Quantum Degenerate Fermi Gas in an Orbital Optical Lattice

Spin-polarized samples and spin mixtures of quantum degenerate fermionic atoms are prepared in selected excited Bloch bands of an optical checkerboard square lattice. For the spin-polarized case, extreme band lifetimes above 10 s are observed, reflecting the suppression of collisions by Pauli’s exclusion principle. For spin mixtures, lifetimes are reduced by an order of magnitude by two-body collisions between different spin components, but still remarkably large values of about 1 s are found. By analyzing momentum spectra, we can directly observe the orbital character of the optical lattice. The observations demonstrated here form the basis for exploring the physics of Fermi gases with two paired spin components in orbital optical lattices, including the regime of unitarity.

Figure 1

(a) Lattice geometry in the $xy$ plane for $\mathrm{\Delta }V=0$ (left) and $\mathrm{\Delta }V<0$ (right). The gray squares denote the unit cell of the lattice. (b) Sections of the lattice potential along the dashed lines in (a).

Figure 2

(a) Band mapping images showing the population of the $n$th band in the $n$th Brillouin zones (BZs). Panel (a1) shows the case if no excitation is applied; the other panels [(a2)–(a4)] show the cases of excitation to the second, fourth, and seventh bands, respectively. (b) The map of BZs is shown with (from left to right) the first, second, fourth, and sixth and seventh BZs highlighted. (c) Regular momentum spectra corresponding to the band mapping images in (a). The color map on the left edge shows the normalized optical density. (d) Horizontal (red line graphs) and diagonal (blue line graphs) sections through the momentum spectra in (c) along the red dashed and blue dashed lines in (c1), respectively. (e) Momentum spectra for completely filled first, second, fourth, and seventh bands (from left to right) calculated for the same parameters as used in (c). The particle numbers in (c) and (e) are normalized to unity and parametrized with the same color map, shown in (c). In all plots in (a),(c)–(e) $V_0=12E_{\mathrm{rec}}$.

Figure 3

(a) Model for band relaxation dynamics of spin-polarized samples after the second band is selectively populated, according to the band mapping image showing dominant population of the second BZ. (b) Observed populations in the first ($N_1$, red symbols) and second ($N_2$, blue symbols) bands are plotted versus the holding time. The solid traces result from the fit model in (a). (c) Extended relaxation model for balanced spin mixtures, including a class of atoms with population $Z_1$ residing in the first band with additional excitation of motion along the $z$ axis. Binary collision processes (illustrated by blue arrows) exchange pairs of spin-up and spin-down particles between $|N_2⟩$ and $|Z_1⟩$. (d) Observed populations in the first ($N_1+Z_1$, red symbols) and second ($N_2$, blue symbols) bands are plotted versus the holding time. The solid traces result from the fit model in (c). In (b) and (d), $V_0=7E_{\mathrm{rec}}$ and $\mathrm{\Delta }V=3.1E_{\mathrm{rec}}$. The error bars in (b) and (d) show statistical errors for averages of 20–30 experimental runs.