Coherent Control of Dressed Matter Waves

We demonstrate experimentally that matter waves can be coherently and adiabatically loaded and controlled in one-, two-, and three-dimensional strongly driven optical lattices. This coherent control is then used in order to reversibly induce the superfluid-Mott insulator phase transition by changing the strength of the driving. Our findings pave the way for studies of driven quantum systems and new methods for controlling matter waves.

Figure 1

(a) Principle of the coherent control of the tunneling parameter $J$. A condensate in a lattice is characterized by $J$ and the on-site interaction $U$ (above). While varying the lattice depth changes both $U$ and $J$ (left) to $U^{\prime }$ and $J^{\prime }$, strong driving selectively changes $J$ to $J^{\prime }=J_{\mathrm{eff}}$ (right). (b) Experimental setup for a three-dimensional driven optical lattice.

Figure 2

Coherent control of a BEC inside a driven 1D lattice. (a) Time-of-flight interference patterns. The length scales have been converted into momentum units, with $1p_{\mathrm{rec}}$ corresponding to $138\mu \mathrm{m}$. Here $\omega /2\pi =6\mathrm{kHz}$ and $V_0=18E_{\mathrm{rec}}$. (b) Time dependence of $K_0$ and $U/J_{\mathrm{eff}}$. Inset: $U_{\mathrm{eff}}/U$ as a function of $K_0$. For comparison, the (theoretical) behavior of $|J_{\mathrm{eff}}/J|$ is also shown.

Figure 3

Adiabaticity in driven optical lattices. (a) Dependence of $\sigma /{\sigma }_0$ (see text) on $V_0$ in a 1D lattice for a linear ramp $K_0=0$ to $K_0=2.3$ in 15 ms, a holding time at $K_0=2.3$ of 200 ms, and an identical ramp back to $K_0=0$. Here $\omega /2\pi =3\mathrm{kHz}$ (open triangles) and $\omega /2\pi =6\mathrm{kHz}$ (solid squares). (b) Dependence of $\sigma /{\sigma }_0$ on the driving frequency for a fixed $V_0=5.7E_{\mathrm{rec}}$. The ramp time was 10 ms with 2 ms holding time. (c) Minimum value of $\hslash \omega /J$ (solid squares) and $\hslash \omega /Jz$ (open triangles) for different lattice dimensions.

Figure 4

Driving-induced Mott insulator transition. (a) In a driven 3D lattice of constant depth ($V_0=11E_{\mathrm{rec}}$, $\omega /2\pi =6\mathrm{kHz}$), $K_0$ was ramped from 0 to $K_0=1.62$ in 4 ms and back. (b) Visibility of the interference pattern as a function of $U/6J_{\mathrm{eff}}$ varying $K_0$ for $V_0=11E_{\mathrm{rec}}$ (black symbols) and $V_0=12.2E_{\mathrm{rec}}$ (red symbols) with the dotted lines indicating the respective visibilities after returning to $K_0=0$. The blue region is a fit (its width indicating the statistical error) to the data for varying $V_0$ at $K_0=0$. Vertical grey line: border between the superfluid (SF) and MI regions. (c) Excitation spectrum measured by modulating $J_{\mathrm{eff}}$. Plotted here is the thermal fraction (normalized to the thermal fraction without excitation) calculated from a bimodal fit to the BEC after ramping down the lattice to $V_0=4E_{\mathrm{rec}}$. Here $V_0=10.3E_{\mathrm{rec}}$, $K_0=0.7$ (red circles) and $V_0=11E_{\mathrm{rec}}$, $K_0=1.8$ (black squares). The modulation depths for $K_0$ were 0.8 and 0.3, respectively. The solid lines are fits to guide the eye, and the vertical scales have been offset for clarity.