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arXiv:1101.0913 · Physical Review B

Supersolid polar molecules beyond pairwise interactions

Lars Bonnes, Stefan Weßel

Published Apr 11, 2011• 6 citations
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Abstract

We explore the phase diagram of ultracold bosonic polar molecules confined to a planar optical lattice of triangular geometry. External static electric and microwave fields can be employed to tune the effective interactions between the polar molecules into a regime of extended two- and three-body repulsions of comparable strength, leading to a rich quantum phase diagram. In addition to various solid phases, an extended supersolid phase is found to persist deep into the three-body dominated regime. While three-body interactions break particle-hole symmetry explicitly, a characteristic supersolid-supersolid quantum phase transition is observed, which indicates the restoration of particle-hole symmetry at half-filling. We revisit the spatial structure of the supersolid at this filling, regarding the existence of a further supersolid phase with three inequivalent sublattices, and provide evidence that this state is excluded also at finite temperatures.

DOI
10.1103/physrevb.83.134511

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We explore the phase diagram of ultracold bosonic polar molecules confined to a planar optical lattice of triangular geometry. External static electric and microwave fields can be employed to tune the effective interactions between the polar molecules into a regime of extended two- and three-body repulsions of comparable strength, leading to a rich quantum phase diagram. In addition to various solid phases, an extended supersolid phase is found to persist deep into the three-body dominated regime. While three-body interactions break particle-hole symmetry explicitly, a characteristic supersolid-supersolid quantum phase transition is observed, which indicates the restoration of particle-hole symmetry at half-filling. We revisit the spatial structure of the supersolid at this filling, regarding the existence of a further supersolid phase with three inequivalent sublattices, and provide evidence that this state is excluded also at finite temperatures.
We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in (Büchler et al 2007 Nat. Phys. 3 726), such a system is described by an extended Bose–Hubbard model of hard-core bosons that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground-state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime and determine the stability of the crystalline phases towards strong two-body interactions.
We investigate the finite-temperature phase diagram of polar molecules confined in a quasi-two-dimensional geometry by a harmonic potential along the polarization axis. We employ quantum Monte Carlo simulations to explore the strongly correlated regime accessible with current experimental setups. By tuning temperature and confinement strength, we identify a rich set of phases, including normal fluid, superfluid, supersolid, cluster crystal, and bilayer crystal states. Our results reveal the emergence of crystallization upon increasing temperature, highlighting the nontrivial role of thermal fluctuations in dipolar systems. In particular, we show that a bilayer crystal with one molecule per lattice site can be stabilized by varying the confinement strength at fixed interaction. Moreover, we show evidence of layering of superfluid states with phase coherence between the two layers. These findings provide insight into the interplay between interactions, confinement, and temperature in low-dimensional dipolar systems, and suggest new directions for engineering quantum phases with ultracold polar molecules.
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 the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.
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 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.