In this paper, we study two-body bound states in two-component Bose gas with a one-dimensional spin-orbit coupling induced by Raman lasers. The finite Raman coupling strength generates coupling among three spin channels, resulting in the reconstruction of three bound-state bands. In addition, multiple resonances can be induced at finite scattering lengths. By tuning the interaction in one intraspecies channel, one bound-state band can be lifted and three resonances can be achieved, which can be observable under current experimental conditions in
87Rb atoms. This induced resonance is helpful for imaging the density modulation in the stripe phase.
We investigate the pairing physics in a three-component Fermi-Fermi mixture, where a few fermionic impurities are immersed in a noninteracting two-component Fermi gas with synthetic spin-orbit coupling (SOC), and interact attractively with one spin species in the Fermi gas. Because of the interplay of SOC and the spin-selective interaction, the molecular state intrinsically acquires a nonzero center-of-mass momentum, which results in a new type of Fulde-Ferrell (FF) pairing in spin-orbit coupled Fermi systems. The existence of the Fermi sea can also lead to the competition between FF-like molecular states with different center-of-mass momenta, which corresponds to a first-order transition between FF phases in the thermodynamic limit. As the interaction strength is tuned, a polaron-molecule transition occurs in the highly imbalanced system, where the boundary varies nonmonotonically with SOC parameters and gives rise to the reentrance of polaron states. The rich physics in this system can be probed using existing experimental techniques.
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
s-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 (
a,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.
We derive the universal relations for an ultracold two-component Fermi gas with a spin-orbit coupling (SOC) ${\ensuremath{\sum}}_{\ensuremath{\alpha},\ensuremath{\beta}=x,y,z}{\ensuremath{\lambda}}_{\ensuremath{\alpha}\ensuremath{\beta}}{\ensuremath{\sigma}}_{\ensuremath{\alpha}}{p}_{\ensuremath{\beta}}$, where
px,y,z and ${\ensuremath{\sigma}}_{x,y,z}$ are the single-atom momentum and Pauli operators for pseudospin, respectively, and the SOC intensity ${\ensuremath{\lambda}}_{\ensuremath{\alpha}\ensuremath{\beta}}$ could take an arbitrary value. We consider the system with an
s-wave short-range interspecies interaction, and ignore the SOC-induced modification for the value of the scattering length. Using the first-quantized approach developed by Tan [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)], we obtain the short-range and high-momentum expansions for the one-body real-space correlation function and momentum distribution function, respectively. For our system these functions are a $2\ifmmode\times\else\texttimes\fi{}2$ matrix in the pseudospin basis. We find that the leading-order (
1/k4) behavior of the diagonal elements of the momentum distribution function, i.e., ${n}_{\ensuremath{\uparrow}\ensuremath{\uparrow}}(\mathbf{k})$ and ${n}_{\ensuremath{\downarrow}\ensuremath{\downarrow}}(\mathbf{k})$, are not modified by the SOC. However, the SOC can significantly modify the large-
k behaviors of the distribution difference $\ensuremath{\delta}n(\mathbf{k})\ensuremath{\equiv}{n}_{\ensuremath{\uparrow}\ensuremath{\uparrow}}(\mathbf{k})\ensuremath{-}{n}_{\ensuremath{\downarrow}\ensuremath{\downarrow}}(\mathbf{k})$ as well as the nondiagonal elements of the momentum distribution function, i.e., ${n}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}(\mathbf{k})$ and ${n}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(\mathbf{k})$. In the absence of the SOC, the leading order of $\ensuremath{\delta}n(\mathbf{k})$, ${n}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}(\mathbf{k})$, and ${n}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(\mathbf{k})$ is
O(1/k6). When SOC appears, it can induce a term on the order of
1/k5 for these elements. We further derive the adiabatic relation and the energy functional. Our results show that the SOC can induce an additional term in the energy functional, which describes the contribution from the SOC to the total energy. In addition, the form of the adiabatic relation for our system is not modified by the SOC. Our results are applicable for the systems with any type of single-atom trapping potential, which could be either diagonal or nondiagonal in the pseudospin basis.
In this Letter we address the issue of how synthetic spin-orbit (SO) coupling can strongly affect three-body physics in ultracold atomic gases. We consider a system which consists of three fermionic atoms, including two spinless heavy atoms and one spin-1/2 light atom subjected to an isotropic SO coupling. We find that SO coupling can induce universal three-body bound states with a negative s-wave scattering length at a smaller mass ratio, where no trimer bound state can exist if in the absence of SO coupling. The energies of these trimers are independent of the high-energy cutoff, and therefore they are universal ones. Moreover, the resulting atom-dimer resonance can be effectively controlled by SO coupling strength. Our results can be applied to systems like a 6Li and 40K mixture.
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.