Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of the $s$-wave scattering length

We consider interacting bosons in a two-dimensional square and a three-dimensional cubic optical lattice with a periodic modulation of the $s$-wave scattering length. At first we map the underlying periodically driven Bose-Hubbard model for large enough driving frequencies approximately to an effective time-independent Hamiltonian with a conditional hopping. Combining different analytical approaches with quantum Monte Carlo simulations then reveals that the superfluid–Mott-insulator quantum phase transition still exists despite the periodic driving and that the location of the quantum phase boundary turns out to depend quite sensitively on the driving amplitude. A more detailed quantitative analysis shows that the effect of driving can even be described within the usual Bose-Hubbard model provided that the hopping is rescaled appropriately with the driving amplitude.

Figure 1

First-order EPLT results (30) (solid) compared with GMFT results (34) (dots) for a 3D cubic lattice when the driving parameter $A/\left(\hslash \omega \right)$ is equal to 1 (red) and $2.2$ (blue), respectively.

Figure 2

Phase boundary of (a) a 2D square lattice and (b) a 3D cubic lattice for $J_0[A/\left(\hslash \omega \right)]=0.4$: third-order strong-coupling expansion result according to Eqs. (36) and (37) (red solid line), the QMC result in the thermodynamic limit (blue dots), and the second-order EPLT result (35) (green dashed line).

Figure 3

Relative critical (a) hopping $\Delta t_c=t_c\left(A\right)/t_c(A=0)$ and (b) chemical potential $\Delta {\mu }_c=[{\mu }_c\left(A\right)-(n-1)U]/$ $[{\mu }_c(A=0)-(n-1)U]$ from second-order EPLT as a function of driving parameter $A/\left(\hslash \omega \right)$ for a 3D cubic lattice at the tip of Mott lobes with $n=1$ (blue dots), $n=2$ (brown squares), $n=3$ (green diamonds), and $n=100$ (red triangles) as well as for a 2D square lattice (symbols with lines).

Figure 4

Quantum phase diagram of the effective model (20) (red solid line) and the new effective model (38) (dashed blue line) with the driving parameter $A/\left(\hslash \omega \right)=1$ for a 3D cubic lattice.

Figure 5

Total density difference and superfluid density of the original model (20) and the effective model (38) for $t/U=0.05$, $A/\left(\hslash \omega \right)=0.4$, $N=8\times 8$, and $T=U/\left(20N\right)$ in a 2D square lattice.