Realization of a $\mathrm{SU}(2)\times \mathrm{SU}(6)$ System of Fermions in a Cold Atomic Gas

We report the realization of a novel degenerate Fermi mixture with an $\mathrm{SU}(2)\times \mathrm{SU}(6)$ symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium ${}^{171}\mathrm{Yb}$ with the nuclear spin $I=1/2$ and ${}^{173}\mathrm{Yb}$ with $I=5/2$ below the Fermi temperature $T_F$ as $0.46T_F$ for ${}^{171}\mathrm{Yb}$ and $0.54T_F$ for ${}^{173}\mathrm{Yb}$. The same scattering lengths for different spin components make this mixture featured with the novel $\mathrm{SU}(2)\times \mathrm{SU}(6)$ symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the $\mathrm{SU}(2)\times \mathrm{SU}(6)$ Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.

Figure 1

Experimental setup. Laser beams for the OSG separation, optical pumping, and an optical lattice are shown. The OSG laser beam, whose wavelength is close to that of the lattice, is slightly tilted with respect to others. This does not cause any serious errors in the observed spin population.

Figure 2

Optical Stern-Gerlach separation of nuclear spins. (a) Time-of-flight image of a degenerate Fermi gas of ${}^{173}\mathrm{Yb}$ without the OSG separation. The image is taken after 12 ms ballistic expansion. The azimuthally averaged distribution is also shown on the right hand side. The temperature of $0.14T_F$ is determined from the Thomas-Fermi fit (red line). The observed distribution clearly deviates from the classical Gaussian shape, indicated by the gray line. (b) Schematic view of an OSG effect. The atoms in the $m_F=+5/2$ state is pushed downward in the figure, whereas the $m_F=-5/2$ upward. (c) Optical Stern-Gerlach separation of spin components in the Fermi gas of ${}^{173}\mathrm{Yb}$. The expansion time is 8 ms. Integration of the images along the horizontal axis are also shown on the right hand side. (d) The simulated distribution under the current experimental condition is shown.

Figure 3

Time-of-flight images of the quantum degenerate Fermi-Fermi mixture with spin degrees of freedom, (a) for two-spin mixture of ${}^{171}\mathrm{Yb}$ and (b) for 6-spin mixture of ${}^{173}\mathrm{Yb}$. The expansion time is 9 ms for ${}^{171}\mathrm{Yb}$ and 8 ms for ${}^{173}\mathrm{Yb}$. The density distributions integrated over the vertical direction $y$ are also shown on the right hand side. From the Gaussian fits we can estimate the temperatures $T=95\mathrm{nK}$ and $T=87\mathrm{nK}$ for ${}^{171}\mathrm{Yb}$ and ${}^{173}\mathrm{Yb}$, respectively. The dotted lines correspond to the Fermi velocities $v_F=\sqrt{2k_B{T}_F/m}$ for each isotope. The images are averaged over 5 independent measurements.

Figure 4

Left: Optical Stern-Gerlach separation of spin components in the ${}^{171}\mathrm{Yb}-{}^{173}\mathrm{Yb}$ quantum degenerate mixture (a) for ${}^{171}\mathrm{Yb}$ and (b) for ${}^{173}\mathrm{Yb}$. The expansion time is 6 ms and the images are averaged over 8 independent measurements. Integrations of the images along the horizontal axis are also shown on the right hand side. Right: Spin manipulation by optical pumping, applied to single-species samples. (c) The OSG separation is applied after optical pumping to the $m_F=+1/2$ state of ${}^{171}\mathrm{Yb}$. (d) For ${}^{173}\mathrm{Yb}$, optical pumping allows us to prepare either a single-component gas in the $m_F=+5/2$ state (left) or a two-component mixture of the $m_F=+3/2$ state and the $m_F=+5/2$ state (right).

Figure 5

Quasimomentum distribution of (a) ${}^{171}\mathrm{Yb}$ and (b) ${}^{173}\mathrm{Yb}$ in the $\mathrm{SU}(2)\times \mathrm{SU}(6)$ two-species mixture in an optical lattice. The density distributions integrated along the vertical direction are also shown below. The atom numbers are $0.4\times {10}^4$ for ${}^{171}\mathrm{Yb}$ and $1.5\times {10}^4$ for ${}^{173}\mathrm{Yb}$, respectively. The images are taken after linear ramping down of the lattice in 0.5 ms, followed by a ballistic expansion of (a) 12 and (b) 13 ms. The dotted lines indicate the domain of the 1st Brillouin zone, which equals twice the recoil momentum $\hslash k$. The tails in the measured distribution may be due to the breakdown of adiabaticity during the band-mapping sequence.