Figure 1

(Color online) (a) Numerical results for the quasienergy spectrum of the driven mean-field Bose-Hubbard model for an eight-site system with $\omega =16$. The width of the spectrum is modulated by the Bessel function ${\mathcal{J}}_0\left(K/\omega \right)$ and displaced by the interaction energy $g=0.5$, in full agreement with the analytical solution [Eq. (7)]. (b) Plot of the critical interaction, $g_c$, at which the system becomes dynamically unstable when prepared in the $p=0$ state. The driving frequencies are $\omega =4$ (solid black line) and $\omega =8$ (dotted-dashed blue line). The critical interaction diverges at $K/\omega =0$ and peaks at the Bessel function zeros (vertical dashed lines). When $J_{\text{eff}}$ is negative $g_c$ becomes zero, indicating that dynamical instability occurs for any positive value of $g$.Reuse & Permissions

Figure 2

(Color online) Critical interaction, $g_c$, for a system driven at frequencies of $\omega =4$ (solid black line) and $\omega =5$ (dotted-dashed blue line). The Bessel function zeros are marked by the vertical dashed (red) lines. The labels $p=0$ and $p=\pi$ indicate the momentum of the Floquet state about which the instability analysis is made; when $J_{\text{eff}}$ is positive we use $p=0$, but when the effective tunneling is negative the analysis is done for $p=\pi$ (see text). For the higher driving frequency instability does not occur for $g\le 1$, in agreement with experimental results [4].Reuse & Permissions

Figure 3

(Color online) Dynamics of a condensate in a parabolic trap. Time is measured in units of the inverse tunneling $J^{-1}$. At $t=0$ the trap is shifted by 25 lattice spacings to induce the condensate into motion. System parameters are $g=0.1$ and $\omega =4$. (a) In the absence of driving, the condensate sloshes periodically from side to side of the trap with a well-defined frequency. (b) For $K/\omega =2$, $J_{\text{eff}}$ is reduced in amplitude, and so the frequency of the oscillation is correspondingly reduced. (c) For $K/\omega =2.40$, the tunneling is completely suppressed since $J_{\text{eff}}\simeq 0$, and the time evolution of the condensate is thus frozen. (d) For $K/\omega =3$, $J_{\text{eff}}$ becomes negative. The trap potential thus appears inverted to the condensate, which is rapidly expelled from the center.Reuse & Permissions