Feshbach resonances with large background scattering length: Interplay with open-channel resonances

Marcelis, B Bout; Kempen, van Egm Eric; Verhaar, BJ Boudewijn; Kokkelmans, Sjjmf Servaas

doi:10.1103/physreva.70.012701

Cited by 70 publications

(87 citation statements)

References 66 publications

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“…2. At zero field, a bg is 3 and positive, while for large field values a bg is large and negative, indicating the presence of a nearby virtual state in the open-channel subspace P [28]. Consequently several important quantities, such as the S and T matrices, which summarize the collision process, depend nontrivially on the collision energy E. Here we will apply the model discussed in Ref.…”

Section: Formation Of Fermionic Molecules Via Interisotope Feshbach Rmentioning

confidence: 99%

“…Consequently several important quantities, such as the S and T matrices, which summarize the collision process, depend nontrivially on the collision energy E. Here we will apply the model discussed in Ref. [28] to this s-wave Feshbach resonance. This model takes the virtual state into account explicitly, and gives an analytical description of all the important two-body quantities near the Feshbach resonance.…”

Section: Formation Of Fermionic Molecules Via Interisotope Feshbach Rmentioning

confidence: 99%

“…2 we compare the dressed (quasi-)molecular state calculated by coupled-channels methods and by our analytical model, which agrees excellently. Therefore, this model can be used to analytically describe the S and T matrices [28], scattering phase shifts, etc., with similar precision as a full coupledchannels calculation, for a large range of energies and magnetic fields. We note also that the narrow 543 G Feshbach resonance (width of order 0.1 G) can be described by Feshbach theory.…”

Section: Formation Of Fermionic Molecules Via Interisotope Feshbach Rmentioning

confidence: 99%

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Formation of fermionic molecules via interisotope Feshbach resonances

2004

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We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For 6 Li a consistent description can be given. We discuss theoretical uncertainties for the position of the wide 6 Li Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6 Li-7 Li system, and their importance for different types of crossover superfluidity models is discussed.

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Section: Formation Of Fermionic Molecules Via Interisotope Feshbach Rmentioning

confidence: 99%

Section: Formation Of Fermionic Molecules Via Interisotope Feshbach Rmentioning

confidence: 99%

Section: Formation Of Fermionic Molecules Via Interisotope Feshbach Rmentioning

confidence: 99%

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Formation of fermionic molecules via interisotope Feshbach resonances

2004

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“…Theoretical discussion of the properties of these resonances can be found in Refs. [8,9,10,11]. The interaction between the atoms at ultra-cold temperature can be characterized by a single parameter, the scattering length [12,13], which can be controlled in sign and magnitude using these resonances.…”

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confidence: 99%

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

2005

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It is possible to tune the scattering length for the collision of ultra-cold 1 S0 ground state alkaline-earth 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 1 S0-3 P1 transition. Simple resonant scattering theory, illustrated by the example of 40 Ca, 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 line width of the molecular photoassociation transition. This raises prospects for control of atomic interactions for a system without magnetically tunable Feshbach resonance levels.PACS numbers: 34.50. Rk, 34.10.+x, 32.80.Pj In recent years the ability to change the interaction between ultra-cold colliding atoms has opened the way for new and exciting experiments with ultra-cold atomic gases. The observation of a Bose-Einstein condensate (BEC) in atomic cesium [1] would have been impossible without the ability to change the interaction from being attractive to being repulsive. More impressively, time-varying interactions have allowed the creation of condensates of two-atom molecules starting from an atomic Bose condensate [2,3]. Most recently, the observation of the condensation of pairs of fermionic [4] atoms has started investigations into the so-called BEC-BCS crossover [5], where BCS is the abbreviation for the BardeenCooper-Schrieffer phase transition in a fermionic gas [6].The key to these developments has been the ability to change the interaction between atoms by a magnetically-tuned Feshbach resonance [7]. Theoretical discussion of the properties of these resonances can be found in Refs. [8,9,10,11]. The interaction between the atoms at ultra-cold temperature can be characterized by a single parameter, the scattering length [12,13], which can be controlled in sign and magnitude using these resonances.Another way to change the scattering length of two colliding atoms is to optically couple the ground scattering state with an excited bound state [14]. These optical Feshbach resonances are theoretically analyzed in Refs. [15,16] and implemented experimentally in Refs. [17,18]. The recent experiment of Theis et al. [18] with 87 Rb atoms showed, however, that a significant change of the scattering length is accompanied with substantial loss of atoms. The same is true if a twocolor Raman process is used [19].In this paper we discuss the optical tuning of scattering lengths in ultra-cold alkaline-earth atom vapors. To do so we will assume that the laser is far detuned from excited molecular states near the intercombination transition, 1 S 0 -3 P 1 , as recently analyzed in Ref. [20]. We show that significant changes of the scattering strength can be achieved without the excessive atom loss that plagues experiments with alkali-metal gases [18]. Prospects for an optically tuned scattering length in ultra-cold alkaline-earth vapors seems to be particularly a...

