Chaos, localization, and transport in kicked rotor and its variants

Abstract

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, 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 determined using 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 and will discuss the unusual properties that have been observed in these systems. (i) One of the variants considered is the kicked rotor in a periodic finite well potential. This system is special because it violates the assumptions of the Kolmogorov-Arnold-Moser (KAM) theorem and hence, abrupt transitions from integrability to chaos becomes possible. The quantum manifestations of the non-KAM chaotic system have been studied, and the effect of the non-KAM feature on the behavior of its spectra and also on its 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 L\'{e}vy distribution, $\omega(\tau) \sim \tau^{-1-\alpha}$. For, $\alpha<1$, it is theoretically shown that this scenario leads to non-exponential coherence decay, thus effectively slowing down the decoherence to the classical domain. While, for $\alpha > 1$, an anomalous diffusion characteristic is observed. Both of these results have been experimentally realized and displays an excellent agreement with the theoretical results.