Momentum-resolved radio-frequency spectroscopy of a spin-orbit-coupled atomic Fermi gas near a Feshbach resonance in harmonic traps

We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wave function, binding energy, and effective mass, are determined from the two-particle solution of two interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Fermi golden rule and take into account the effect of harmonic traps within local density approximation. The total radio-frequency spectroscopy is discussed as functions of temperature and spin-orbit coupling strength. Our results give a qualitative picture of radio-frequency spectroscopy of a resonantly interacting spin-orbit-coupled Fermi gas and can be directly tested in atomic Fermi gases of ${}^{40}$K atoms at Shanxi University and ${}^6$Li atoms at the Massachusetts Institute of Technology.

Figure 1

Binding energies $-{\varepsilon }_B/E_{\lambda }$ of two atoms with zero c.m. momentum $\mathbf{q}=0$ as functions of the $s$-wave scattering length $1/\left(k_R{a}_s\right)$ for three typical values of the Zeeman field. The horizontal dotted lines are the threshold energies $2E_{\min }$ where the bound states disappear. Here, we have introduced $k_R=m\lambda /{\hslash }^2$ and $E_{\lambda }=m{\lambda }^2/{\hslash }^2$ as the units of the wave vector and energy, respectively.

Figure 2

The effective mass of weakly bound molecules, $\gamma \equiv M_x/\left(2m\right)$, as functions of the interaction strength $1/\left(k_R{a}_s\right)$ for three typical values of the Zeeman field.

Figure 3

The rf spectroscopy of the atomic component in a harmonic trap at different values of the Zeeman field, that is, $h/E_{\lambda }=0.6,0.8,1.0$. Here, we have taken $E_B/E_{\lambda }=2$, $E_F/E_{\lambda }=1$, and $T/T_F=1$.

Figure 4

The momentum-resolved rf spectroscopy of the harmonically trapped atomic component for different values of the Zeeman field and interaction strength. Here, we have taken $E_F/E_{\lambda }=2$, $T/T_F=1$, and $\sigma =0.1$. In addition, we have also defined $K_x=k_x-k_R$ (see text), which moves the whole spectra to the right by an amount $k_R$.

Figure 5

The rf spectroscopy of a single molecule for different values of the Zeeman field at given c.m. momenta $\mathbf{q}/k_R=0$ and $\mathbf{q}/k_R=0.5$. Here, we have chosen an interaction strength $E_B/E_{\lambda }=1$.

Figure 6

The momentum-resolved rf spectroscopy of a single molecule for different values of the Zeeman field at given c.m. momenta ${\mathbf{q}}_x/k_R=0$ and $\mathbf{q}/k_R=0.5$. Here, we have chosen the interaction strength $E_B/E_{\lambda }=1$.

Figure 7

The total rf spectroscopy of a harmonically trapped ideal gas mixture of fermionic atoms and bosonic molecules at different Zeeman fields. Here, we take $E_B/E_{\lambda }=1$, $E_F/E_{\lambda }=1$, and $T/T_F=0.2$.

Figure 8

The total rf spectroscopy of a harmonically trapped ideal gas mixture of fermionic atoms and bosonic molecules as a function of temperature at a fixed Zeeman field strength $h/E_{\lambda }=0.5$. Here, we use $E_B/E_{\lambda }=1$ and $E_F/E_{\lambda }=1$.

Figure 9

The total momentum-resolved rf spectroscopy of a harmonically trapped ideal gas mixture of fermionic atoms and bosonic molecules. The left panel shows the spectra at different Zeeman field strengths at a fixed temperature $T/T_F=0.2$, while the right panel shows the temperature dependence of spectroscopy at a fixed Zeeman field $h/E_{\lambda }=0.5$. Here, we take $E_B/E_{\lambda }=1$ and $E_F/E_{\lambda }=1$. Note the different color scales in the left and right panels.