Session T4: Vortices, Rotation, and Synthetic Gauge Fields

Rotating Ultracold Fermi Gases: Reduction in the Moment of Inertia Above the Superfluid Transition Temperature

There has been considerable interest in the viscosity of ultracold Fermi gases which is found to be anomalously suppressed even in the normal phase. This suppression, believed to derive from pseudogap effects, is also associated with a reduction in the moment of inertia, as measured by the Duke group. In this talk we address the relationship between viscosity and the reduced moment of inertia. We emphasize the very strong relation of the latter to the anomalous normal state diamagnetism of the high temperature superconductors. We present a simple physical picture for the origin of these related phenomena. Our picture gains strong support from establishing sum rule compatibility and leads to testable predictions.   

Vortices in spin-orbit-coupled Bose-Einstein condensates

We discuss realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates. We show that, contrary to common intuition, rotation of the trap containing a spin-orbit-coupled condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to intrinsically time-dependent Hamiltonian. We propose alternative methods to create stable static vortex configurations: (1) to rotate both the lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We derive the effective Hamiltonians for spin-orbit condensates under such perturbations for most currently known realistic laser schemes that induce synthetic spin-orbit couplings and we solve the Gross-Pitaevskii equation for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates and the appearance of unusual vortex arrangements.   

2D Vortex Dynamics and Quantum Tunneling in the Lowest Landau Level Limit

We examine the collective excitation spectrum of a rapidly rotating cold Bose gas in the lowest Landau level regime. The Gross-Pitaevskii action can be equivalently expressed in terms of the angular momentum state expansion of the boson field or in terms of 2D vortex positions. We emphasize the very different role of visible and invisible vortices in the latter formulation and discuss the significance of non-standard non-local Berry phase coupling between separated vortices in the boson action. We also consider dissipative quantum tunneling of a single vortex, allowing for linear coupling to a bath of quadratic fluctuations of the lattice following the Caldeira-Leggett model, and comment on differences between the lowest Landau level limit and the case of vortices in a slowly rotating superfluid.   

Screening properties and phase transitions in unconventional plasmas for Ising-type quantum Hall states

Utilizing large-scale Monte-Carlo simulations, we investigate an unconventional two-component classical plasma in two dimensions that interacts with two different Coulomb interactions. This plasma controls the behavior of the norms and overlaps of the quantum-mechanical wavefunctions of Ising-type quantum Hall states. It also relates to a model for a rotating two-component Bose-Einstein condensate with an Andreev-Bashkin drag interaction. The plasma differs fundamentally from that which is associated with the two-dimensional XY model and Abelian fractional quantum Hall states. We find that this unconventional plasma undergoes a Berezinskii-Kosterlitz-Thouless phase transition from an insulator to a metal and that the parameter values corresponding to Ising-type quantum Hall states lie on the metallic side of this transition. This result verifies the required properties of the unconventional plasma used to demonstrate that Ising-type quantum Hall states possess quasiparticles with non-Abelian braiding statistics.   

Edge excitations of bosonic fractional quantum Hall phases in optical lattices

With the rapid development in ultracold gases, the realization of a fractional quantum Hall state on a lattice draws nearer. We investigate the impact of finite size effects in these kind of systems including different trapping potentials. A good understanding of finite size effects is essential for designing experiments and the edge excitations will likely be the best way to experimentally determine the topological order of the bulk. We find different fractional quantum Hall phases for bosons in a circular harmonic trap as the flux of the synthetic gauge field is varied, including phases like $\nu=1/2$ and $\nu=2/3$ with different edge spectra.   

Finite temperature phase structures of hard-core bosons in an optical lattice with a synthetic magnetic field

We study finite temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to a synthetic magnetic field by employing the gauged CP$^1$ model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model with only the phase as a dynamical variable.   

