physique Théorique
Toulouse - UMR 5152

Quantum chaos is the study of a quantum system whose classical counterpart is chaotic. One of the central questions of quantum chaos is the relation between the quantum and the classical regimes. In this work, periodically driven systems are used to study the transport and decoherence processes in quantum systems that display classically chaotic dynamics. The periodically kicked rotor (KR), the motion of a particle on a ring experiencing kicks at a periodic time intervals, is a paradigmatic model of Hamiltonian chaos. Its classical dynamics can be reduced to a difference equation while its quantum dynamics can be written as a Floquet operator. This system is experimentally realizable in cold atomic cloud interacting with a flashing optical lattice. Two different variants of kicked rotor system will be presented to demonstrate the following ;

(i) Kicked rotor in a finite well potential is special because it violates the assumptions of Kolmogorov-Arnold-Moser (KAM) theorem and hence abrupt transitions from integrability to chaos becomes possible. The quantum manifestations of non-KAM chaotic system in its spectra and transport and localization properties are demonstrated.

(ii) In another variant, we introduce decoherence in the quantum kicked rotor by suppressing kicks during certain time intervals drawn from Levy distribution. It is theoretically shown that this scenario leads to non-exponential coherence decay, thus effectively slowing down the decoherence to classical domain. This has been experimentally realized and displays an excellent agreement with theoretical results.