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arXiv:physics/0609145 · Physical Review A

Optical Feshbach resonances of alkaline-earth-metal atoms in a one- or two-dimensional optical lattice

Pascal Naidon, Paul S. Julienne

Published Dec 20, 2006• 31 citations
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Abstract

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.

DOI
10.1103/physreva.74.062713

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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.
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.
With ultracold 88Sr in a 1D magic wavelength optical lattice, we performed narrow-line photoassociation spectroscopy near the 1S0 - 3P1 intercombination transition. Nine least-bound vibrational molecular levels associated with the long-range 0u and 1u potential energy surfaces were measured and identified. A simple theoretical model accurately describes the level positions and treats the effects of the lattice confinement on the line shapes. The measured resonance strengths show that optical tuning of the ground state scattering length should be possible without significant atom loss.
We model two bosons in an optical lattice near a Feshbach or photoassociation resonance, focusing on the Bose-Hubbard model in one dimension. Whereas the usual atoms-only theory with a tunable scattering length yields one bound state for a molecular dimer for either an attractive or repulsive atom-atom interaction, for a sufficiently small direct background interaction between the atoms a two-channel atom-molecule theory may give two bound states that represent attractively and repulsively bound dimers occurring simultaneously. Such unusual molecular physics may be observable for an atom-molecule coupling strength comparable to the width of the dissociation continuum of the lattice dimer, which is the case, for instance, with narrow Feshbach resonances in Na, 87Rb^{87}\mathrm{Rb}87Rb, and 133Cs^{133}\mathrm{Cs}133Cs or low-intensity photoassociation in 174Yb^{174}\mathrm{Yb}174Yb.
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.
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.