Quantum Coherent Control of Atoms in a Classically Chaotic Regime

The classical delta-kicked rotor (DKR) exhibits chaotic behaviour in certain parameter regimes, characterized by a linear increase of the energy of the system as a function of time. Applying the DKR to a quantum system however, will eventually result in states that are localized in momentum space. Therefore, the delta kicks can only increase the energy of the system up to a finite limit given by the momentum localization length[1,2]. This localization has been observed in a system of cooled atoms in a pulsed optical lattice, which is mathematically equivalent to the DKR[3]. Recent extensions of the quantum DKR by P. Brumer, J.Gong and H. Woerner predict coherent control of the relaxation of the system into the localized eigenstates through manipulation of the coherence properties of the initial state and spatial phase of the pulsed potential[4][5]. This can result in either a further suppression of diffusion or superheating in which the system absorbs energy faster than classically allowed. In this presentation we present our experimental results of these predictions. [1]Ott ``Chaos in Dynamical Systems'' (Cambridge 1993) [2]Fishman et. al PRL 49 p509 (1982) [3]Moore et. al. PRL 75 p4598 (1995) [4]Gong et. al. PRL 86 p1741 (2001) [5]Gong et. al. PRE 68 026209 (2003)