Session A32: Focus Session: Rotating Quantum Gases

Rotation of fermions in a two dimensional lattice with a harmonic trap

Rotation of fermions in a lattice is studied using a Hubbard model. It is found that the fermions are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in continuum. Bragg scattering and coupling between angular and radial motion are believed to make this stability possible. In this regime, density depletion at the center of the trap can be developed for spin polarized fermions.   

Using custom potentials to access quantum Hall states in rotating Bose gases

The exact ground states of zero-temperature rotating Bose gases confined in quasi-two-dimensional harmonic traps are studied 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. We have investigated the possibility of facilitating access to specific quantum Hall states through the addition of customized potentials to the existing trapping potential. For the right choice of potential, we show that creation of predetermined quantum Hall states in rotating Bose gases should be possible using current experimental setups. (Research supported by NSERC, iCORE and CFI)   

Quantized vortex states of strongly interacting bosons in a rotating optical lattice

The analogy between ultracold atoms in optical lattices and electrons in crystal lattices is a manifestly rich one. If the optical lattice is rotating rapidly, many of the features associated with electrons in strong magnetic fields emerge. Even high correlated effects and quantum states like those underlying the fractional quantum Hall effect can potentially be realized. We examine small square two-dimensional systems with low filling via exact diagonalization of a modified Bose-Hubbard Hamiltonian. In this talk I will present some results showing the effects of the quantization of circulation, the appearance of vortices, and some of the novel features of quantum phase transitions in these systems.   

Quantum Hall physics in rotating Bose-Einstein condensates

A few years ago it was realized theoretically that there is a close analogy between the physics of rapidly rotating atomic Bose condensates (BEC) and the quantum Hall effect (i.e. a two-dimensional electron gas in a strong magnetic field). Due to an extremely rapid development in experimental techniques over the past few years, experiments on BEC are now very close to reaching the quantum Hall regime. In this talk I will review the theoretical connection between these two seemingly very different physical systems, and show how intuition and techniques from quantum Hall physics can be applied to study the properties of rotating Bose condensates.   

Vortices in two-component weakly interacting Bose-Einstein condensates

Weakly interacting Bose-Einstein condensates that are set rotating, are studied by numerical diagonalization of the many-body Hamiltonian. In particular, we investigate the structure of the lowest-energy states as a function of angular momentum, when pseudospin is introduced. Coreless vortices and vortex lattices in the exact soutions are compared to the results earlier obtained within the Goss-Pitaevskii mean field approach (see for example, Kasamatsu, Tsubota and Ueda, Phys Rev Lett 93, 250406 (2004) and Phys Rev A 91, 150406 (2005)).   

Persistent flow in a Bose-Einstein condensate

We will describe experiments on the study of quantized ~flow of Bose-condensed atoms in a multiply-connected trap. This torus-shaped trap is formed by the combination of an elliptically shaped, magnetic trap with a blue detuned laser beam in the middle to exclude atoms from the center of the magnetic trap. The rotation was initiated by transferring the orbital angular momentum from Laguerre-Gaussian photons to the atoms. We have observed that the rotational flow of atoms persists for several seconds, even when the condensate fraction is less than 10{\%}. We have also observed flow with high angular momentum and its splitting into singly charged vortices when the trap in no longer multiply-connected.   

Vortex-Lattice Phases in the Strongly-Interacting Limit of the Bose-Hubbard Model

We observe a structural phase transition in the vortex lattice described by the rotating Bose-Hubbard model as the system approaches the insulating phase. A weak optical lattice potential pins vortices to the potential maxima (S. Tung, et. al. arXiv:cond-mat/0607697). However, using Gutzwiller mean-field theory in the strongly-interacting limit of the rotating Bose-Hubbard model, we find an interaction driven phase transition from the potential maximum centered vortex lattice to a potential minimum centered configuration. In addition, even closer to the insulating phase, our results suggest a recurrence of the maximum-centered phase.   

Lifshitz-like transition and enhancement of correlations in a rotating bosonic ring lattice.

