Mean-field analysis of quantum phase transitions in a periodic optical superlattice

We analyze the various phases exhibited by a system of ultracold bosons in a periodic optical superlattice using the mean-field decoupling approximation. We investigate for a wide range of commensurate and incommensurate densities. We find the gapless superfluid phase, the gapped Mott insulator phase, and gapped insulator phases with distinct density wave orders.

Figure 1

Variation of average density $\rho$ as a function of the chemical potential $\mu$ for $U=2$, but for different values of $\lambda$ starting from 0.5 (red solid curve) to 5.5 (magenta double dash dot curve) at the intervals of 1.0.

Figure 2

Variation of average superfluid density ${\rho }^s$ as a function of $\mu$ for the same set of parameters as in Fig. 1.

Figure 3

Variation of average density of a unit cell $\rho$ as a function of the chemical potential $\mu$ for $U=5$, but for different values of $\lambda$ starting from 0.2 (red solid curve) to 7.2 (orange large dashed curve) at intervals of 1.0.

Figure 4

Variation of average superfluid density of a unit cell as a function of $\mu$ for the same set of parameters as in Fig. 3.

Figure 5

Variation of average density of a unit cell $\rho$ as a function of the chemical potential $\mu$ for $U=10$, but for different values of $\lambda$, varying from 0.2 (red solid curve) to 14.2 (orange large dashed curve) at intervals of 2.0.

Figure 6

Variation of average superfluid density of a unit cell as a function of $\mu$ for the same set of parameters as in Fig. 5.

Figure 7

Variation of average density of a unit cell $\rho$ as a function of the chemical potential $\mu$ for $U=15$, but for different values of $\lambda$, varying from 0.2 (red solid curve) to 18.2 (violet large dot dashed curve) at intervals of 3.0.

Figure 8

Variation of average superfluid density of a unit cell as a function of $\mu$ for the same set of parameters as in Fig. 7.