Modulated superfluid phases of lattice bosons in a non-abelian gauge field

We consider the two-component Bose-Hubbard model subject to non-abelian gauge fields that give rise to spin-orbit coupling. We obtain the phase diagram based on an extended mean field theory and find many exotic superfluid phases (polarized, striped, checkerboard). We characterize the superfluid phases by finding their collective excitations within random phase approximation (RPA) and discuss the possibility of novel topological defects.   

Bosons under an artificial staggered magnetic field in an optical ladder

We calculate the ground state properties of cold bosons in an frustrated optical ladder due to an artificial staggered magnetic field. By investigating the momentum distribution of bosons via a Lanczos diagonalization method, we find the signature of the transition from the Meissner to vortex states as a function of the staggering strength of the field. Various states with different frustrations are discussed.   

Chiral Mott insulator of kinetically frustrated bosons

We study the phase diagram of the fully frustrated Bose Hubbard (FFBH) model - the presence of a $\pi$-flux through each plaquette leads to kinetic frustration for the bosons making this a nontrivial model of quantum frustration. The FFBH model is equivalent to a model of frustrated quantum XY spins, or a fully frustrated Josephson junction array where one tunes the ratio of the charging energy to the Josephson coupling. Using Monte Carlo simulations and DMRG calculations on a ladder, we show that the ground state of this model is, at intermediate correlations, a Chiral Mott insulator which supports staggered loop currents. We characterize this Mott phase as a vortex supersolid or an exciton condensate and discuss experimental observables and generalizations.   

Mean Field Dynamics of Spin-Orbit Coupled Bose-Einstein Condensates

We derive the mean-field Gross-Pitaevskii equation for spin-orbit coupled Bose-Einstein conden-sates by taking account that the pseudospin states of atoms are superpositions of the hyperfine states with different scattering lengths. The ground state phases of the condensate in a harmonic trap are obtained numerically in various parameter regions. We find a new oscillation period in the center of mass motion of the condensate subject to a sudden shift of the harmonic trap. The oscillation period is dependent on the direction of the shift of the harmonic trap, linearly proportional to the spin-orbit coupling strength, and independent on the interaction strength.   

Rotation of supersolids in cold atomic condensates

In the framework of Gross Pitaevskii equation, with non-local interaction, we study the formation of Supersolid phase and the effect of rotation on such a system. The effect of rotation is to induce vortex patterns in such Supersolid phase, whose structures are in principle, different from the ordinary vortex in Superfluids. At sufficiently high rotation, these vortices arrange in the form of a lattice and thus, one has to take into account the interplay of two lattice structures, the Supersolid crystal lattice and the vortex lattice induced by rotation. We aim to study the elastic properties of such a system and compare it with the corresponding superfluid phase.   

Rashbons: Emergent bosonic fermion-pairs in synthetic non-Abelian gauge fields

In presence of a synthetic non-Abelian gauge field that produces a Rashba like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a BCS ground state to a BEC ground state when the strength of the gauge field is increased [PRB {\bf 84}, 014512 (2011)]. The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion-pairs called rashbons. This study reveals a new qualitative aspect that the rashbon state ceases to exist when the center of mass momentum of the fermions exceeds a critical value of the order of the gauge coupling strength. The study allows us to estimate the transition temperature of the rashbon BEC, and suggests a route to enhance the exponentially small transition temperature of the system with a fixed weak attraction to the order of the Fermi temperature by tuning the strength of the non-Abelian gauge field. The absence of the rashbon states at large momenta, suggests a regime in parameter space where the normal state of the system will be a dynamical mixture of uncondensed rashbons and unpaired helical fermions. Such a state should show many novel features including pseudogap physics.   

Evolution of the structure of vortex core across the BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We study the evolution of the structure of vortex core of fermionic superfluids with increasing strength of a non-Abelian gauge field which induces a spin-orbit interaction. Using the Bogoliubov de-Gennes formulation, we study the spectrum of core states both in the BCS limit (small gauge coupling) and in the rashbon BEC limit where the superfluid is a condensate of rashbons. We show that the novel features of rashbon dispersion, the vanishing of the bound state at finite centre of mass momentum, result in a larger core region for vortices in the rashbon BEC.