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arXiv:1411.5485 · Ukrainian Journal of Physics

Investigation of the Bosonic Spectrum of Two-Dimensional Optical Graphene-Type Lattices. Superfluid Phase

Ihor V. Stasyuk, O. V. Velychko, I. R. Dulepa

Published Nov 15, 2015• 1 citation
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Abstract

The energy spectrum of a system of Bose atoms in the superfluid phase in an optical lattice of the graphene type has been studied. The dispersion laws for the energy bands and the single particle spectral densities are calculated in the random phase approximation and in the framework of the hard-core boson formalism, and their changes at the transition from the normal phase to the superfluid one are described. As a result of this transformation, the number of subbands doubles. In the case of the subband energetic equivalence, the Dirac points in the spectrum survive, and their number becomes twice as much. When the subbands are energetically nonequivalent, the Dirac points are absent. The shape of spectral densities is shown to be sensitive to the changes in the temperature and the chemical potential position.

DOI
10.15407/ujpe59.10.0993

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The energy spectrum of a system of Bose atoms in the superfluid phase in an optical lattice of the graphene type has been studied. The dispersion laws for the energy bands and the single particle spectral densities are calculated in the random phase approximation and in the framework of the hard-core boson formalism, and their changes at the transition from the normal phase to the superfluid one are described. As a result of this transformation, the number of subbands doubles. In the case of the subband energetic equivalence, the Dirac points in the spectrum survive, and their number becomes twice as much. When the subbands are energetically nonequivalent, the Dirac points are absent. The shape of spectral densities is shown to be sensitive to the changes in the temperature and the chemical potential position.
The band spectrum of bosonic atoms in two-dimensional honeycomb optical lattices with the graphene-type structure has been studied. The dispersion laws in the bands and the one-particle spectral densities are calculated for the normal phase in the random phase approximation. The temperature-dependent gapless spectrum with Dirac points located at the Brillouin zone boundary is obtained for the lattice with energetically equivalent sites, with the corresponding chemical potential lying outside the allowed energy band. Different on-site energies in the sublattices are shown to induce the appearance of a gap in the spectrum, so that the chemical potential can be located between the subbands, which gives rise to a substantial reconstruction of the band spectrum. The frequency dependences of the one-particle spectral density for both sublattices are determined as functions of the chemical potential level, the spectral gap magnitude, and the temperature.
The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated.Such excitations appear due to displacements of particles with respect to their local equilibrium positions.The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used.Calculations are performed within the random phase approximation in the hard-core boson limit.It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears.The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature.The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.
The energy spectrum, spectral density and phase diagrams have been obtained for two-sublattice hard-core boson model in frames of random phase approximation approach.Reconstruction of boson spectrum at the change of temperature, chemical potential and energy difference between local positions in sublattices is studied.The phase diagrams illustrating the regions of existence of a normal phase which can be close to Mottinsulator (MI) or charge-density (CDW) phases as well as the phase with the Bose-Einstein condensate (SF phase) are built.
We investigate the fermion spectrum within the Bose–Fermi–Hubbard model used for the description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on the Hubbard operator approach for an on-site basis. The equation for fermion Green’s function in the Bose–Fermi–Hubbard model is built; Green’s functions of higher orders are decoupled in the Hubbard-I approximation (the case of the strong on-site interaction). The corresponding spectral densities are calculated. In the case of hard-core bosons, the condition of appearance of additional bands in the fermion spectrum is investigated. It is shown that these bands exist only in the state with a Bose–Einstein condensate and appear because of the mixing of states with different numbers of bosons. These additional bands can be interpreted as a manifestation of composite excitations (when the appearance of a fermion on the site is accompanied by the simultaneous creation (or annihilation) of a boson).
The superfluid-to-Anderson-insulator transition of a strongly repulsive Bose gas is studied in a one-dimensional incommensurate optical lattice. In the hard-core limit, the Bose-Fermi mapping allows us to deal with the system using the exact numerical method. Based on the Aubry-Andr\'e model, we exploit the phase transition of the hard-core boson system from the superfluid phase with all single-particle states extended to the Bose-glass phase with all the single-particle states being Anderson localized as the strength of the incommensurate potential increases relative to the hopping amplitude. We evaluate the superfluid fraction, one-particle density matrices, momentum distributions, the natural orbitals, and their occupations. All of these quantities show that there exists a superfluid-to-insulator phase transition in the system.
We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-T(c) superconductors.