Spin-orbit-coupled two-electron Fermi gases of ytterbium atoms

We demonstrate all-optical implementation of spin-orbit coupling (SOC) in a two-electron Fermi gas of ${}^{173}\mathrm{Yb}$ atoms by coupling two hyperfine ground states with a narrow optical transition. Due to the $\mathrm{SU}\left(N\right)$ symmetry of the ${}^{1}S_0$ ground-state manifold which is insensitive to external magnetic fields, an optical ac Stark effect is applied to split the ground spin states, which exhibits a high stability compared with experiments on alkali-metal and lanthanide atoms, and separate out an effective spin-$\frac{1}{2}$ subspace from other hyperfine levels for the realization of SOC. The dephasing spin dynamics when a momentum-dependent spin-orbit gap is suddenly opened and the asymmetric momentum distribution of the spin-orbit-coupled Fermi gas are observed as a hallmark of SOC. The realization of all-optical SOC for ytterbium fermions should offer a route to a long-lived spin-orbit-coupled Fermi gas and greatly expand our capability of studying spin-orbit physics with alkaline-earth-metal-like atoms.

Figure 1

Schematic diagram of the Raman transition configuration. (a) A single-component Fermi gas of ${}^{173}\mathrm{Yb}$ atoms is prepared with a bias magnetic field along the $(-\widehat{x}+\widehat{y})$ direction and exposed to a pair of 556-nm Raman beams (linearly and circularly polarized, respectively) at ${45}^{\circ }$ relative to the $\widehat{y}$ axis. The direction of the gravity is along the $(\widehat{x}-\widehat{y})$ direction. (b) A pair of Raman beams couples two ground-state hyperfine levels with the single-photon detuning $\mathrm{\Delta }=1$ GHz from the excited state $F^{\prime }=\frac{7}{2}$. (c) A six-component Fermi gas of ${}^{173}\mathrm{Yb}$ atoms with $N=5.0\times {10}^4$ is obtained at $T/T_F\le 0.27$. A time-of-flight image is obtained after 11-ms free expansion using the 399-nm ${}^{1}S_0-{}^{1}P_1$ transition. Each spin state $|m_F\rangle$ is spatially separated by the OSG light, followed by 399-nm absorption imaging. (d) With optical pumping during evaporative cooling, a single-component Fermi gas in $\left|m_F=\frac{5}{2}\right.〉$ is cooled down to $T/T_F\simeq 0.5$. (e) Using the ${}^{1}S_0-{}^{3}P_1$ intercombination line, $m_F$ states are resolved. The spectrum of ${}^{173}\mathrm{Yb}$ atoms is obtained by a ${\sigma }^{+}$-polarized light in the 5-G bias field along the imaging axis. The black solid curve indicates the expected relative line strength of the transition.

Figure 2

Spin dynamics with spin-orbit coupling. Two-photon Rabi oscillation is monitored with a two-photon detuning of $\delta =-4.0\left(3\right)E_r$ and a Rabi frequency ${\mathrm{\Omega }}_R=4.8\left(3\right)E_r$. (a) The single-particle energy dispersion of dressed states. (b) The spin imbalance, defined as $\left(N_{|\downarrow \rangle }-N_{|\uparrow \rangle }\right)/\left(N_{|\downarrow \rangle }+N_{|\uparrow \rangle }\right)$ for the atom number $N_{|\uparrow \rangle }$ and $N_{|\downarrow \rangle }$, is measured via 399-nm imaging together with the OSG light. The predicted spin dynamics for noninteracting fermions (blue solid curve) is consistent with the measurement (blue circle). The data points represent the average of ten measurements.

Figure 3

Momentum distribution of a spin-orbit-coupled Fermi gas of ${}^{173}\mathrm{Yb}$ atoms. The Raman coupling with $\mathrm{\Omega }=1.6\left(3\right)E_R$ and $\delta =0.1\left(3\right)$ is abruptly switched off for a gas of $N=9\times {10}^3$ atoms followed by 399-nm absorption imaging, as shown in the inset. (a) Atomic clouds after time-of-flight expansion for a spin $\sigma =\{\uparrow ,\downarrow \}$ shift in the opposite direction due to SOC. (b) The integrated momentum reveals an asymmetric feature for $|\uparrow \rangle$ (blue circle) and $|\downarrow \rangle$ (red diamond) while the momentum distribution is symmetric without SOC (gray curve).

Figure 4

Integrated momentum asymmetry along the $\widehat{x}$ direction for different values of two-photon detuning. The momentum asymmetry of the spin-orbit-coupled Fermi gas is characterized by $[n_{\sigma }\left(k\right)-n_{\sigma }(-k)]/n_{\sigma }^o$, where $n_{\sigma }^o=\text{max}\left[n_{\sigma }\left(k\right)\right]$ denotes the maximum peak density of the momentum distribution in $k$ space for $\sigma =\{\uparrow ,\downarrow \}$. Two-photon detuning takes different values of $\delta =\{-2.9,-1.9,0.1,1.1,3.6\}\times E_r$ from the top to bottom. (b) The theoretical momentum asymmetry is shown for different values of detuning. As $\delta >0$ becomes large where most of atoms are loaded into the $|{\downarrow }^{\prime }\rangle$ state, the momentum asymmetry of $|\downarrow \rangle$ disappears after projection onto the bare state while $|\uparrow \rangle$ atoms show prominent momentum asymmetry due to spin-orbit coupling.