Figure 1

Top: Expansion of an initial Gaussian wave packet in a flat lattice potential, obtained by the numerical propagation under Hamiltonian (2). When no driving potential is applied ($K=0$), $\sigma (t)$ increases following Eq. (4). For $J=0.1E_{\mathrm{rec}}$ (black solid line) the expansion is clearly quadratic initially and becomes linear at long times. Setting $J=0.05E_{\mathrm{rec}}$ [red (gray) solid line] reduces the expansion rate as expected. By applying a periodic driving potential the tunneling can be renormalized to an effective value $J_{\mathrm{eff}}$. Tuning $K_0=1.22$ reduces $J_{\mathrm{eff}}$ so that the expansion of the condensate (dashed red line) reproduces the $J=0.05E_{\mathrm{rec}}$ result. Setting $K_0=2.404$—first zero of the Bessel function—produces coherent destruction of tunneling (CDT), and the condensate no longer expands with time (blue dash-dotted line). Inset: Detail of the periodically driven result ($K_0=1.22$). The driven expansion on average reproduces the $J=0.05E_{\mathrm{rec}}$ result, but shows small oscillations with the same frequency of the driving. The amplitude of these oscillations decreases with increasing driving frequency. Bottom: Experimental comparison of the free expansion of a condensate ($K_0=0$) with a condensate experiencing CDT ($K_0=2.4$). As predicted, the expansion of the second condensate is strongly suppressed.Reuse & Permissions

Figure 2

Dynamical suppression of tunneling in a periodically driven lattice. The effective tunneling parameter was calculated assuming a simple linear expansion (open symbols) and by taking into account the exact expansion dynamics (solid symbols). In the latter case the agreement with the theoretically expected scaling (solid line) is clearly better. The experimental parameters were $J/h=240\hspace{0.5em}\mathrm{Hz}$ and $\omega /2\pi =4\hspace{0.5em}\mathrm{kHz}$, and the expansion time was 150 ms.Reuse & Permissions

Figure 3

(a) Effective tunneling for resonant driving in a tilted lattice (photon-assisted tunneling). The effective tunneling parameters were calculated for two different initial condensate sizes [around 15 $\mathrm{\mu }\mathrm{m}$ (open symbols) and around 17 $\mathrm{\mu }\mathrm{m}$ (solid symbols)] using Eq. (4). For comparison, (b) shows the same experimental data with the renormalized tunneling parameter calculated assuming linear expansion. One clearly sees that in this case the experimental data interpolate between a linear Bessel scaling (solid line) and a quadratic scaling (dashed line).Reuse & Permissions