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arXiv:1101.5633 · Physical Review A

Supersolid phase of cold fermionic polar molecules in two-dimensional optical lattices

Liang He, Walter Hofstetter

Published May 25, 2011• 34 citations
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Abstract

We study a system of ultracold fermionic polar molecules in a two-dimensional square lattice interacting via both the long-range dipole-dipole interaction and a short-range on-site attractive interaction. Singlet-superfluid, change density wave, and supersolid phases are found to exist in the system. We map out the zero-temperature phase diagram and find that the supersolid phase is considerably stabilized by the dipole-dipole interaction and thus can exist over a large region of filling factors. We study the melting of the supersolid phase with increasing temperature, map out a finite-temperature phase diagram of the system at fixed filling, and determine the parameter region where the supersolid phase can possibly be observed in experiments.

DOI
10.1103/physreva.83.053629

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We study a system of ultracold fermionic polar molecules in a two-dimensional square lattice interacting via both the long-range dipole-dipole interaction and a short-range on-site attractive interaction. Singlet-superfluid, change density wave, and supersolid phases are found to exist in the system. We map out the zero-temperature phase diagram and find that the supersolid phase is considerably stabilized by the dipole-dipole interaction and thus can exist over a large region of filling factors. We study the melting of the supersolid phase with increasing temperature, map out a finite-temperature phase diagram of the system at fixed filling, and determine the parameter region where the supersolid phase can possibly be observed in experiments.
We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.
We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by means of the dynamical mean-field approximation. It is demonstrated that a supersolid state, where an s-wave superfluid coexists with a density-wave state with a checkerboard pattern, is stabilized by attractive onsite interactions on a square lattice. Our new finding here is that a confining potential plays an invaluable role in stabilizing the supersolid state. We establish a rich phase diagram at low temperatures, which clearly shows how the insulator, the density wave and the superfluid compete with each other to produce an intriguing domain structure. Our results shed light on the possibility of the supersolid state in fermionic optical lattice systems.
We model a system of ultracold fermionic dipolar molecules on a two-dimensional square lattice. Assuming that the molecules are in their nondegenerate hyperfine ground state, and that the dipole moment is polarized perpendicular to the plane (as in the recent experiments on 40K^{40}\mathrm{K}40K-87Rb^{87}\mathrm{Rb}87Rb molecules), we approximate these molecules as spinless fermions with long-range repulsive dipolar interactions. We use mean-field theory to obtain the restricted phase diagram as a function of the filling, the strength of interaction, and the temperature. We find a number of ordered density-wave phases in the system, as well as phase separation between these phases. A Monte Carlo analysis shows that the higher-period phases are usually suppressed in the exact solution.
In this work we discuss the emergence of p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic p-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological px + ipy superfluid of identical microwave-dressed polar molecules.
We consider a mixture of hard-core bosonic polar molecules, interacting via repulsive dipole-dipole interaction, and one atomic bosonic species. The mixture is confined on a two-dimensional square lattice and, at low enough temperatures, can be described by the two-component Bose-Hubbard model. The latter displays an extremely rich phase diagram including solid, superfluid, and supersolid phases. Here, we mainly focus on the checkerboard molecular solid, stabilized by the long-range dipolar interaction, and study how the presence of atoms affects its robustness both at zero and finite temperatures. We find that, due to atom-molecule interactions, solid phases can be stabilized at both (much) lower strengths of dipolar interaction and higher temperatures, than when no atoms are present. As a byproduct, atoms also order in a solid phase with the same melting temperatures as for molecules. Finally, we find that for large enough interaction between atoms and molecules, a paired supersolid phase can be stabilized.
A high-finesse optical cavity allows the establishment of long-range interactions between bosons in an optical lattice when most cold-atom experiments are restricted to short-range interactions. Supersolid phases have recently been experimentally observed in such systems. Using both exact quantum Monte Carlo simulations and the Gutzwiller approximation, we study the ground-state phase diagrams of a two-dimensional Bose-Hubbard model with infinite-range interactions which describes such experiments. In addition to superfluid and insulating Mott phases, the infinite-range checkerboard interactions introduce charge-density waves and supersolid phases. We study here the system at various particle densities, elucidate the nature of the phases and quantum phase transitions, and discuss the stability of the phases with respect to phase separation. In particular we confirm the existence and stability of a supersolid phase detected experimentally.