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New Journal of Physics

Probing the unitarity limit at low laser intensities

Philippe Pellegrini, Robin Côté

Published May 14, 2009• 16 citations
Publisher

Abstract

We show how photoassociation (PA) near a magnetically tuned Feshbach resonance can probe the unitarity limit at low laser intensities. This limit occurs when the scattering matrix element in the PA process reaches its quantum limit of one, and is usually difficult to access, requiring large laser intensities. We show how giant enhancements of the PA rate in the vicinity of a Feshbach resonance can reach it, and we predict the appearance of new features with varying magnetic fields and laser intensities. We investigate these effects for a Bose gas of 7 Li atoms at temperatures near quantum degeneracy and give a simple analytical model. We discuss potential applications of our results, obtained without adjustable parameters, to high-precision spectroscopy.

DOI
10.1088/1367-2630/11/5/055047

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We show how photoassociation (PA) near a magnetically tuned Feshbach resonance can probe the unitarity limit at low laser intensities. This limit occurs when the scattering matrix element in the PA process reaches its quantum limit of one, and is usually difficult to access, requiring large laser intensities. We show how giant enhancements of the PA rate in the vicinity of a Feshbach resonance can reach it, and we predict the appearance of new features with varying magnetic fields and laser intensities. We investigate these effects for a Bose gas of 7 Li atoms at temperatures near quantum degeneracy and give a simple analytical model. We discuss potential applications of our results, obtained without adjustable parameters, to high-precision spectroscopy.
The photoassociation (PA) spectrum is analysed in the presence of a magnetic Feshbach resonance. A nonperturbative solution of the problem yields analytical expressions for PA linewidth and shift which are applicable for arbitrary PA laser intensity and magnetic field tuning of Feshbach resonance. We show that by tuning the magnetic field close to the Fano minimum, it is possible to suppress power broadening at increased laser intensities. This occurs due to quantum interference of PA transitions from unperturbed and perturbed continuum. Line narrowing at high laser intensities is accompanied by large spectral shifts. We briefly discuss the important consequences of line narrowing in cold collisions.
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 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.
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 demonstrate that for ultracold, optically trapped Cs atoms the photoassociation (PA) can be manipulated by using external uniform magnetic fields due to the alteration of the scattering wavefunction in the region of the free-bound optical transition. We present PA-induced atom loss measurements with the same intensity for PA laser but different external magnetic fields, and analyze main contributions of the PA to the variation of the number of atoms in the trap. The PA rate exhibits a strong dependence on the changing uniform magnetic field. The experimental data are simulated within the model of a single-channel one-well rectangular potential, whose depth is adjusted so as to assure the predicted variation of the scattering length with the magnetic field. The computational and experimental results are in a reasonable agreement to each other. The same model is used to illustrate some general properties of the two-body quantum system in the near-threshold state.