Relaxation Dynamics of a Fermi Gas in an Optical Superlattice

This Letter comprises an experimental and theoretical investigation of the time evolution of a Fermi gas following fast and slow quenches of a one-dimensional optical double-well superlattice potential. We investigate both the local tunneling in the connected double wells and the global dynamics towards a steady state, i.e., a time-independent state. The local observables in the steady state resemble those of a thermal equilibrium state, whereas the global properties indicate a strong nonequilibrium situation.

Figure 1

(a) Sketch of the preparation and of the detection of the local odd-even density imbalance according to the lattice ramp sequence shown in (b).

Figure 2

(a) Odd-even contrast $C_{\exp }$ together with a fit of a damped oscillation for $V_G=11.7(9)E_{\mathrm{rec},G}$. Error bars show the statistical error of four averaged data sets. The dashed red line is the adapted solid line from panel (d). (b) Measured oscillation period vs lattice depth together with the tight-binding prediction $T=h/(4J_G)$, where $J_G$ is obtained from a band structure calculation. (c) Experimental power-law exponent of the damped oscillation. In (b) and (c) error bars are the fit errors. (d) Theoretical results for the odd-even contrast ($V_G=11.7E_{\mathrm{rec},G}$). Dots show the local results for the center of the trap $c_0=\sum \mathbf{(}(n_{2l+1}-n_{2l})/(n_{2l+1}+n_{2l})\mathbf{)}$ in the continuum model, averaged over 10 double wells, which is approximately reproduced by the Bessel-like function with an initial potential offset of $\mathrm{\Delta }=4J$ (black line) [20]. The red solid line shows the density-averaged contrast $C$ as defined in the text. (e) Theoretical evolution of the local odd-even density imbalance $(n_{2l+1}-n_{2l})/n_1(t=0)$ in the trap in the continuum model. The black dashed line shows the predicted Bloch period $T_B(l)$.

Figure 3

Evolution of the quasimomentum distribution after the slow quench for $V_{R,f}=0$ for experiment (a) and the theory for the continuum model (b). (c) Experimental data for a slow quench for $V_{R,f}<0.2E_{\mathrm{rec},R}$ compared with the theoretical result for $V_{R,f}=0.1E_{\mathrm{rec},R}$ (d). (e),(f) Evolution of the quasimomentum contrast $C_{12}$ for different values of $V_{R,f}$. Experimental data (e) and corresponding theoretical results (f). The time axis of the theoretical result at $V_{R,f}=0$ is rescaled by a factor 0.87 in order to better match the experimentally observed features. This factor can stem from the uncertainty of the experimental parameters.

Figure 4

(a) Hopping amplitude and local gap of the corresponding homogeneous model (calculated by band-structure calculations) versus the depth of the red lattice potential. (b) Theoretical density profiles for $V_{R,f}=0$ of the continuum model. Gray lines show the densities $n_{2l+1}$ and $n_{2l}$ versus double-well index $l$ before the slow quench. The colored lines show the steady state after a slow (${\tau }_{\text{quench}}=6\mathrm{ms}$), a sudden (${\tau }_{\text{quench}}=0.5\mathrm{ms}$), and an adiabatic quench.