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arXiv:quant-ph/0312229 · Physical Review A

Revivals of coherence in chaotic atom-optics billiards

Mikkel F. Andersen, Tzahi Grünzweig, Ariel Kaplan, Nir Davidson

Published Jun 21, 2004• 30 citations
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Abstract

We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of Anderson et al. [Phys. Rev. Lett. 90, 023001 (2003)] shows that it is a function of the survival probability or fidelity of eigenstates of the motion of the atoms in the trap. The echo coherence and the survival probability display ``system specific'' features, even when the underlying classical dynamics is chaotic. In particular, partial revivals in the echo signal and the survival probability are found for a small shift of the potential. Next, a ``semiclassical'' expression for the averaged echo signal is presented and used to calculate the echo signal for atoms in a light sheet wedge billiard. Revivals in the echo coherence are found in this system, indicating that they may be a generic feature of dipole traps.

DOI
10.1103/physreva.69.063413

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We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of Anderson et al. [Phys. Rev. Lett. 90, 023001 (2003)] shows that it is a function of the survival probability or fidelity of eigenstates of the motion of the atoms in the trap. The echo coherence and the survival probability display system specific'' features, even when the underlying classical dynamics is chaotic. In particular, partial revivals in the echo signal and the survival probability are found for a small shift of the potential. Next, a semiclassical'' expression for the averaged echo signal is presented and used to calculate the echo signal for atoms in a light sheet wedge billiard. Revivals in the echo coherence are found in this system, indicating that they may be a generic feature of dipole traps.
We perform echo spectroscopy on ultracold atoms in atom-optics billiards to study their quantum dynamics. The detuning of the trapping laser is used to change the "perturbation", which causes a decay in the echo coherence. Two different regimes are observed: first, a perturbative regime in which the decay of echo coherence is nonmonotonic and partial revivals of coherence are observed in contrast with the predictions of random matrix theory. These revivals are more pronounced in traps with mixed dynamics as compared to traps where the dynamics is fully chaotic. Next, for stronger perturbations, the decay becomes monotonic and independent of the strength of the perturbation. In this regime no clear distinction can be made between chaotic traps and traps with mixed dynamics.
We report on experimental observations of chaotic and regular motion of ultracold atoms confined by a billiard-shaped optical dipole potential induced by a rapidly scanning laser beam. To investigate the dynamics of the atoms confined by such an "atom-optics" billiard we measure the decay of the number of trapped atoms through a hole on the boundary. A fast and purely exponential decay, the clear signature of chaotic motion, is found for a stadium billiard, but not for a circular or an elliptical billiard, in agreement with theory. We also investigated the effects of decoherence, velocity spread, and gravity on regular and chaotic motion.
We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as ”echo spectroscopy ” [M.F. Andersen et. al., Phys. Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely sensitive experimental tool for investigating quantum dynamics of trapped atoms even when a large number of states are thermally populated. We show numerical results for the stability of eigenstates of an atom-optics billiard of the Bunimovich type, and discuss its behavior under different types of perturbations. Finally, we propose to use special geometrical constructions to make a dephasing free dipole trap. Key words: PACS:
We use an atom interferometer to investigate the dynamics of matter waves in a periodically pulsed optical standing wave: an atom optics realization of the quantum kicked rotor that exhibits chaotic classical dynamics. We experimentally show that a measure of the coherence between the interferometer diffraction orders can revive after a quick initial loss, and can approach a finite asymptote as the number of kicks increases. This observation demonstrates that quantum fidelity of a classically chaotic system can survive strong perturbations over long times without decay.
A semiclassical theory of chaotic atomic transport in a one-dimensional nondissipative optical lattice, when the standing-wave field and center-of-mass motion are treated classically, is developed. Using the basic equations of motion for the Bloch and translational atomic variables, we derive a stochastic map for the synchronized component of the atomic dipole moment that determines the center-of-mass motion. We find the analytical relations between the atomic and lattice parameters under which atoms typically alternate between flying through the lattice and being trapped in the wells of the optical potential. We use the stochastic map to derive formulas for the probability density functions (PDFs) for the flight and trapping events. Statistical properties of chaotic atomic transport strongly depend on the relations between the atomic and lattice parameters. We show that there is a good quantitative agreement between the analytical PDFs and those computed with the stochastic map and the basic equations of motion for different ranges of the parameters. Typical flight and trapping PDFs are shown to be broad distributions with power law segments with the slope $\ensuremath{-}1.5$ and exponential ``tails.'' The lengths of the power law and exponential segments of the PDFs depend on the values of the parameters. We find analytical conditions under which deterministic atomic transport has fractal properties and explain a hierarchical structure of the dynamical fractals.