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arXiv:0912.5035 · Physical Review A

Theory of combined photoassociation and Feshbach resonances in a Bose-Einstein condensate

Matt Mackie, Catherine DeBrosse

Published Apr 23, 2010• 4 citations
arXivHTMLPDF

Abstract

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate, where the shared dissociation continuum allows for quantum interference in losses from the condensate, as well as a dispersive-like shift of resonance. A seemingly oversimplified model is revisited, explaining it as based on the limit of weakly bound molecules, reinforcing it with a comparison to numerical experiments that explicitly include dissociation to noncondensate modes, comparing it against the unitarity limit on condensate losses, and lastly, checking its universal implications. In particular, for a resonant laser and an off-resonant magnetic field, these numerical experiments reveal a rate limit on condensate losses that is larger for smaller condensate densities, approaches the rate limit for magnetoassociation alone near the Feshbach resonance, and agrees best with the analytical model for low density. Comparing the analytical rate limit against the unitary limit, which is set by the size of the condensate, agreement is found only for a limited range of near-resonant magnetic fields. Finally, for a resonant magnetic field and an off-resonant laser, the analytical shift of the Feshbach resonance is found to depend on the size of the Feshbach molecule, signifying nonuniversal physics in a strongly interacting system.

DOI
10.1103/physreva.81.043625

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We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate, where the shared dissociation continuum allows for quantum interference in losses from the condensate, as well as a dispersive-like shift of resonance. A seemingly oversimplified model is revisited, explaining it as based on the limit of weakly bound molecules, reinforcing it with a comparison to numerical experiments that explicitly include dissociation to noncondensate modes, comparing it against the unitarity limit on condensate losses, and lastly, checking its universal implications. In particular, for a resonant laser and an off-resonant magnetic field, these numerical experiments reveal a rate limit on condensate losses that is larger for smaller condensate densities, approaches the rate limit for magnetoassociation alone near the Feshbach resonance, and agrees best with the analytical model for low density. Comparing the analytical rate limit against the unitary limit, which is set by the size of the condensate, agreement is found only for a limited range of near-resonant magnetic fields. Finally, for a resonant magnetic field and an off-resonant laser, the analytical shift of the Feshbach resonance is found to depend on the size of the Feshbach molecule, signifying nonuniversal physics in a strongly interacting system.
We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate. When the magnetic field is far-off resonance, cross coupling between the two target molecules--enabled by the shared dissociation continuum--leads to an anomalous dispersive shift in the position of laser resonance, as well as unprecedented elimination and enhancement of resonant photoassociation via quantum interference. For off-resonant lasers, a dispersive shift and quantum interference appear similarly in resonant three-body Feshbach losses, except that the Feshbach node is tunable with intensity.
We measure the effect of a magnetic Feshbach resonance (FR) on the rate and light-induced frequency shift of a photoassociation resonance in ultracold 7Li. The photoassociation-induced loss-rate coefficient K_{p} depends strongly on magnetic field, varying by more than a factor of 10;{4} for fields near the FR. At sufficiently high laser intensities, K_{p} for a thermal gas decreases with increasing intensity, while saturation is observed for the first time in a Bose-Einstein condensate. The frequency shift is also strongly field dependent and exhibits an anomalous blueshift for fields just below the FR.
The rate of photoassociation (PA) determines how quickly molecules form from atoms illuminated by a resonant laser pulse. Knowledge of limits of this molecular formation rate provide a fundamental component on the maximum rate that a tightly bound ground state molecular Bose-Einstein condensate (BEC) could be formed using a two-photon transition. This molecular synthesis represents the beginning of a new era of ultracold quantum chemistry. The available Feshbach resonance in this system is an indispensable tool to increase the molecular formation rate due to PA in the anticipation of revealing these fundamental rate limits. While the rate saturates in a thermal gas, no evidence of saturation has yet been observed in a BEC. A loss of atoms due to a PA pulse tuned to the v " = 83 excited state molecular vibrational level provides the measurement of the PA rate. The rate varies by several orders of magnitude either by tuning the magnetic field near a Feshbach resonance or by adjusting the PA intensity. We measure the PA rate at magnetic fields between 550-900 Gauss in a BEC and a thermal gas, which is near the Feshbach resonance at 736 Gauss. The rapidly changing rate near the Feshbach resonance reflects the overlap between the ground state and the excited state wavefunctions. We present the first quantitative measurement of the PA rate near a Feshbach resonance. We measure the magnetic field dependence of the molecular resonance position near the Feshbach resonance. We introduce the first observation of a positive energy shift associated with photoassociation. The measured energy shift asymptotically diverges as it approaches the Feshbach resonance and agrees qualitatively with described theory at all magnetic fields. We observe intensity dependent saturation in the PA rate in a thermal gas and the measurements qualitatively agree with a unitarity limited rate. The first conclusive evidence for a suppression of the PA rate occurs for intensities above the saturation intensity. We report the first observed saturation of the PA rate in a BEC. Three separate theories present possible mechanisms for the observed saturation.
We revisit the mean-field treatment of photoassociation and Feshbach resonances in a Bose-Einstein condensate previously used by various authors. Generalizing the Cherny and Shanenko approach [Phys. Rev. E 62, 1646 (2000)] where the finite size of the potentials is explicitly introduced, we develop a two-channel model for a mixed atomic-molecular condensate. Besides the individual dynamics of the condensed and noncondensed atoms, the model also takes into account their pair dynamics by means of pair wave functions. We show that the resulting set of coupled equations can be reduced to the usual coupled Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} equations when the time scale of the pair dynamics is short compared to that of the individual dynamics. Such time scales are discussed in the case of typical photoassociation experiments with cw lasers. We show that the individual dynamics plays a minor role, demonstrating the validity of the rates predicted by the usual models describing photoassociation in a nondegenerate gas.
We briefly report on zero-temperature photoassociation of a Bose-Einstein condensate, focusing on the many-body rate limit for atom-molecule conversion. An upgraded model that explicitly includes spontaneous radiative decay leads to an unanticipated shift in the position of the photoassociation resonance, which affects whether the rate (constant) maximizes or saturates, as well as the limiting value itself. A simple analytical model agrees with numerical experiments, but only for high density. Finally, an explicit comparison with the two-body unitary limit, set by the size of the condensate, finds that the many-body rate limit is generally more strict.
Recent Feshbach-resonance experiments with 85Rb Bose-Einstein condensates have led to a host of unexplained results: dramatic losses of condensate atoms for an across-resonance sweep of the magnetic field, a collapsing condensate with a burst of atoms emanating from the remnant condensate, increased losses for decreasing interaction times, and coherent oscillations between remnant and burst atoms. Using a simple yet realistic mean-field model, we find that rogue dissociation, molecular dissociation to noncondensate atom pairs, is strongly implicated as the physical mechanism responsible for these observations.