Session P43: Novel Phases in Quantum Gases

Stability of Bosonic atomic and molecular condensates near a Feshbach Resonance

Fermions near a Feshbach resonance exhibit a smooth crossover between a Bose-Einstein condensed state of molecules and a BCS superfluid of Cooper pairs. We study the analogous problem in Bosons, where there is a possibility of a phase transition between a molecular condensate (MC) and an atomic condensate (AC). We show that on the molecular side of the resonance at low densities, a MC-AC continuous transition is precluded by the AC state having a negative compressibility [cond-mat/0507460]. Instead, there is a mechanical collapse to a liquid-like state, analogous to a first order phase transition. We predict that sufficiently high densities (beyond those currently achieved in experiments) will push the system beyond its tricritical point and allow a continuous MC-AC phase transition.   

Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices

The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish between phase separation, a Luttinger liquid phase and a phase characterized by strong singlet pairing between the species. True long-range charge density waves exist with unequal hopping strengths.   

Luttinger's theorem and Phase Transitions in Bose-Fermi mixtures

A mixture of bosonic and fermionic atoms with a Feshbach resonance between the two can exhibit a range of phases as the energy of a fermionic bound state is varied. In each uniform phase a generalized statement of Luttinger's theorem can be made regarding the two Fermi surfaces, one associated with the atomic fermion and one with the bound-state molecule. The various phases can then be characterized by their different Luttinger constraints, which also depend on the presence or absence of a bosonic condensate. Interesting parallels can be drawn between this system and two others: the transition to the fractionalized Fermi liquid in Kondo lattice models, and fermion-pair condensation in the presence of mismatched Fermi surfaces.   

Spontaneous Symmetry Breaking and Defect Formation in a Quenched Ferromagnetic Spinor Bose-Einstein Condensate

We observe spontaneous symmetry breaking in a spinor Bose condensate of $^{87}$Rb that is quenched across a quantum phase transition to a ferromagnetic state. Using high spatial resolution maps of the vector magnetization of the condensate, we directly observe the spontaneous formation of inhomogeneous ferromagnetic regions separated by un-magnetized defects. The growth of these ferromagnetic regions are due to a dynamical instability, which determines their typical size and the time for their formation in accord with our observations.   

Thermodynamic properties of Bose-Hubbard model.

We perform Monte Carlo simulations of bosons in a three-dimensional optical lattice. We present accurate data for the ground state phase diagram and for the finite-temperature thermodynamic properties, including specific heat and entropy. Our data form a basis for an accurate thermometry of the system.   

Existence of Roton Excitations in Bose Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

Within the last decade, artificially engineered Bose Einstein Condensation has been achieved in atomic systems. Bose Einstein Condensates are superfluids just like bosonic Helium is and all interacting bosonic fluids are expected to be at low enough temperatures. One difference between the two systems is that superfluid Helium exhibits roton excitations while Bose Einstein Condensates have never been observed to have such excitations. The reason for the roton minimum in Helium is its proximity to a solid phase. The roton minimum is a consequence of enhanced density fluctuations at the reciprocal lattice vector of the stillborn solid. Bose Einstein Condensates in atomic traps are not near a solid phase and therefore do not exhibit roton minimum. We conclude that if Bose Einstein Condensates in an optical lattice are tuned near a transition to a Mott insulating phase, a roton minimum will develop at a reciprocal lattice vector of the lattice. Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition.   

Supersolid Bosons on Frustrated Optical Lattices

We consider an ultra-cold Bose gas on a triangular optical lattice subject to nearest neighbor repulsion, and determine the phase diagram using quantum Monte Carlo simulations. Already in the hard-core limit the system is found to exhibit an extended supersolid phase emerging from an order-by-disorder effect as a novel way of a quantum system to avoid classical frustration. We analyze the nature of the supersolid phase and its stability in competition with phase-separation, which we find to occurs in other regions of parameter space. Possible experimental realizations of our scenario and extensions to other lattice geometries are discussed as well as the connection to the physics of frustated quantum antiferromagnets.   

Frustrated two-dimensional XY models with cold atoms in optical lattices

We consider a system of cold bosonic atoms in a rotating optical lattice at finite temperature. We show that such system exhibits a non-trivial dependence of the condensation temperature and the superfluid order parameter on the vortex density due to commensuration effects of the vortex and optical lattices. We identify several vortex filling/lattice geometry combinations for which the vortex ordering pattern exhibits subtle order-by- disorder effects due to an interplay between multiple degeneracy of frustrated vortex configurations and thermal fluctuations.   

Winding Numbers in Rotating Bose Gases

The exact ground states of zero-temperature rotating Bose gases confined in quasi-two-dimensional harmonic traps are investigated numerically, for small numbers of alkali atoms. As the rotation frequency increases, the interacting Bose gas undergoes a series of transitions from one quantum Hall state to another. By tracking the change in ground state energy with an applied phase twist, we are able to calculate the winding (Chern) number characterizing the topological nature of the various bosonic quantum Hall states.   

Parafermionic states in rotating Bose-Einstein condensates

Rotating Bose-Einstein condensates in a trap are the place of a very rich physics. It has been predicted that, under appropriate conditions, they will behave like two dimensional electron systems in the fractional quantum Hall effect regime. In addition to the usual fractions, more exotic phases have also been predicted at filling factor $\nu=k/2$. These parafermionic states are described by the Read-Rezayi (RR) wave functions. We study how the system size and interaction act on the overlap between the true ground state and corresponding RR state. The quasihole excitations of the RR states are known to obey non-Abelian statistics. We numerically evaluate the degeneracy of these states and show it is in agreement with a formula given by E. Ardonne. We compute overlap between low-energy true eigenstates and quasihole ground states, and discuss in which cases such description is valid.   

Quantum magnetism with multicomponent polar molecules in an optical lattice

We consider dipolar molecules in an optical lattice prepared as a mixture of states with angular momentum $\ell=0$ and $\ell=1$. The $1/r^3$ interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that Mott states of such systems have a large variety of non-trivial spin orderings including SDW state at a wavevector that can be controlled by changing parameters of the system. As the Mott insulating phase is melted, we also show that an interesting winding in the phase of the order parameter can occur. Finally, we consider ways of detecting such phases experimentally.   

Biaxial nematic phase of two dimensional disordered rotor models and spin-one bosons in optical lattices

We show that the ground state of disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense. We present a mean-field analysis of the model and demonstrate that the biaxial phase is stable against small quantum fluctuations. We point out the possibility of experimental realization of such rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice in the limit of a large number of atoms per site and also suggest an imaging experiment to detect the biaxial nematicity in such systems.