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Simple Theoretical Models for Resonant Cold Atom Interactions

Julienne, P S, Gao, B

Published Sep 1, 2006• 11 citations
OpenAlex

Abstract

Magnetically tunable scattering resonances have been used with great success for precise control of s-wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with $^{87}$Rb, $^{85}$Rb, $^{40}$K, and $^{6}$Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.

Related papers

Simple Theoretical Models for Resonant Cold Atom Interactions

Paul S. Julienne, Bo Gao

Magnetically tunable scattering resonances have been used with great success for precise control of s‐wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87Rb, 85Rb, 40K, and 6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.

arXiv:physics/0609013•AIP conference proceedings•Jan 1, 2006•23 citations

Optical tuning of the scattering length of cold alkaline-earth-metal atoms

R. Ciuryło, Eite Tiesinga, Paul S. Julienne

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.

arXiv:physics/0412111•Physical Review A•Mar 25, 2005•110 citations

Observation of Optically Induced Feshbach Resonances in Collisions of Cold Atoms

Fredrik K. Fatemi, K. M. Jones, Paul D. Lett

We have observed optically induced Feshbach resonances in a cold ( <1 mK) sodium vapor. The optical coupling of the ground and excited-state potentials changes the scattering properties of an ultracold gas in much the same way as recently observed magnetically induced Feshbach resonances, but allows for some experimental conveniences associated with using lasers. The scattering properties can be varied by changing either the intensity or the detuning of a laser tuned near a photoassociation transition to a molecular state in the dimer. In principle this method allows the scattering length of any atomic species to be altered. A simple model is used to fit the dispersive resonance line shapes.

Physical Review Letters•Nov 20, 2000•215 citations

The atom and atom scattering model to control ultracold collisions

Hasi Ray

A modified static exchange model is introduced, it could be useful to control the elastic s-wave scattering length in studying cold-atomic interaction. The theory includes the long-range van der Waals interaction in addition to short-range exchange force. The model is applied on Ps-H system to study the Feshbach resonances e.g. the s-wave elastic phase shifts and the corresponding cross sections at ultracold energies. These are compared with the data obtained using the static exchange model. A very interesting features are observed when we vary the interatomic separation i.e. the strength of dipole-dipole interaction.

arXiv:1206.5476•Jun 24, 2012•0 citations

Resonant Magnetic Field Control of Elastic Scattering in Cold R 85 b

Jacob Roberts, N. R. Claussen, James P. Burke +3 more

A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2$ state of ${}^{85}\mathrm{Rb}$. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 1${0}^{4}$, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient ${C}_{6}$, the singlet scattering length ${a}_{S}$, and the triplet scattering length ${a}_{T}$.

Physical Review Letters•Dec 7, 1998•499 citations

Analytic approximations to the strengths of near-threshold optical Feshbach resonances

Mateusz Borkowski

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 $s$-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 $s$-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.

arXiv:1911.07063•Physical Review A•Jun 1, 2023•1 citation
Magnetically tunable scattering resonances have been used with great success for precise control of s-wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87^{87}87Rb, 85^{85}85Rb, 40^{40}40K, and 6^{6}6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.
Magnetically tunable scattering resonances have been used with great success for precise control of s‐wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87Rb, 85Rb, 40K, and 6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.
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.
We have observed optically induced Feshbach resonances in a cold ( <1 mK) sodium vapor. The optical coupling of the ground and excited-state potentials changes the scattering properties of an ultracold gas in much the same way as recently observed magnetically induced Feshbach resonances, but allows for some experimental conveniences associated with using lasers. The scattering properties can be varied by changing either the intensity or the detuning of a laser tuned near a photoassociation transition to a molecular state in the dimer. In principle this method allows the scattering length of any atomic species to be altered. A simple model is used to fit the dispersive resonance line shapes.
A modified static exchange model is introduced, it could be useful to control the elastic s-wave scattering length in studying cold-atomic interaction. The theory includes the long-range van der Waals interaction in addition to short-range exchange force. The model is applied on Ps-H system to study the Feshbach resonances e.g. the s-wave elastic phase shifts and the corresponding cross sections at ultracold energies. These are compared with the data obtained using the static exchange model. A very interesting features are observed when we vary the interatomic separation i.e. the strength of dipole-dipole interaction.
A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2$ state of 85Rb{}^{85}\mathrm{Rb}85Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 104{0}^{4}04, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient C6{C}_{6}C6​, the singlet scattering length aS{a}_{S}aS​, and the triplet scattering length aT{a}_{T}aT​.
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.