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arXiv:1210.2158 · Physical Review A

Two-channel-model description of confinement-induced Feshbach molecules

Shi-Guo Peng, Hui Hu, Xia-Ji Liu, Kaijun Jiang

Published Sep 4, 2012• 8 citations
arXivHTMLPDF

Abstract

Using a two-channel model, we investigate theoretically the binding energy of confinement-induced Feshbach molecules in two- and one-dimensional ultracold atomic systems near a Feshbach resonance. We show that the two-channel prediction will evidently deviate from the simple single-channel theory as the width of Feshbach resonances decreases. For the one-dimensional system, we perform a full two-channel calculation, with the inclusion of bare interatomic interactions in the open channel. Away from the resonance, we find a sizable correction to the binding energy, if we neglect the bare interatomic interactions as in the previous work [D. B. M. Dickerscheid and H. T. C. Stoof, Phys. Rev. A 72, 053625 (2005)]. We compare our theoretical results with the existing experimental data and present predictions for narrow Feshbach resonances that could be tested in future experiments.

DOI
10.1103/physreva.86.033601

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Using a two-channel model, we investigate theoretically the binding energy of confinement-induced Feshbach molecules in two- and one-dimensional ultracold atomic systems near a Feshbach resonance. We show that the two-channel prediction will evidently deviate from the simple single-channel theory as the width of Feshbach resonances decreases. For the one-dimensional system, we perform a full two-channel calculation, with the inclusion of bare interatomic interactions in the open channel. Away from the resonance, we find a sizable correction to the binding energy, if we neglect the bare interatomic interactions as in the previous work [D. B. M. Dickerscheid and H. T. C. Stoof, Phys. Rev. A 72, 053625 (2005)]. We compare our theoretical results with the existing experimental data and present predictions for narrow Feshbach resonances that could be tested in future experiments.
We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [Phys. Rev. A 79, 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of sss-, ddd-, and ggg-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of sss-wave resonant scattering.
We present a two-channel model to describe the quantum state of two atoms with finite-range interaction near a Feshbach resonance. This model provides a simple picture to analytically derive the wave function and the binding energy of the molecular bound state. The results agree excellently with the measurements and multichannel calculations. For small binding energies, the system enters a threshold regime in which the Feshbach molecules are identical to long range atom pairs in single channel. According to their threshold behavior, we find Feshbach resonances can be classified into two types.
The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.
Abstract By including the effect of a trap with characteristic energy given by the Fermi temperature T F in a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a 40 K atomic Fermi gas. We also reproduce the experimental closed-channel fraction Z across the BEC–BCS crossover and into the BCS regime of a 6 Li atomic Fermi gas. We obtain the expected behavior Z ∝ T F at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the Z dependency on T F on the BCS side, where a significant quantitative discrepancy between experimental data and theory’s predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity between Z and T F predicted by our model for a 40 K atomic Fermi gas.
Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy ${\ensuremath{\varepsilon}}_{0}$ and the resonance is triggered by the microscopic interchannel coupling U12{U}_{12}U12​. The binding energy ${\ensuremath{\varepsilon}}_{0}$ naturally serves as an energy scale of the system, which has been sent to infinity in the atom-molecule theory. We show that the atom-molecule theory can be viewed as a leading-order low-energy effective theory of the underlying fermionic theory in the limit ${\ensuremath{\varepsilon}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ and ${U}_{12}\ensuremath{\rightarrow}0$, while keeping the phenomenological atom-molecule coupling finite. The resulting two-band description of the superfluid state is in analogy to the BCS theory of two-band superconductors. In the dilute limit ${\ensuremath{\varepsilon}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$, the two-band description recovers precisely the atom-molecule theory. The two-band theory provides a natural approach to study the corrections because of a finite binding energy ${\ensuremath{\varepsilon}}_{0}$ in realistic experimental systems. For broad and moderate resonances, the correction is not important for current experimental densities. However, for extremely narrow resonance, we find that the correction becomes significant. The finite binding energy correction could be important for the stability of homogeneous polarized superfluid against phase separation in imbalanced Fermi gases across a narrow Feshbach resonance.