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arXiv:0803.1167 · Physical Review Letters

Photoassociation of a Bose-Einstein Condensate near a Feshbach Resonance

Mark D. Junker, D. Dries, C. Welford, J. M. Hitchcock, Y. P. Chen, Randall G. Hulet

Published Aug 8, 2008• 90 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.101.060406

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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 study the effects of magnetic Feshbach resonance on the shifts in photoassociation (PA) spectra of ultracold Cs atoms. A series of atom loss spectra show a linear variation of the frequency shift with the PA laser intensity at different magnetic fields near the d-wave Feshbach resonance of optically trapped Cs atoms. The magnetic field-dependence of the slope of the shift on the PA laser intensity exhibits a dispersive change near the Feshbach resonance. The theoretical formula derived from a model based on Fano resonance fits well with the experimental data. Using a model rectangular potential with tunable well depth and applying the Franck-Condon principle, we obtain numerical results, which are found to be largely in disagreement with the experimental findings.
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 theoretically investigate the effect of anomalous quantum correlations on the light-induced frequency shift in the photoassociation spectrum of a Bose-Einstein condensate. Anomalous quantum correlations arise because, although formed from a pair of zero-momentum condensate atoms, a condensate molecule need not dissociate back to the atomic condensate, but may just as well form a noncondensate atom pair with equal and opposite momentum, i.e., due to rogue photodissociation. The uncorrelated frequency shift of the photoassociation spectrum is to the red and linearly dependent on the laser intensity I. In contrast, anomalous correlations due to rogue dissociation lead to a blueshifted photoassociation spectrum. For sufficiently low light intensities, the rogue blueshift is dominant and proportional to sqrt[I].
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.
A light-induced frequency shift is observed in single-photon photoassociative spectra of magnetically trapped, quantum degenerate 7Li.{}^{7}\mathrm{Li}.7Li. The shift is a manifestation of the coupling between the threshold continuum scattering states and discrete bound levels in the excited-state molecular potential induced by the photoassociation laser. The frequency shift is observed to be linear in the laser intensity with a measured proportionality constant that is in good agreement with theoretical predictions. This phenomenon has important implications for a scheme to alter the interactions between atoms in a Bose-Einstein condensate using photoassociation resonances.