Driven optical lattices as strong-field simulators

We argue that ultracold atoms in strongly shaken optical lattices can be subjected to conditions similar to those experienced by electrons in laser-irradiated crystalline solids, but without introducing secondary polarization effects. As a consequence, one can induce nonperturbative multiphoton-like resonances due to the mutual penetration of ac-Stark-shifted Bloch bands. These phenomena can be detected with a combination of currently available laboratory techniques.

Figure 1

Lowest three Bloch bands of a 1D optical lattice with depth $V_0=5.7E_{\mathrm{r}}$. The lowest band gap is $2.763E_{\mathrm{r}}$ at $k=k_{\mathrm{L}}$.

Figure 2

Escape probabilities from the lowest Bloch band after pulses with linear switch-on and switch-off ramps of 10-ms duration each, and a holding time of 2 ms, during which a specified value $K_0^{\max }$ of the scaled amplitude (4) is reached. Driving frequencies $\omega /(2\pi )$ correspond to ${}^{87}\mathrm{Rb}$ in an optical lattice with $\lambda =842$ nm. Light, $K_0^{\max }=0.7$; black, $K_0^{\max }=1.3$. Of particular interest is the unexpected, strong, and narrow resonance at $\omega /(2\pi )=5.3$ kHz.

Figure 3

Escape probability versus both driving frequency $\omega /(2\pi )$ and maximum scaled amplitude $K_0^{\max }$, for the same pulse shape as employed in Fig. 2.

Figure 4

Quasienergies ${\varepsilon }_n(k)$ for the 1D optical lattice driven with frequency $\omega /(2\pi )=5.30$ kHz, and scaled amplitudes $K_0=0.7$ (a), $1.0$ (b), and $1.3$ (c). The areas shaded in gray, extending from $k=-0.1k_{\mathrm{L}}$ to $k=+0.1k_{\mathrm{L}}$, mark the range of wave numbers explored by the initial wave packet. The insets show how the quasienergy band $n=1$ (above) is pinched through with increasing $K_0$ by the band $n=2$, displaced downward by $3\hslash \omega$. This causes the nonperturbative resonance observed in Fig. 2.

Figure 5

Stückelberg oscillations of the escape probability in response to prolongation of the plateau duration $t_{\mathrm{hold}}$, for $\omega /(2\pi )=5.30$ kHz, and $K_0^{\max }=1.0$ (dashed) and $1.3$ (solid line).