M.Sc Student | Shmuel Osovski |
---|---|

Subject | Fingerprints of Classical Chaos in Manipulation of Cold Atoms in One-dimensional Optical Lattices |

Department | Department of Chemistry |

Supervisor | Professor Emeritus Moiseyev Nimrod |

The recent
pioneering experiments of the Phillips [Nature, 412, 52 (2001) ] and Raizen [Science,
293, 274 (2001) ] groups have demonstrated the dynamical tunnelling of cold atoms
interacting with standing electromagnetic waves,creating a 1D optical lattice. Our
calculations showed, that one can achieve a control of the tunneling period
over orders of magnitude range, simply by changing the frequency difference of the
waves by about 10% only. In this narrow parameter region, the mechanism of the tunnelling
oscillations evolves from the two-state to the three-state one. It was demonstrated
that the change in the underlying mechanism leads to a dramatic enhancement of
the dynamical tunnelling. Moreover, a complete suppression of the dynamical
tunnelling can also be achieved. In both of the experiments the effective* ħ
*is large and the quantum system is far from its semi-classical limit.
Therefore, one may wonder, whether there are fingerprints of the classical
mixed phase space in the quantum dynamics.

It is shown
that despite of the large effective *ħ*, the quantum Floquet-Bloch
quasienergy states can still be classified as regular and chaotic states, by
the calculations of Shannon’s entropy . Husimi distributions of the Floquet-Bloch
states show that the regular states are exponentially localized at regular
islands located around fixed points in the mixed phase space. In both
experiments the quantum and the classical phase-space entropies^{ }are
quite similar, although the classical phase space is a^{ }mixed
regular-chaotic space. In both experiments a decay of the mean momentum
amplitude, *< P*(*t*) *> *was measured. An explanation is
provided through a study of the band structure of the Floquet-Bloch quasi-energy
spectrum. It was found that the oscillations in the mean momentum, is very
sensitive to the population of the *k *= 0 Bloch quasi-momentum state, and
appear if and only if the k=0 Bloch quasi-momentum state is populated by more
than 99%. This result is in complete harmony with the experimental observation.
The random phase distribution of the population probability amplitudes of the *k*=
0 Bloch quasi-momentum states by the initial wavepacket causes the decay of the
mean momentum amplitude. The random phase distribution of the probability
amplitudes are in a way, a fingerprint of the classical chaos in the quantum
dynamics. This kind of fingerprints of chaos in quantum-mechanics is novel and
has been first indirectly measured in the NIST and AUSTIN experiments.