Multiband Spectroscopy of Ultracold Fermions: Observation of Reduced Tunneling in Attractive Bose-Fermi Mixtures

We perform a detailed experimental study of the band excitations and tunneling properties of ultracold fermions in optical lattices. Employing a novel multiband spectroscopy for fermionic atoms, we can measure the full band structure and tunneling energy with high accuracy. In an attractive Bose-Fermi mixture we observe a significant reduction of the fermionic tunneling energy, which depends on the relative atom numbers. We attribute this to an interaction-induced increase of the lattice depth due to the self-trapping of the atoms.

Figure 1

(a) Experimental sequence. (b) Experimental procedure in momentum space. (c) Typical absorption image and column sum with nonresonant modulation. The atoms occupy the first Brillouin zone. (d) With resonant modulation: Particle-hole excitations are clearly visible.

Figure 2

Momentum-resolved band structure of noninteracting fermions in an optical lattice of $5E_r$: Shown are the column densities of the momentum distributions for different modulation frequencies. Atoms in the first Brillouin zone are represented by the central plateau. Missing particles are holes, representing the reduced zone scheme. Narrow peaks at higher momenta are the outcoupled particles, representing the extended zone scheme.

Figure 3

(a) Extracted dispersion of the third band. Red circles are the center-of-mass of the excited atoms. The dashed line is an inhomogeneous 1D calculation, reproducing the data qualitatively. The red solid line is a fit to the data for $0.55<q<0.85k_{\mathrm{BZ}}$ with a homogeneous 1D band structure. Shaded areas show the dispersion for slightly different lattice depths. (b) Histogram showing the relative number of outcoupled atoms.

Figure 4

(a) Sketch of the effective potential for different bosonic fillings. Fermions are more tightly bound if attractive bosons are added. (b) Shift of the outcoupled momentum against the relative atom number $N_{\mathrm{Rb}}/N_{\mathrm{K}}$ at $5E_r$ at a fixed modulation frequency of 34 kHz. Lower outcoupled momenta correspond to a deeper lattice. The shaded area is a guide to the eye. (c) Fermionic band structure for different bosonic admixtures. The red squares correspond to $N_{\mathrm{K}}=5.7\times {10}^4$, the green diamonds to $N_{\mathrm{K}}=5.3\times {10}^4$ and $N_{\mathrm{Rb}}=1.56\times {10}^5$, and the blue circles to $N_{\mathrm{K}}=2.2\times {10}^4$ and $N_{\mathrm{Rb}}=2.63\times {10}^5$. Solid lines are fitted dispersions. (d) Histogram showing the relative number of outcoupled atoms.