Radio-frequency spectroscopy of weakly bound molecules in spin-orbit-coupled atomic Fermi gases

We investigate theoretically radio-frequency spectroscopy of weakly bound molecules in an ultracold spin-orbit-coupled atomic Fermi gas. We consider two cases with either equal Rashba and Dresselhaus coupling or pure Rashba coupling. The former system has been realized very recently at Shanxi University [Wang et al., Phys. Rev. Lett. 109, 095301 (2012)] and MIT [Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)]. We predict realistic radio-frequency signals for revealing the unique properties of anisotropic molecules formed by spin-orbit coupling.

Figure 1

Franck-Condon factor of weakly bound molecules formed by equal Rashba and Dresselhaus spin-orbit coupling, in units of $E_B^{-1}$. Here we take $h=E_{\lambda }/2$ or ${\Omega }_R={\hslash }^2{k}_R^2/m$ and set $E_{\lambda }/E_B=0.5$, 1, and 2. The result without spin-orbit coupling is plotted by the thin dashed line. The inset shows the different contribution from the two final states at $E_{\lambda }/E_B=1$. The one with a remaining atom in the lower (upper) helicity branch is plotted by the dashed (dot-dashed) line.

Figure 2

Linear contour plot of momentum-resolved Franck-Condon factor, in units of ${\left(E_B{k}_R\right)}^{-1}$. Here we take $h=E_{\lambda }/2$ and consider $E_{\lambda }/E_B=0.1$, $0.5$, 1, and 2.

Figure 3

Energy distribution curve of the momentum-resolved Franck-Condon factor, in units of ${\left(E_B{k}_R\right)}^{-1}$. We consider several values of the rf frequency $\omega$ as indicated, under given parameters $h=E_{\lambda }/2$ and $E_{\lambda }=E_B$.

Figure 4

Zeeman-field dependence of the Franck-Condon factor at $E_{\lambda }=E_B$. Here we vary the effective Zeeman fields $h/E_{\lambda }=0.4$, $0.6$, $0.8$, and $1.0$. The inset shows the momentum-resolved Franck-Condon factor at $h=E_{\lambda }$.

Figure 5

Franck-Condon factor of weakly bound molecules formed by Rashba spin-orbit coupling, in units of $E_{\lambda }^{-1}$. Here we take ${\hslash }^2/\left(m\lambda a_s\right)=-1$ (dashed line), 0 (solid line), and 1 (dot-dashed line). In the deep BCS limit, ${\hslash }^2/\left(m\lambda a_s\right)\to -\infty$, the Franck-Condon factor peaks sharply at $\hslash \omega \simeq E_{\lambda }/2$ and becomes a $\delta$-like distribution.

Figure 6

Contour plot of momentum-resolved Franck-Condon factor of weakly bound molecules formed by Rashba spin-orbit coupling, in units of ${\left(E_{\lambda }{k}_R\right)}^{-1}$. The intensity increases from blue to red in a logarithmic scale. We consider ${\hslash }^2/\left(m\lambda a_s\right)=-1$ (a), 0 (b), and 1 (c).

Figure 7

Momentum-resolved Franck-Condon factor of Rashba molecules at ${\hslash }^2/\left(m\lambda a_s\right)=0$, shown in the form of energy distribution curves at several rf frequencies as indicated.