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Physical Review A

Stationary phase approximation for the strength of optical Feshbach resonances

R. Ciuryło, Eite Tiesinga, Paul S. Julienne

Published Aug 7, 2006• 20 citations
Publisher

Abstract

Analytic expressions for the width and shift of a photoassociative resonance or an optically induced Feshbach resonance in ultracold collisions are derived using the quasi-classical stationary phase approximation. This approach for the width is applicable over a wider range of cases than the reflection approximation. Possible applications for optical Feshbach resonances between ultracold alkaline-earth-metal atoms, such as Ca and Sr, are discussed. Our approach also applies to photoassociation in gases of heteronuclear alkali-metal atoms.

DOI
10.1103/physreva.74.022710

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Analytic expressions for the width and shift of a photoassociative resonance or an optically induced Feshbach resonance in ultracold collisions are derived using the quasi-classical stationary phase approximation. This approach for the width is applicable over a wider range of cases than the reflection approximation. Possible applications for optical Feshbach resonances between ultracold alkaline-earth-metal atoms, such as Ca and Sr, are discussed. Our approach also applies to photoassociation in gases of heteronuclear alkali-metal atoms.
Motivated by a recent experiment by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)], we present the theory for photoassociation and optical Feshbach resonances of atoms confined in a tight one-dimensional (1D) or two-dimensional (2D) optical lattice. In the case of an alkaline-earth-metal intercombination resonance, the narrow natural width of the line makes it possible to observe clear manifestations of the dimensionality, as well as some sensitivity to the scattering length of the atoms. Among possible applications, a 2D lattice may be used to increase the spectroscopic resolution by about one order of magnitude. Furthermore, a 1D lattice induces a shift that provides an alternative way of determining the strength of a resonance by spectroscopic measurements.
It is possible to tune the scattering length for the collision of ultracold ground-state alkaline-earth-metal atoms using an optical Feshbach resonance. This is achieved with a laser far detuned from an excited molecular level near the frequency of the atomic intercombination transition. Simple resonant-scattering theory, illustrated by the example of , allows an estimate of the magnitude of the effect. Unlike alkali metal species, large changes of the scattering length are possible while atom loss remains small, because of the very narrow linewidth of the molecular photoassociation transition. This raises prospects for control of atomic interactions for a system without magnetically tunable Feshbach resonance levels.
Optical Feshbach resonances allow one to control cold atomic scattering, produce ultracold molecules, and study atomic interactions via photoassociation spectroscopy. In the limit of ultracold sss-wave collisions, the strength of an optical Feshbach resonance can be expressed via an energy-independent parameter called the optical length. Here we give fully analytic approximate expressions for its magnitude applicable to near-threshold bound states of an excited molecular state dominated by a single resonant-dipole or van der Waals interaction. We express these magnitudes in terms of intuitive quantities, such as the laser intensity, the excited-state binding energy, the sss-wave scattering length, and the Condon point. Additionally, we extend the utility of the optical length to associative stimulated Raman adiabatic passage in three-dimensional optical lattices by showing that the free-bound Rabi frequency induced by a laser coupling a pair of atoms in an optical lattice site can be approximately related to the trap frequency and the optical length.
Using a narrow intercombination line in alkaline earth atoms to mitigate large inelastic losses, we explore the optical Feshbach resonance effect in an ultracold gas of bosonic (88)Sr. A systematic measurement of three resonances allows precise determinations of the optical Feshbach resonance strength and scaling law, in agreement with coupled-channel theory. Resonant enhancement of the complex scattering length leads to thermalization mediated by elastic and inelastic collisions in an otherwise ideal gas. Optical Feshbach resonance could be used to control atomic interactions with high spatial and temporal resolution.
Ultracold molecules offer a broad variety of applications, ranging from metrology to quantum computing. However, forming "real" ultracold molecules, i.e., in deeply bound levels, is a very difficult proposition. Here, we show how photoassociation in the vicinity of a Feshbach resonance enhances molecular formation rates by several orders of magnitude. We illustrate this effect in heteronuclear systems, and find giant rate coefficients even in deeply bound levels. We also give a simple analytical expression for the photoassociation rate and discuss future applications of the Feshbach-optimized photoassociation technique.
We investigate theoretically the influence of magnetically tunable Feshbach collision resonances on the photoassociation spectra of ultracold atoms. As an example we consider recently predicted resonances for 85Rb{}^{85}\mathrm{Rb}85Rb atoms. For excitation to the ${}^{85}{\mathrm{Rb}}_{2}{\mathrm{ }0}_{g}^{\ensuremath{-}}{(S}_{1/2}{+P}_{1/2})$ electronic state, we predict that the photoassociation rate is resonantly enhanced by at least two orders of magnitude. We find that photoassociation could serve as a useful probe with which to study Feshbach resonances in ultracold collisions. In turn, these resonances should be very important to Bose-condensed gases, and more generally, to coherent atom optics.