Exploring dynamic localization with a Bose-Einstein condensate

We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse points with the theoretical predictions, suggests the feasibility of systematic quasienergy band engineering.

Figure 1

Width ${\Delta }_{\sin }$ of the lowest quasienergy band of an optical cosine lattice under sinusoidal driving as function of the dimensionless amplitude (29), for $V_0∕E_{\mathrm{r}}=2$ (dots), 3 (long dashes), 5 (short dashes), and 10 (full line). The inset quantifies the extent of band narrowing for values of $K_0$ close to the first zero $j_{0,1}=2.405$ of the Bessel function $J_0$.

Figure 2

Width ${\Delta }_{\mathrm{sqw}}$ of the lowest quasienergy band of an optical cosine lattice under square-wave driving as function of the dimensionless amplitude (29), for $V_0∕E_{\mathrm{r}}=2$ (dots), 3 (long dashes), 5 (short dashes), and 10 (full line). The inset illustrates that an exact band collapse occurs when $K_0$ is a nonzero integer multiple of 2.

Figure 3

(Color online) Absolute value of the effective hopping matrix element $J_{\mathrm{eff}}$ for a condensate in an optical lattice with depth $V_0∕E_{\mathrm{r}}=6$ under the influence of sinusoidal (open boxes) and square-wave (triangles) driving, normalized to the “bare” hopping element $J$ which governs the condensate spreading in the undriven lattice. The lines correspond to the approximations (43, 44). The driving frequencies $\omega ∕2\pi$ were $1.0\mathrm{kHz}$ for sinusoidal driving, and $1.5\mathrm{kHz}$ for the square-wave case.

Figure 4

(Color online) Dephasing times for a condensate in an optical lattice with depth $V_0∕E_{\mathrm{r}}=9$ under the influence of square-wave (triangles; left scale) and sinusoidal (boxes; right scale) driving.