Finite-momentum dimer bound state in a spin-orbit-coupled Fermi gas

We investigate the two-body properties of a spin-1/2 Fermi gas subject to a spin-orbit coupling induced by laser fields. When an attractive $s$-wave interaction between unlike spins is present, the system may form a dimer bound state. Surprisingly, in the presence of a Zeeman field along the direction of the spin-orbit coupling, the bound state obtains finite center-of-mass mechanical momentum, whereas under the same condition but in the absence of the two-body interaction, the system has zero total momentum. This unusual result can be regarded as a consequence of the broken Galilean invariance by the spin-orbit coupling. Such a finite-momentum bound state will have profound effects on the many-body properties of the system.

Figure 1

(a, b) Single-particle dispersion in the lower helicity branch. The horizontal dashed lines represent the chemical potential of the Fermi sea. Energy is in units of $E_r$. (c, d) Momentum distribution along the $z$ axis for the noninteracting Fermi gas is represented by (a) and (b), respectively. The relative population of the two spin components are listed in the plot, blue dashed line for spin-down atoms, and red thick line for spin-up atoms. (e, f) Momentum distribution along the $z$ axis of the dimer bound state. (g, h) Difference between $n_{\uparrow }\left(k_z\right)$ and $n_{\downarrow }(-k_z)$ for the cases shown in (e) and (f), respectively. For the left column [(a), (c), (e), and (g)] we have $\delta =0$ and $h=0.6E_r$; for the right column [(b), (d), (f), and (h)] we have $\delta =0.4E_r$ and $h=0.6E_r$. For the interacting case [(e)–(h)], the interaction strength is given by $1/\left(k_r{a}_s\right)=1$.

Figure 2

Binding energy ${\epsilon }_b$ and the magnitude of the bound-state momentum $q_0$ as functions of Zeeman field strengths $\delta$ and $h$. The coloring in (a) represents ${\epsilon }_b/E_r$, and that in (b) represents $q_0/k_r$. The white region is where no bound states can be found. The scattering length is given by $1/\left(k_r{a}_s\right)=1$.

Figure 3

(a) For spherical SOC, bound-state energy $E_q$ as a function of $q$ (momentum along the $z$ axis) for different values of Zeeman field strength, from top to bottom $\delta /E_r=0,0.2,0.4,0.6,0.8$ and $1/\left(k_r{a}_s\right)=1/2$ for all curves. (b) Ground-state momentum $q_0$ as a function of $\delta$ at different values of scattering length. From left to right, the curves correspond to $1/\left(k_r{a}_s\right)=-1$, $-1/2$, 0, 1/2, and 1, respectively. (c) $q_0$ as a function of $1/\left(k_r{a}_s\right)$ at $\delta /E_r=0.1$.