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arXiv:1305.4750 · Physical Review A

Ultracold collisions in the presence of synthetic spin-orbit coupling

Hao Duan, Li You, Bo Gao

Published May 20, 2013• 24 citations
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Abstract

We present an analytical description for ultracold collisions between two spin-$\frac{1}{2}$ fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin-$\frac{1}{2}$ fermions such as electrons in condensed matter and to ultracold pseudo-spin-$\frac{1}{2}$ atoms such as ${}^{6}$Li in its ground hyperfine state.

DOI
10.1103/physreva.87.052708

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We present an analytical description for ultracold collisions between two spin-12\frac{1}{2}21​ fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin-12\frac{1}{2}21​ fermions such as electrons in condensed matter and to ultracold pseudo-spin-12\frac{1}{2}21​ atoms such as 6{}^{6}6Li in its ground hyperfine state.
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-12\frac{1}{2}21​ 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.
We derive a pseudopotential in two dimensions (2D) with a 2D Rashba spin-orbit coupling (SOC), following in the same spirit of the frame transformation by Guan and Blume [Q. Guan and D. Blume, Phys. Rev. A 95, 020702(R) (2017)]. The frame transformation correctly describes the nontrivial phase accumulation and partial-wave couplings due to the presence of SOC, which modifies the original Fermi pseudopotential in free space, even when the length scale of the SOC is significantly larger than the two-body potential range. As an application, we apply our pseudopotential within the Lippmann-Schwinger equation to obtain an analytical scattering matrix. To demonstrate the validity of our approach, we compare our results with a numerical scattering calculation of the finite-range potential that shows excellent agreement over a wide range of scattering energies and SOC strengths. Our pseudopotential is applicable in the cases of a strong energy-dependent sss-wave scattering length and/or non-negligible ppp-wave interaction, where the original free-space pseudopotential fails. It sets an ideal starting point to explore many-body physics in the presence of synthetic SOC in cold atoms.
In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge fields using cold atoms. In the experiment it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range interatomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, paving the way for future characterizations of topological superfluid states in the experimentally relevant systems.
We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective 2D scattering amplitude and the algebraic equations for the two-atom bound-state energy. We further derive the effective 2D contact potential for the interaction between ultracold atoms in the quasi-2D confinement. This effective potential can be used in the research on many-body physics of quasi-2D ultracold Fermi gases with Rashba SOC.
Quantum droplets have aroused much attention recently in view of their successful observations in ultracold homonuclear atoms. In this paper, we demonstrate an alternative mechanism for the formation of quantum droplets in heteronuclear atomic systems, i.e., by applying synthetic spin-orbit coupling (SOC). Taking the Bose-Fermi mixture, for example, we show that by imposing a Rashba SOC between the spin states of fermions such that all fermions occupy the lower helicity branch, the greatly suppressed Fermi pressure can enable the formation of Bose-Fermi droplets even for very weak boson-fermion attractions, which are insufficient to bound a droplet if without SOC. In such SOC-induced quantum droplets, the boson-fermion density ratio universally depends on the SOC strength, and they occur in the mean-field collapsing regime but with a negative fluctuation energy, distinct from the interaction-induced droplets found in literature. The accessibility of these Bose-Fermi droplets in ultracold Cs-Li and Rb-K mixtures is also discussed. Our results shed light on the droplet formation in a vast class of heteronuclear atomic systems through the manipulation of single-particle physics.
We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective-2D scattering amplitude and the algebraic equations for the two-atom bound state energy. Based on these results, we further derive the effective 2D interaction potential between two ultracold atoms in the quasi-2D confinement with Rashba SOC. These results are crucial for the control of the 2D effective physics in quasi-2D geometry via the confinement intensity and the atomic three-dimensional scattering length.