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“…In the general case, Feshbach resonances are richer, as e.g. a form or potential resonance may take place in the open channel, in which case the background scattering length a bg is large and the modified Bethe-Peierls conditions [9][10][11] may not reproduce correctly the momentum dependence of the two-body scattering amplitude at low energy [41] [20][21][22][23]. Using a two-channel model, with the description of the direct atomic interaction in the open channel by a separable potential, is then the simplest way to have a reasonably accurate description of the atomic physics behind the Feshbach resonance, while keeping the simplicity of the integral equations resulting from zero-range models.…”

Section: Introductionmentioning

confidence: 99%

Integral equations for the four-body problem

Mora

Pricoupenko

2011

Comptes Rendus. Physique

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We consider the four-boson and 3+1 fermionic problems with a model Hamiltonian which encapsulates the mechanism of the Feshbach resonance involving the coherent coupling of two atoms in the open channel and a molecule in the closed channel. The model includes also the pair-wise direct interaction between atoms in the open channel and in the bosonic case, the direct molecule-molecule interaction in the closed channel. Interactions are modeled by separable potentials which makes it possible to reduce the four-body problem to the study of a single integral equation. We take advantage of the rotational symmetry and parity invariance of the Hamiltonian to reduce the general eigenvalue equation in each angular momentum sector to an integral equation for functions of three real variables only. A first application of this formalism in the zero-range limit is given elsewhere [Y. Castin, C. Mora, L. Pricoupenko, Phys. Rev. Lett. 105, 223201 (2010)]. Résumé :Équations intégrales pour le problèmeà quatre corpsNous considérons les problèmesà quatre bosons età 3+1 fermions en utilisant un Hamiltonien modèle incluant le mécanisme de la résonance de Feshbach avec un couplage cohérent entre deux atomes dans la voie ouverte et une molécule dans la voie fermée. Le modèle comprend aussi une interaction directe entre atomes dans la voie ouverte, et dans le cas bosonique, l'interaction entre deux molécules de la voie fermée. Les interactions sont modélisées par des potentiels séparables, ce qui permet de ramener le problèmeà quatre corpsà la résolution d'uneéquation intégrale unique. L'invariance par rotation et par parité du Hamiltonien permet de réduire l'équation aux valeurs propres générale dans chaque secteur de moment cinétique fixéà uneéquation intégrale portant sur des fonctions de trois variables réelles seulement. Une première application de ces considérations a déjàété mise en oeuvre dans [Y. Castin, C. Mora, L. Pricoupenko, Phys. Rev. Lett. 105, 223201 (2010)].

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Feshbach resonances with large background scattering length: Interplay with open-channel resonances

Cited by 70 publications

References 66 publications

Formation of fermionic molecules via interisotope Feshbach resonances

Formation of fermionic molecules via interisotope Feshbach resonances

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

Integral equations for the four-body problem

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