Supersolid phase in atomic gases with magnetic dipole interaction

A major obstacle for the experimental realization of a supersolid phase with cold atomic gases in an optical lattice is the weakness of the nearest-neighbor interactions achievable via magnetic dipole-dipole interactions. In this paper, we show that by using a large filling of atoms within each well, the characteristic energy scales are strongly enhanced. Within this regime, the system is well described by the rotor model, and the qualitative behavior of the phase diagram derives from mean-field theory. We find a stable supersolid phase for realistic parameters with chromium atoms.

Figure 1

Phase diagram for $U\sim V$: The Mott insulating or solid phases appear at commensurate fillings (solid bars) and the critical hopping at the tip of the incompressible lobes scales as $t_c\sim 1/n$. In turn, the transition from the superfluid (SF) into a supersolid (SS) phase behaves as $t_{\mathit{ss}}\sim n$, i.e., for large fillings $n\gg 1$ the influence of quantum fluctuations is reduced and the transition from the superfluid into the supersolid phase is well described within mean-field theory.

Figure 2

(a) Shape of the Fourier-transformed dipole-dipole interaction ${\chi }_{\mathbf{k}}$ plotted in the $M$ direction. (b) Superfluid dispersion relation for different values of $\gamma$. At $\gamma ={\gamma }_c$ the roton minima occurs. The inset shows the different directions within the Brillouin zone.

Figure 3

Supersolid dispersion relation, given in different directions of the reduced Brillouin zone, as shown in the inset. The results are in qualitative agreement with previous analysis in the Hubbard model[22, 23].