Orbital-driven melting of a bosonic Mott insulator in a shaken optical lattice

In order to study the interesting interplay between localized and dispersive orbital states in a system of strongly interacting ultracold atoms in an optical lattice, we investigate the possibility to coherently couple the lowest two Bloch bands by means of resonant periodic forcing. For bosons in one dimension we show that a strongly interacting Floquet system can be realized, where at every lattice site two (and only two) near-degenerate orbital states are relevant, whose tunneling matrix elements differ in sign and magnitude. By smoothly tuning both states into resonance, the system is predicted to undergo an orbital-driven Mott-insulator-to-superfluid transition. As a consequence of kinetic frustration, this transition can be either continuous or first order, depending on parameters such as lattice depth and filling.

Figure 1

(a) Dimerized lattice with $V_1/V_0=0.5$. (b) Impact of $V_1/V_0$ on $J_2/J_1,{\Delta }_{10}$, and ${\Delta }_{21}$ for $V_0/E_R=10$. (c) Most dominant loss channels, scattering into the third band (zero-photon process) and driving-induced coupling (single-photon process), are off resonant due to dimerization. (d) Lattice parameters vs $V_0/E_R$ for $V_1/V_0=0.5$ and ${\mathrm{Rb}}^{87}$.

Figure 2

(a) Sketch of the effective model, gray (white) circles correspond to the $\alpha =1$ (0) state at each site $\ell$, with energy $\delta$ (0). (b) Ground-state compressibility ${\partial }_{\mu }n{E}_R$ in the $\mu \text{−}\delta$ plane for $V_0/E_R=10$ and $V_1/V_0=1/2$. (c) Correlations ${\chi }_{{\alpha }^{\prime }\alpha }^{\ell }\equiv \langle {\widehat{b}}_{{\alpha }^{\prime }\ell }^{†}{\widehat{b}}_{\alpha 0}\rangle /\sqrt{n_{{\alpha }^{\prime }}{n}_{\alpha }}$ and imbalance $n_0-n_1$ for fixed filling $n=1$ vs $\delta$, with $V_1/V_0=0.5$ and $V_0/E_R=15,10,5$ (from top to bottom). Numerical data in (b) and (c) are obtained for $M=30$ rungs under periodic boundary conditions using TEBD in imaginary time [48, 49], with bond dimensions (b) 14 and (c) 30.

Figure 3

Real-time (RT) evolution of the effective model (4) with three bands (3B) $\alpha =0,1,2$, obtained by TEBD [48, 49] with bond dimensions (a) 24, (b) 22, and (c) 22–40. (a) Occupations and overlaps with the [imaginary time-evolved (IT)] ground states of the 3B and 2B model. Starting in the ground state at $\delta ={\epsilon }_1-\omega =1E_R,\delta$ is lowered linearly to $\delta =-0.5E_R$ within a time of $T_r=500\hslash /E_R$, for $n=1,V_0/E_R=10,V_1/V_0=0.5,K/E_R=0.5$, and $M=16$ rungs under periodic boundary conditions. (b) After-ramp overlap for $M=10$, like in (a), but varying $T_r$ and $K$. (c) After-ramp overlap for $M=10$, like in (a), but varying $V_1/V_0$.