Tkachenko modes and structural phase transitions of the vortex lattice of a two component Bose-Einstein condensate

We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long-wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second-order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first-order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components.Comment: 24 pages, 13 figures, typos corrected, references added, final versio

Pairing and Vortex Lattices for Interacting Fermions in Optical Lattices with a Large Magnetic Field

We study the structure of pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy in the single-particle spectrum, the wave function has both zero and finite momentum components co-existing, and their relative phases are determined by a self-consistent mean-field theory. We present a microscopic calculation that can determine the vortex lattice structure in the superfluid phase for different flux densities. Phase transition from a Hofstadter insulator to a superfluid phase is also discussed.Comment: 4 pages, 3 figures, one table, published versio

Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice

We consider the Bose-Hubbard model in a two dimensional rotating optical lattice and investigate the consequences of the effective magnetic field created by rotation. Using a Gutzwiller type variational wavefunction, we find an analytical expression for the Mott insulator(MI)-Superfluid(SF) transition boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The dependence of phase boundary on the effective magnetic field is complex, reflecting the self-similar properties of the single particle energy spectrum. Finally, we argue that fractional quantum Hall phases exist close to the MI-SF transition boundaries, including MI states with particle densities greater than one.Comment: 5 pages,3 figures. High resolution figures available upon reques

Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

Cataloged from PDF version of article.We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac's quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations

Quantum correlated light pulses from sequential superradiance of a condensate

We discover an inherent mechanism for entanglement swap associated with sequential superradiance from an atomic Bose-Einstein condensate. Based on careful examinations with both analytical and numerical approaches, we conclude that as a result of the swap mechanism, Einstein-Podolsky-Rosen (EPR)-type quantum correlations can be detected among the scattered light pulses.Comment: 10 pages, 6 figure

P-band in a rotating optical lattice

We investigate the effects of rotation on the excited bands of a tight binding lattice, focusing particulary on the first excited (p-) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a non-trivial splitting and magnetic fine structure of the p-band. We show that Peierls substitution can be modified to describe p-band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p-band can be investigated starting from this effective Hamiltonian.Comment: 7 pages, 4 figures, new discussion of effective Hamiltonian, references adde

Hall conductance in graphene with point defects

Cataloged from PDF version of article.We investigate the Hall conductance of graphene with point defects within the Kubo formalism, which allows us to calculate the Hall conductance without constraining the Fermi energy to lie in a gap. For pure graphene, which we model using a tight-binding Hamiltonian, we recover both the usual and the anomalous integer quantum Hall effects depending on the proximity to the Dirac points. We investigate the effect of point defects on Hall conduction by considering a dilute but regular array of point defects incorporated into the graphene lattice. We extend our calculations to include next nearest neighbor hopping, which breaks the bipartite symmetry of the lattice. We find that impurity atoms which are weakly coupled to the rest of the lattice result in gradual disappearance of the high conductance value plateaus. For such impurities, especially for vacancies which are decoupled from the lattice, strong modification of the Hall conductance occurs near the E = 0 eV line, as impurity states are highly localized. In contrast, if the impurities are strongly coupled, they create additional Hall conductance plateaus at the extremum values of the spectrum, signifying separate impurity bands. Hall conductance values within the original spectrum are not strongly modified

Hofstadter butterfly of graphene with point defects

Cataloged from PDF version of article.We investigate the structure of Hofstadter's butterfly of graphene with point defects under a perpendicular magnetic field. We use a tight-binding method with interactions up to second-nearest neighbors. First of all, we present the Hofstadter butterfly spectrum of pure graphene, including all four valence orbitals with second-order hopping. To model defects, we perform calculations within an enlarged unit cell of seven carbon atoms and one defect atom. We find that impurity atoms with smaller hopping constants result in highly localized states which are decoupled from the rest of the system. The bands associated with these states form a nearly E = 0 eV line. On the other hand, impurity atoms with higher hopping constants are strongly coupled with the neighboring atoms. These states modify the Hofstadter butterfly around the minimum and maximum values of the energy by forming two self-similar bands decoupled from the original butterfly. We also show that the bands and gaps due to the impurity states are robust with respect to the second-order hopping