Rashba spin-orbit-coupled atomic Fermi gases

We investigate theoretically BEC-BCS crossover physics in the presence of Rashba spin-orbit coupling in a system of a two-component Fermi gas with and without a Zeeman field that breaks the population balance between the two components. A bound state (Rashba pair) emerges because of the spin-orbit interaction. We study the properties of Rashba pairs using standard pair fluctuation theory. At zero temperature, the Rashba pairs condense into a macroscopic mixed-spin state. We discuss in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various physical observables which characterize the properties of the system and can be measured in experiment.

Figure 1

Left panel: Bound-state energies $E_B$ as functions of scattering length for different Zeeman fields $h$. The horizontal dashed lines represent the threshold energy $2{\epsilon }_{\min }$. Right panel: Corresponding two-body phase shifts $\delta (\mathbf{q}=\mathbf{0},\omega )$ for different Zeeman fields $h$. $E_B$ and $h$ are in units of $m{\lambda }^2/{\hslash }^2$; $a_s$ is in units of ${\hslash }^2/\left(m\lambda \right)$.

Figure 2

Effective mass $\gamma \equiv M_{\perp }/\left(2m\right)$ as function of scattering length for different Zeeman fields $h$. $h$ is in units of $m{\lambda }^2/{\hslash }^2$ and $a_s$ in units of ${\hslash }^2/\left(m\lambda \right)$. For $h⩾1$, the two-body bound state exists only for $a_s>0$.

Figure 3

Chemical potential $\mu$ (a), pairing gap ${\Delta }_0$ (b), and population of spin-up component $n_{\uparrow }$ (c) as functions of scattering length $a_s$ for different values of the Zeeman field $h$ at $\lambda k_F/E_F=2$. Here $k_F={\left(3{\pi }^{2}n\right)}^{1/3}$ and $E_F={\hslash }^2{k}_F^2/\left(2m\right)$ are the Fermi momentum and Fermi energy, respectively.

Figure 4

Quasiparticle dispersion spectra $E_{\mathbf{k}+}$ (solid lines) and $E_{\mathbf{k}-}$ (dashed lines) shown in units of $E_F$ for $\mathbf{k}$ in the transverse plane [(a), $\theta =\pi /2$] and along the $z$ axis [(b), $\theta =0$] for $\lambda k_F/E_F=2$, $h/E_F=2$.

Figure 5

Pairing fields at unitarity (i.e., $1/a_s=0$) for $h=0$ (top row), $h=1E_F$ (middle row), and $h=2E_F$ (bottom row) with $\lambda k_F/E_F=2$. In each row, from left to right, we display $|\langle {\psi }_{\mathbf{k}\uparrow }{\psi }_{-\mathbf{k}\downarrow }\rangle |$, $|\langle {\psi }_{\mathbf{k}\uparrow }{\psi }_{-\mathbf{k}\uparrow }\rangle |$, and $|\langle {\psi }_{\mathbf{k}\downarrow }{\psi }_{-\mathbf{k}\downarrow }\rangle |$ (all in units of $E_F$), respectively.

Figure 6

Densities of states ${\rho }_{\uparrow }$ (a) and ${\rho }_{\downarrow }$ (b) at unitarity and $\lambda k_F/E_F=2$.

Figure 7

(a) Zero-temperature dynamic spin structure factor $S_S(0,\omega )$ at unitarity and $\lambda k_F/E_F=2$. (b) Static spin structure factor $S_S\left(0\right)$ as a function of the SO coupling strength.