Bosonic hard spheres in quasi-one-dimensional bichromatic optical lattices

We calculated the phase diagram of a continuous system of hard spheres loaded in a quasi-one-dimensional bichromatic optical lattice. The wavelengths of both lattice-defining lasers were chosen to model an incommensurate arrangement. Densities of one particle and half a particle per potential well were considered. Our results can be compared directly to those of the experimental system [L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. 98, 130404 (2007)] from which our initial parameters were taken. The phase diagrams for both densities are significatively different from those obtained by describing the same experimental setup with a Bose-Hubbard model.

Figure 1

Energy per particle (minus the harmonic contribution, $E_{HO}/N)$ for $s_1$ = 16 in units of $E_{R_1}$ vs the filling fraction. Symbols correspond to the simulation results for different values of $s_2$ (from bottom to top $s_2$ = 1.2, $s_2$ = 1.3, and $s_2$ = 1.4, all of them in units of $E_{R_2})$. Full symbols correspond to simulation cells with 36 potential wells, open symbols correspond to cells with 54 minima, and the remaining ones display the case for 72 wells. Lines correspond to least-squares fits to the simulation data considering only the cell with 36 potential minima.

Figure 2

Phase diagram for the case of an average density of one particle per potential well. SF, superfluid; BG, Bose glass; MI, Mott insulator. $s_1$ and $s_2$ are the parameters defined in Eq. (3), in units of their respective recoil energies. See further explanation in the text.

Figure 3

Diffusion of the center of mass as a function of the Monte Carlo step index, $\tau$. All cases correspond to $s_2/E_{R_2}$ = 1.5 and different values of $s_1/E_{R_1}$. From bottom to top: $s_1$ = 16, 12, 10, 8, and 5. The solid line gives the slope corresponding to ${\rho }_s/\rho$ = 1. The error bars are only displayed in one case for simplicity.

Figure 4

Superfluid fraction as a function of $s_2$ (in units of $E_{R_2})$ for different $s_1$ values (in units of $E_{R_1})$. Open squares, $s_1/E_{R_1}$ = 16; full squares, $s_1/E_{R_1}$ = 12; open circles, $s_1/E_{R_1}$ = 8; full circles, $s_1/E_{R_1}$= 5. The error bars are only displayed in the last two cases for simplicity, the ones not shown being of the same size $[\Delta ({\rho }_s/\rho )\sim 0.01]$.

Figure 5

Same as Fig. 4, but for a density of half a particle per potential well. Full squares, $s_1/E_{R_1}$ = 10; open squares, $s_1/E_{R_1}$ = 8.

Figure 6

Same as in Fig. 2, but for an average density of half a particle per potential well. The full symbols correspond to our simulation results while the open symbols are from Ref. [21]. All the lines displayed are guides to the eye. See further explanation in the text.