We study the effects of rotation on one-dimensional ultra-cold bosons confined to a ring lattice. For commensurate systems, at a critical value of the rotation frequency, an infinitesimal interatomic interaction energy opens a gap in the excitation spectrum, fragments the ground state into a macroscopic superposition of two states with different circulation and generates a sudden change in the topology of the momentum distribution. These features are reminiscent of the topological changes in the Fermi surface that occurs in the Lifshitz transition in fermionic systems. The entangled nature of the ground state induces a strong enhancement of quantum correlations and decreases the threshold for the Mott insulator transition. In contrast to the commensurate case, the incommensurate lattice is rather insensitive to rotation. Our studies demonstrate the utility of noise correlations as a tool for identifying new physics in strongly correlated systems.   

Vortices of Lattice Bosons Acquire Spin and Fermi Statistics

Lattice bosons a respond differently to a magnetic field, or a rotation, than continuum bosons, e.g. their Hall conductivity is not a linear function of their density. Such effects are mostly pronounced for hard-core bosons at half filling. For a periodic lattice on a torus threaded by fluxes, we can explicitly construct a conserved SU(2) `vortex spin' algebra. For odd total vorticity, even-fold spectral degeneracies are discovered on every lattice site. In particular, {\em the single vortex has spin half}. The vortex effective mass and spin-orbit coupling are extracted by diagonalizing the Hamiltonian on a 4x4 lattice. For two vortices, numerical `vortex-spin' correlations and orbital symmetries are consistent with Fermi and not Bose statistics. We discuss implications of the our results on the `vortex metal' phase at large magnetic fields.   

Spin Hall effects for cold atoms in a light induced gauge potential

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.   

Rapidly rotating strongly-correlated few bosons

A small number, $N \leq 11$, of bosons in a rapidly rotating harmonic trap, interacting via a contact potential or a Coulomb repulsion, is studied via an exact diagonalization in the lowest Landau level. For both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. As a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling $\nu$ than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions $\nu < 1/2$, we observe well developed crystallinity in the CPDs (two-point correlation functions). For larger filling fractions $\nu > 1/2$, observation of similar molecular patterns requires consideration of even higher-order correlation functions.   

Symmetry breaking and symmetry restoration for bosonic gases in rotating traps: Rotating boson molecules and Gross-Pitaevskii vortex structures.

We recently introduced a new variational wave function for strongly repelling bosons in two-dimensional rotating traps.\footnote{Phys. Rev. Lett. {\bf 97}, 090401 (2006); {\bf 93}, 230405 (2004)} The approach consists of constructing a single permanent out of displaced Gaussian orbitals that break the rotational symmetry and of subsequent symmetry restoration via projection techniques, thus taking into account correlations beyond the mean field. In our approach, the bosons are localized and form rotating boson molecules (RBMs). The projected wave functions of the RBMs do not violate the circular symmetry; nevertheless, they exhibit crystalline patterns in their intrinsic frame of reference. Gross-Pitaevskii (GP) vortex solutions are also known to break the circular symmetry. Here, we apply projection techniques to restore the broken-symmetry GP solutions. We find that the spectral decomposition of the GP vortex solutions are drastically different from that of the RBMs. The RBM spectra, however, are in agreement with exact diagonalization results in the lowest Landau level.   

Statistics of vortex trapping in cyclically coupled Bose-Josephson junctions

We investigate the problem of vortex trapping in cyclically coupled Bose-Josephson junctions. Starting with $N$ independent BECs we allow the system to reach a stable circulation by adding a dissipative term in our semi-classical equations of motions. We then ask, ${\it inter \, alia}$ the question: ``Starting with an initial normal distribution of total phases with variance $ \sim \sqrt{N} $ and allowing for phase slips, what is the probability to trap a stable vortex with winding number $2 \pi m$''? We find that the final distribution of winding numbers is narrower than the initial distribution of total phases, indicating an increased probability for no-vortex configurations. The role of dissipation has been studied in determining the final probability distibution. It is also possible to get a non-zero circulation starting with zero total phase around the loop. The final width of the distribution scales as $ \sim d \times N^{\alpha } $, where $ \alpha = 0.47 $ and $ d<1 $ (indicating a shrinking of the final distribution), the actual value of $ d $ depending on the strength of dissipation.