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Echo spectroscopy and Atom Optics Billiards

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

Published Jan 1, 2002• 2 citations
OpenAlex

Abstract

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:

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Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations
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 investigate the dephasing of ultra cold 85Rb atoms trapped in an optical dipole trap and prepared in a coherent superposition of their two hyperfine ground states by interaction with a microwave pulse. We demonstrate that the dephasing, measured as the Ramsey fringe contrast, can be reversed by stimulating a coherence echo with a pi pulse between the two pi / 2 pulses, in analogy to the photon echo. We also demonstrate that "echo spectroscopy" can be used to study the quantum dynamics in the trap even when more than 10(6) states are thermally populated and to study the crossover from quantum to classical dynamics.
Summary form only given. The motion of a particle inside a closed area surrounded by reflecting walls can be integrable or chaotic, depending on the shape of the boundary. These billiards serve as a good and simple model to study chaotic dynamics both classically and quantum mechanically. Recently, we realized an "atom-optics billiard", where ultra-cold atoms are trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics. In this work we describe how scattering and wall softness influence the dynamics of the atoms, and destroy or create stability.
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 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.