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arXiv:1404.6676 · Physical Review A

Multichannel quantum-defect theory for magnetic Feshbach resonances in heteronuclear group-I systems

Constantinos Makrides, Bo Gao

Published Jun 27, 2014• 11 citations
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Abstract

We present a multichannel quantum-defect theory for magnetic Feshbach resonances in the interaction of two heteronuclear group-I atoms. The theory provides a unified and a uniform description of resonances in all partial waves and enables the characterization of a large number of resonances in terms of very few parameters. For the sample system of $^{6}\mathrm{Li} ^{40}\mathrm{K}$, we present descriptions of all resonances in $aa$, $ab$, and $ba$ channels, in partial waves $s$ ($l=0$) through $h$ ($l=5$), and in a magnetic field of 0--1000 G. All resonances, including those in nonzero partial waves, are fully characterized using the newly developed parametrization of Gao [Phys. Rev. A 84, 022706 (2011)].

DOI
10.1103/physreva.89.062718

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We present a multichannel quantum-defect theory for magnetic Feshbach resonances in the interaction of two heteronuclear group-I atoms. The theory provides a unified and a uniform description of resonances in all partial waves and enables the characterization of a large number of resonances in terms of very few parameters. For the sample system of 6Li40K^{6}\mathrm{Li} ^{40}\mathrm{K}6Li40K, we present descriptions of all resonances in aaaaaa, ababab, and bababa channels, in partial waves sss (l=0l=0l=0) through hhh (l=5l=5l=5), and in a magnetic field of 0--1000 G. All resonances, including those in nonzero partial waves, are fully characterized using the newly developed parametrization of Gao [Phys. Rev. A 84, 022706 (2011)].
Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave lll and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary lll, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary lll, (b) rigorous definitions of ``broad'' and ``narrow'' resonances of arbitrary lll and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.
Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled-channel calculations for several cases of overlapping resonances in the collisions of two 7{}^{7}7Li atoms or two Cs atoms.
We present analytic descriptions of atomic interaction at ultracold temperatures using both single-channel and multichannel quantum-defect theories. In the case of a single channel, addressed in this paper, the expansion of Gao [Phys. Rev. A 58, 4222 (1998)] is generalized to higher orders for angular momentum $l\ensuremath{\ge}2$ to give a more complete description of ultracold scattering, including an analytic description of ultracold shape resonances of arbitrary lll. We also introduce a generalized scattering length that is well defined and useful for all partial waves to replace the traditional definition that fails for $l\ensuremath{\ge}2$ due to the long-range van der Waals interaction. The results are used in a companion paper to derive analytic descriptions of atomic interaction around a magnetic Feshbach resonance of arbitrary angular momentum lll.
Feshbach resonance is a fundamental phenomenon in cold atomic physics, where interatomic interactions can be precisely changed into a scattering resonance by varying an external magnetic field. This effect plays a crucial role in ultracold atomic experiments, enabling the control of interaction strength, the formation of molecular bound states, and the realization of strongly correlated quantum systems. With the rapid development of cold atom experiments, numerous Feshbach resonances corresponding to different partial waves, such as s-wave, p-wave, and even higher partial wave ones, have been experimentally identified. While s-wave resonances have been widely utilized due to their isotropic nature and strong coupling, and higher partial-wave resonances (including p-wave and d-wave resonances), provide unique opportunities for exploring anisotropic interactions and novel quantum phases. In this study, by using the multichannel quantum defect theory (MQDT), we predict that two d-wave Feshbach resonances are existent in 7Li at 1039.24 G and 1055.64 G, repectively. Physical properties of the two resonances are presented, such as the resonance width and closed channel dimer energy. In addition, we optimize the computational parameters by using the Nelder-Mead algorithm and investigate the possible resonance splitting induced by dipole-dipole interactions in higher partial waves. The presence of these d-wave resonances at high magnetic fields provides a new platform for investigating the interplay between higher-order partial wave interactions and quantum many-body effects. Our results provide opportunities for investigating the effects of higher partial wave Feshbach resonances in high magnetic fields. Our theoretical predictions thus serve as a useful reference for future experimental studies of higher-order resonance phenomena in lithium and other atomic species.
We investigate the modulating action of an external electric field on the magnetically tuned Feshbach resonance in ultracold heteronuclear atomic collision by using the multichannel quantum-defect theory (MQDT). The coupling between different partial wave states induced by an electric field is included into the singlet and triplet quantum defect matrices y(0) and y(1). By taking the truncated −C6/R6 − C8/R8 − C10/R10 potential as the reference potential, the threshold behaviors of four quantum-defect parameters for the lowest three partial waves are described. The results calculated by using the MQDT agree with those calculated using the coupled channel method. Moreover, we present an analytical expression used for describing the variation of the position and width of the magnetically tuned Feshbach resonance modulated by an electric field.
A comprehensive search for broad Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multichannel quantum-defect theory assisted by the analytic wave functions for a long-range van der Waals potential. A number of broad sss-, ppp-, and ddd-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of ppp- or ddd-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.