Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices

We report on the experimental observation of an analog to a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. While particles in the excited band exhibit long-lived oscillations with a momentum-dependent frequency, a strikingly different behavior is observed for holes in the lowest band. An initial fast collapse is followed by subsequent periodic revivals. Both observations are fully explained by mapping the system onto a nonlinear pendulum.

Figure 1

(a) Principle of particle and hole excitation at a certain quasimomentum $q_0$ via lattice amplitude modulation (dotted lines) and subsequent band mapping process (solid lines) in momentum space. (b) Sketch of the semiclassical phase space of the lowest band (bottom) and second excited band (top). Solid lines depict equal-energy orbits. The shaded area corresponds to the occupied phase space after the lattice amplitude modulation. Due to the different bandwidths, the excited particles occupy only a small region of phase space around a single equal-energy orbit, while the holes are spread over many different orbits. The phase space evolution takes place clockwise along equal-energy orbits (indicated by arrows). (c) Typical photocurrent measurement after excitation to the excited band at $10E_{\mathrm{r}}$. Shown are the column densities of the momentum distribution at different times after the excitation. Atoms in the lowest band are represented by the central plateau. The excitations in the upper band clearly oscillate in momentum space.

Figure 2

(a) Comparison of measured frequencies with the results of (3) for different lattice depths and quasimomenta. Filled symbols represent measurements with noninteracting mixtures. Open symbols show data with interacting mixtures. (b) Oscillations in momentum space of the particles in the excited band at $10E_{\mathrm{r}}$ for two different trapping frequencies, ${\omega }_0=2\pi \times 66\mathrm{Hz}$ (circles) and ${\omega }_0=2\pi \times 50\mathrm{Hz}$ (diamonds). Solid lines are fits to the data. Extracted oscillation frequencies are $\omega =2\pi \times (148\pm 5)\mathrm{Hz}$ (circles) and $\omega =2\pi \times (107\pm 2)\mathrm{Hz}$ (diamonds). (c) $1/e$ lifetime of particles in the second excited band as a function of the scattering length for a three-dimensional lattice of $8E_{\mathrm{r}}$. All error bars solely correspond to fit errors, representing two standard deviations.

Figure 3

(a) Time evolution of hole depth relative to the maximum depth at $10E_{\mathrm{r}}$ and $q_0=0.5$ for different trapping frequencies $\omega /2\pi$, as given in the legend. Solid lines are semiclassical simulations as described in the text. (b) Rephasing of the hole in quasimomentum for longer evolution times at $2E_{\mathrm{r}}$, $q_0=0.0$, and ${\omega }_0=2\pi \times 63\mathrm{Hz}$. Solid line is a semiclassical simulation. (c) Rescaled time evolutions from (a) with scaling factors ${\omega }_0^2$ as derived from (4). The different simulations are not discernible due to the perfect scaling behavior. (d) Momentum resolved data of (b). Only the first Brillouin zone is depicted.

Figure 4

(a)–(d) Sketch of the hole dynamics at $q_0=0$. For short times, the distribution predominantly rotates. For certain parameters a periodic revival of the hole is observed. For long times $t\gg {\tau }_1$ all trajectories dephase and the hole signature is lost. (e)–(f) Projection of the hole distribution onto momentum space.