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arXiv:1701.03857 · Physical Review A

Multichannel molecular state and rectified short-range boundary condition for spin-orbit-coupled ultracold fermions near p -wave resonances

Xiaoling Cui

Published Mar 7, 2017• 7 citations
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Abstract

We study the interplay of spin-orbit coupling (SOC) and strong $p$-wave interactions to the scattering property of spin-$\frac{1}{2}$ ultracold Fermi gases. Based on a two-channel square-well potential generating $p$-wave resonance, we show that the presence of an isotropic SOC, even for its length being much longer than the potential range, can greatly modify the $p$-wave short-range boundary condition (BC). As a result, the conventional $p$-wave BC cannot predict the induced molecules near $p$-wave resonances, which can be fully destroyed due to strong interference between the $s$- and $p$-wave channels. By analyzing the intrinsic reasons for the breakdown of the conventional BC, we propose a $p$-wave BC that can excellently reproduce the exact molecule solutions and also equally apply for a wide class of single-particle potentials besides SOC. This work reveals the significant effect of SOC on both the short- and long-range properties of fermions near $p$-wave resonances, paving the way for future explorations of interesting few- and many-body physics in such systems.

DOI
10.1103/physreva.95.030701

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We study the interplay of spin-orbit coupling (SOC) and strong ppp-wave interactions to the scattering property of spin-12\frac{1}{2}21​ ultracold Fermi gases. Based on a two-channel square-well potential generating ppp-wave resonance, we show that the presence of an isotropic SOC, even for its length being much longer than the potential range, can greatly modify the ppp-wave short-range boundary condition (BC). As a result, the conventional ppp-wave BC cannot predict the induced molecules near ppp-wave resonances, which can be fully destroyed due to strong interference between the sss- and ppp-wave channels. By analyzing the intrinsic reasons for the breakdown of the conventional BC, we propose a ppp-wave BC that can excellently reproduce the exact molecule solutions and also equally apply for a wide class of single-particle potentials besides SOC. This work reveals the significant effect of SOC on both the short- and long-range properties of fermions near ppp-wave resonances, paving the way for future explorations of interesting few- and many-body physics in such systems.
We present exact solutions of a two-body problem for spin-1/21/21/2 fermions with isotropic spin-orbit (SO) coupling and interacting with an arbitrary short-range potential. We find that in each partial-wave scattering channel, the parametrization of a two-body wave function at short interparticle distance depends on the scattering amplitudes of all channels. This reveals the mixed-partial-wave scattering induced by SO couplings. By comparing with results from a square-well potential, we investigate the validity of original pseudopotential models in the presence of SO coupling. We find the sss-wave pseudopotential provides a good approximation for low-energy solutions near sss-wave resonances, given the length scale of SO coupling much longer than the potential range. However, near ppp-wave resonance the ppp-wave pseudopotential gives low-energy solutions that are qualitatively different from exact ones, based on which we conclude that the ppp-wave model can not be applied to the fermion system if the SO coupling strength is larger or comparable to the Fermi momentum.
Synthetic spin-orbit-coupled quantum gases have been widely studied both experimentally and theoretically in the past decade. As shown in previous studies, this modification of single-body dispersion will in general couple different partial waves of the two-body scattering and thus distort the wave function of few-body bound states which determines the short-distance behavior of many-body wave function. In this work, we focus on the two-component Fermi gas with one-dimensional or three-dimensional spin-orbit coupling (SOC) near an sss-wave resonance. Using the method of effective field theory and the operator product expansion, we derive universal relations for both systems, including the adiabatic theorem, viral theorem, and pressure relation, and obtain the momentum distribution matrix $\ensuremath{\langle}{\ensuremath{\psi}}_{a}^{\ifmmode\dagger\else\textdagger\fi{}}(\mathbf{q}){\ensuremath{\psi}}_{b}(\mathbf{q})\ensuremath{\rangle}$ at large q\mathbf{q}q (a,ba,ba,b are spin indices). The momentum distribution matrix shows both spin-dependent and spatial anisotropic features. And the large momentum tail is modified at the subleading order thanks to the SOC. We also discuss the experimental implication of these results depending on the realization of the SOC.
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.
Ultracold gases of interacting spin-orbit-coupled fermions are predicted to display exotic phenomena such as topological superfluidity and its associated Majorana fermions. Here, we experimentally demonstrate a route to strongly interacting single-component atomic Fermi gases by combining an s-wave Feshbach resonance (giving strong interactions) and spin-orbit coupling (creating an effective p-wave channel). We identify the Feshbach resonance by its associated atomic loss feature and show that, in agreement with our single-channel scattering model, this feature is preserved and shifted as a function of the spin-orbit-coupling parameters.