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Few-Body Systems

Effect of Background Scattering on Efimov Scenario for Overlapping Narrow Feshbach Resonances

Fatema Hamodi-Gzal, Lev Khaykovich

Published Jul 8, 2024• 1 citation
Publisher

Abstract

Abstract Efimov physics in the vicinity of two overlapping narrow Feshbach resonances can be explored within a framework of a three-channel model where a non-interacting open channel is coupled to two closed molecular channels. Here, we determine how it compares to the extended two-channel model, which includes an open channel with finite background scattering and a single molecular channel. We identify the parameter range in which the three-channel model surpasses the extended two-channel model. Furthermore, the three-channel model is extended to include background scattering, and then both models are applied to the experimentally relevant system of bosonic lithium atoms polarized on two different energy levels, with an isolated and two overlapping narrow Feshbach resonances, respectively. We confirm, in agreement with previous studies, that being small, the background scattering length in lithium has a negligible effect on the Efimov features in the case of isolated resonance. However, in the case of overlapping Feshbach resonances, the inclusion of background scattering improves the performance of the theory with respect to the experimentally measured position of the Efimov resonance.

DOI
10.1007/s00601-024-01943-z

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Abstract Efimov physics in the vicinity of two overlapping narrow Feshbach resonances can be explored within a framework of a three-channel model where a non-interacting open channel is coupled to two closed molecular channels. Here, we determine how it compares to the extended two-channel model, which includes an open channel with finite background scattering and a single molecular channel. We identify the parameter range in which the three-channel model surpasses the extended two-channel model. Furthermore, the three-channel model is extended to include background scattering, and then both models are applied to the experimentally relevant system of bosonic lithium atoms polarized on two different energy levels, with an isolated and two overlapping narrow Feshbach resonances, respectively. We confirm, in agreement with previous studies, that being small, the background scattering length in lithium has a negligible effect on the Efimov features in the case of isolated resonance. However, in the case of overlapping Feshbach resonances, the inclusion of background scattering improves the performance of the theory with respect to the experimentally measured position of the Efimov resonance.
While Efimov physics in ultracold atoms is usually modeled with an isolated Feshbach resonance, many real world resonances appear in close vicinity to each other and are therefore overlapping. Here we derive a realistic model based on the mutual coupling of an open channel and two closed molecular channels while neglecting short-range physics as permitted by the narrow character of the considered resonances. The model is applied to three distinct scenarios with experimental relevance. We show that the effect of overlapping resonances is manifested most strikingly at a narrow resonance in whose vicinity there is a slightly narrower one. In this system the Efimov ground state extends not only over the scattering length zero crossing between the two resonances but also over the pole of the second resonance to finally meet the dissociation threshold below it. In the opposite scenario, when a narrow resonance is considered in the vicinity of a slightly broader one, we observe that the Efimov features are pushed to lower binding energies and smaller scattering lengths by a significant factor facilitating their experimental investigation. Both scenarios are compared with the case of two narrow resonances which are far enough away from each other to be effectively decoupled. In this case the two-channel model results are recovered. Finally, we analyze the rich excitation spectrum of the system and construct and explain its nodal pattern.
We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in 39K^{39}\mathrm{K}39K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $\ensuremath{-}8$ and $\ensuremath{-}10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.
In the vicinity of a narrow Feshbach resonance Efimov features are expected to be characterized by the resonance's properties rather than the van der Waals length of the interatomic potential. Although this theoretical prediction is well established by now, it still lacks experimental confirmation. Here, we apply our recently developed three-channel model [Y. Yudkin and L. Khaykovich, Efimov scenario for overlapping narrow Feshbach resonances, Phys. Rev. A 103, 063303 (2021)] to the experimental result obtained in a mass-imbalanced $^{6}\mathrm{Li}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ mixture in the vicinity of the narrowest resonance explored to date [J. Johansen, B. J. DeSalvo, K. Patel, and C. Chin, Testing universality of Efimov physics across broad and narrow Feshbach resonances, Nat. Phys. 13, 731 (2017)]. Our analysis suggests that the observed position of the Efimov resonance is dictated mainly by the resonance physics while the influence of the van der Waals tail of the interatomic potential is minor. We show that the resonance position is strongly influenced by the presence of another Feshbach resonance which significantly alters the effective background scattering length at the narrow resonance position.
Feshbach resonances are commonly described by a single-resonance Feshbach model, and open-channel resonances are not taken into account explicitly. However, an open-channel resonance near threshold limits the range of validity of this model. Such a situation exists when the background scattering length is much larger than the range of the interatomic potential. The open-channel resonance introduces strong threshold effects not included in the single-resonance description. We derive an easy-to-use analytical model that takes into account both the Feshbach resonance and the open-channel resonance. We apply our model to 85Rb^{85}\mathrm{Rb}85Rb, which has a large background scattering length, and show that the agreement with coupled-channel calculations is excellent. The model can be readily applied to other atomic systems with a large background scattering length, such as 6Li^{6}\mathrm{Li}6Li and 133Cs^{133}\mathrm{Cs}133Cs. Our approach provides full insight into the underlying physics of the interplay between open-channel (or potential) resonances and Feshbach resonances.
We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. We find corrections to the universal scaling laws for large binding energies. For narrow resonances we find a distinct nonmonotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. The origin of the three-body parameter is related to the two-body atom-atom interactions in a physically clear model. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down the relation of two- and three-body physics in atomic systems.
A distinguishing feature of ultracold collisions of bosonic lithium atoms is the presence of two near-degenerate two-body continua. The influence of such a near degeneracy on the few-body physics in the vicinity of a narrow Feshbach resonance is investigated within the framework of a minimal model with two atomic continua and one closed molecular channel. The model allows analysis of the spin composition of loosely bound dimers and trimers. In the two-body sector the well-established coupled-channel calculation phenomenology of lithium is qualitatively reproduced, and its particularities are emphasized and clarified. In the three-body sector we find that the Efimov trimer energy levels follow a different functional form as compared to a single continuum scenario while the thresholds remain untouched. This three-channel model with two atomic continua complements our earlier developed three-channel model with two molecular channels [Yudkin and Khaykovich, Phys. Rev. A 103, 063303 (2021)] and suggests that the experimentally observed exotic behavior of the first excited Efimov energy level (Yudkin, Elbaz, and Khaykovich, arXiv:2004.02723) is most probably caused by the short-range details of the interaction potential.