Quantum phases of ultracold bosonic atoms in a one-dimensional optical superlattice

We analyze various quantum phases of ultracold bosonic atoms in a periodic one-dimensional optical superlattice. Our studies have been performed using the finite-size density-matrix renormalization group method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.

Figure 1

A superlattice [curve (c)] is formed by the superposition of two optical lattices [curves (a) and (b)], with the frequency of one being the double of the other. This results in an energy shift of $\lambda$ for alternate sites.

Figure 2

Density $\rho$ plotted against the chemical potential for various values of $\lambda$ at a fixed $U=10$ and $t=1$.

Figure 3

The chemical potential $\mu$ plotted against density $\rho$ for various values of $\lambda$, with $U=10$.

Figure 4

On-site number density plotted against lattice site index at density $\rho =0.5$.

Figure 5

On-site number density plotted against lattice site index at density $\rho =1.0$.

Figure 6

Momentum distribution $n(k=0)$ plotted against various values of $\lambda$ for densities $\rho =0.5,0.7$, and 1.0.

Figure 7

Structure function $S(k)$ vs the momentum $k$ for density of $0.5$.

Figure 8

Structure function $S(k)$ vs the momentum $k$ for density of 1.0 for different values of $\lambda$.

Figure 9

Structure function $S(k)$ vs the momentum $k$ for density of 0.7 for different values of $\lambda$.

Figure 10

S($k=\pi$) vs $\lambda$ for three different density values, $\rho =0.5,0.7$, and $1.0$.

Figure 11

Phase diagram for the system of an optical superlattice.