General formalism for ultracold scattering with isotropic spin-orbit coupling

Abstract

A general treatment of ultracold two-body scattering in the presence of isotropic spin-orbit coupling (SOC) is presented. Owing to the mixing of different partial-wave channels, scattering with SOC is in general a coupled multichannel problem. A systematic method is introduced to analytically solve a class of coupled differential equations by recasting the coupled-channel problem as a simple eigenvalue problem. The exact Green's matrix in the presence of SOC is found, which readily gives the scattering solutions for any two identical particles in any total angular momentum subspace having negligible center-of-mass momentum. Application of this formalism to two spin-1 bosons shows the ubiquitous low-energy threshold behavior for systems with isotropic SOC. A modified threshold behavior shows up, which does not occur for the spin-orbit coupled spin-| system. We also confirm the parity-breaking mechanism for the spontaneous emergence of handedness, which has been proposed by Duan et al. [H. Duan, L. You, and B. Gao, Phys. Rev. A 87, 052708 (2013)]. Additionally, a two-body bound state is found for any arbitrarily small and negative scattering length. Our study sheds light on the few-body side of SOC physics and provides one step towards understanding ultracold scattering in a non-Abelian gauge field.

Ultracold collisions between spin-orbit-coupled dipoles: General formalism and universality

“…Similar to Refs. [49][50][51][52][53][54], we focus on the scattering in the center-of-mass frame. With the presence of 3D isotropic SOC, the Hamiltonian in relative coordinates is given by,…”

“…(1) (except for an additional phase associated with the i ℓ term) have been derived previously in Refs. [51,52]:…”

“…[38] in 161 Dy, which allowed for the realization of a long-lived SOC degenerate dipolar Fermi gas. The bosonic system of SOC dipolar gas has also been theoretically investigated previously in BEC of 52 Cr [39].…”

Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law

“…If two-body short-range interactions are added, the modified single-particle dispersion curves can significantly alter the properties of weakly-bound two-and three-body states. This has been demonstrated extensively for two identical fermions for 1D, 2D, and 3D spin-orbit coupling [32][33][34][35][36][37][38][39][40][41] and for two identical bosons for 2D and 3D spin-orbit coupling [41][42][43][44][45] but not for the 1D spin-orbit coupling considered in this work. The present work presents the first study of how the experimentally most frequently realized 1D spin-orbit coupling terms modify the three-boson energy spectrum.…”

Generating an effective magnetic lattice for ultracold atoms

“…For Feshbach resonances with widths much larger than this value, a uniform interacting situation arises; otherwise position dependent interaction strength happens. The SOC gauge field can change low energy atomic interaction properties, leading to modified thresholds [64,65] and p-wave behaviors [66]. When combined with ML, the modified atomic collision interactions will likely bring in rich possibilities of interesting many body physics.…”