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arXiv:cond-mat/0208294 · Physical Review A

Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas

Dave Harber, Heather J. Lewandowski, J. M. McGuirk, Eric Cornell

Published Nov 22, 2002• 231 citations
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Abstract

We have performed precision microwave spectroscopy on ultracold ${}^{87}\mathrm{Rb}$ confined in a magnetic trap, both above and below the Bose-condensation transition. The cold collision frequency shifts for both normal and condensed clouds were measured, which allowed the intrastate and interstate density correlations (characterized by sometimes controversial ``factors of 2'') to be determined. Additionally, temporal coherence of the normal cloud was studied, and the importance of mean-field and velocity-changing collisions in preserving coherence is discussed.

DOI
10.1103/physreva.66.053616

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We have performed precision microwave spectroscopy on ultracold 87Rb{}^{87}\mathrm{Rb}87Rb confined in a magnetic trap, both above and below the Bose-condensation transition. The cold collision frequency shifts for both normal and condensed clouds were measured, which allowed the intrastate and interstate density correlations (characterized by sometimes controversial ``factors of 2'') to be determined. Additionally, temporal coherence of the normal cloud was studied, and the importance of mean-field and velocity-changing collisions in preserving coherence is discussed.
We use precision microwave spectroscopy of magnetically trapped, ultra-cold 87Rb to characterize intra- and inter-state density correlations. The cold collision shifts for both normal and condensed clouds are measured. The results verify the presence of the sometimes controversial "factors of two", in normal-cloud mean-field energies, both within a particular state and between two distinct spin species. One might expect that as two spin species decohere, the inter-state factor of two would revert to unity, but the associated frequency chirp one naively expects from such a trend is not observed in our data.
We use precision microwave spectroscopy of magnetically trapped, ultra-cold ⁸⁷Rb to characterize intra- and inter-state density correlations. The cold collision shifts for both normal and condensed clouds are measured. The results verify the presence of the sometimes controversial "factors of two", in normal-cloud mean-field energies, both within a particular state and between two distinct spin species. One might expect that as two spin species decohere, the inter-state factor of two would revert to unity, but the associated frequency chirp one naively expects from such a trend is not observed in our data.
The use of temporal correlations in scattered photons to probe the microscopic dynamics of ultracold quantum gases has emerged as a powerful, minimally destructive approach for in situ analysis. Here, we demonstrate that temporal coherence spectroscopy can quantitatively characterize atomic motion in a magnetic trap, despite the perturbative effects of the probing light. By measuring the first-order correlation function g (1) (τττ ) of light scattered by a 87 Rb cloud confined in a quadrupole trap, we identify radiation-pressure-induced acceleration and heating as the origin of the apparent discrepancy between coherence spectra and temperatures inferred from time-of-flight measurements. A simple dynamical model incorporating these effects restores agreement between theory and experiment, establishing coherence spectroscopy as a reliable in situ probe of velocity distributions in trapped atomic ensembles. Our results pave the way for time-resolved studies of nonequilibrium dynamics and thermalization processes in confined cold gases, complementing conventional destructive imaging techniques.
We have experimentally demonstrated the absence of spectroscopic resonance shifts in a mixture of two interacting Fermi gases. This result is linked to observations in an ultracold gas of thermal bosons. There, the measured resonance shift due to interstate collisions is independent of the coherence in the system, and twice that expected from the equilibrium energy splitting between the two internal states in a fully decohered cloud. We give a simple theoretical explanation of these observations, which elucidates the effect of coherent radiation on an incoherent mixture of atoms.
We discuss the static and dynamic magnetic properties of cold quantum gas systems. In particular, we investigate and analyze the ground state properties and dynamics of F = 2 spinor Bose-Einstein condensates of 87Rb. The rich physics of these systems is governed by an interplay between mean-field-driven spin dynamics and hyperfine-changing losses in addition to interactions with atoms in the thermal cloud. We find conversion rates on the order of 10-12 cm3 s-1 for spin-changing collisions within the F = 2 manifold and spin-dependent loss rates on the order of 10-13 cm3 s-1 for hyperfine-changing collisions. Our data leads to the conclusion that the F = 2 ground state of 87Rb is polar, while we measure the F = 1 ground state to be ferromagnetic. As remarkable features in the spin dynamics we observe spinor oscillations and a delayed formation of new mF-condensate components.
We have measured the rate of inelastic collisions in a cloud of doubly polarized ground-state cesium atoms ( F=mF=4{F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4F=mF​=4) confined in a magnetic trap for temperatures TTT between 8 and $70\ensuremath{\mu}\mathrm{K}$. We find a two-body rate coefficient varying as ${T}^{\ensuremath{-}0.63}$. At 8 $\ensuremath{\mu}\mathrm{K}$ it reaches $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ which is 3 orders of magnitude larger than predicted, ruling out a Bose-Einstein condensation of Cs in this internal state.