Abstract
One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo- dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.
Highlights
Synthetic spin–orbit coupling (SOC) in ultracold atomic gases has stimulated much interest following its experimental realization [1,2,3,4,5,6,7,8,9]
As we have demonstrated in this review, few-body physics in quasi-low-dimensional atomic gases can be quite different from the physics in a purely low dimensional system
One must be careful in treating quasi-low-dimensional atomic gases, when they are close to the Feshbach resonance or on the Bose– Einstein condensate (BEC) side
Summary
Synthetic spin–orbit coupling (SOC) in ultracold atomic gases has stimulated much interest following its experimental realization [1,2,3,4,5,6,7,8,9]. Recent studies have revealed that it is difficult to do so when the two-body binding energy becomes large [26, 27] In this case, a spectrum of low-lying discrete states in the tightly confined directions can be populated, which makes a direct integration intractable. A spectrum of low-lying discrete states in the tightly confined directions can be populated, which makes a direct integration intractable This can be the case for strongly interacting atomic gases in general, the situation can be even worse in the presence of synthetic SOC, which typically enhances the two-body binding energy [28, 29]. The observations above necessitate a better understanding of the quasi-low-dimensional condition in cold atomic gases under synthetic SOC, as well as a more careful treatment of these systems. This can be done by a systematic investigation of the properties of two-body bound states in a cold atomic gas with quasi-low-dimensional geometry
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