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arXiv:quant-ph/0208052 · Physical Review Letters

Echo Spectroscopy and Quantum Stability of Trapped Atoms

Mikkel F. Andersen, Ariel Kaplan, Nir Davidson

Published Jan 13, 2003• 99 citations
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Abstract

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.

DOI
10.1103/physrevlett.90.023001

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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.
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 study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far-off-resonant standing-wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey-spectroscopy and spin-echo techniques, we measure the reversible and irreversible dephasing times of the ground-state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.
The decay in the hyperfine coherence of optically trapped atoms due to interactions with the environment, is only partly suppressed by ``echo'' spectroscopy [M. F. Andersen et al. Phys. Rev. Lett. 90, 023001 (2003)], primarily due to dynamical (time-dependent) dephasing mechanisms. We demonstrate here an improved pulse sequence, for which the decay of coherence is reduced by a factor of 2.52.52.5 beyond the reduction offered by the ``echo'' spectroscopy. This reduction occurs when each dark period in-between pulses is shorter than the time scale over which substantial dephasing develops. The coherence time is then limited by mixing to other vibrational levels in the trap and, to a lesser extent, the lifetime of the internal states of the atoms.
We perform Ramsey interferometry on an ultracold ^{87}Rb ensemble confined in an optical dipole trap. We use a π pulse set at the middle of the interferometer to restore the coherence of the spin ensemble by canceling out phase inhomogeneities and creating a spin echo in the contrast. However, for high atomic densities, we observe the opposite behavior: the π pulse accelerates the dephasing of the spin ensemble leading to a faster contrast decay of the interferometer. We understand this phenomenon as a competition between the spin-echo technique and an exchange-interaction driven spin self-rephasing mechanism based on the identical spin rotation effect. Our experimental data are well reproduced by a numerical model.
We experimentally study the ground state coherence properties of cesium atoms in a nanofiber-based two-color dipole trap, localized ∼ 200 nm away from the fiber surface. Using microwave radiation to coherently drive the clock transition, we record Ramsey fringes as well as spin echo signals and infer a reversible dephasing time of T(2)(*) = 0.6 ms and an irreversible dephasing time of T(2)(') = 3.7 ms. By modeling the signals, we find that, for our experimental parameters, T(2)(*) and T(2)(') are limited by the finite initial temperature of the atomic ensemble and the heating rate, respectively. Our results represent a fundamental step towards establishing nanofiber-based traps for cold atoms as a building block in an optical fiber quantum network.