The effective action for spin-1 bosonic atom in an optical lattice is derived. The quasiparticle and quasihole dispersions are calculated for different cases by using a functional integral formalism. For all cases, the excitation spectra are analyzed. All the quasiparticle and quasihole excitations start with a gap.
The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.
We investigate the excitations of strongly interacting bosons confined in an optical lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action. This allows us to calculate the density of states for various geometries of optical lattices and its dependence on the presence of the superfluid phase. We observe that the superfluidity is manifested by a sharp coherence peak resulting from long-range order, while the excitation spectrum of the Mott insulator contains a gap.
We study the physics of interacting spin-1 bosons in an optical lattice using a variational Gutzwiller technique. We compute the mean-field ground state wave function and discuss the evolution of the condensate, spin, nematic, and singlet order parameters across the superfluid-Mott transition. We then extend the Gutzwiller method to derive the equations governing the dynamics of low energy excitations in the lattice. Linearizing these equations, we compute the excitation spectra in the superfluid and Mott phases for both ferromagnetic and antiferromagnetic spin-spin interactions. In the superfluid phase, we recover the known excitation spectrum obtained from Bogoliubov theory. In the nematic Mott phase, we obtain gapped, quadratically dispersing particle and hole-like collective modes, whereas in the singlet Mott phase, we obtain a nondispersive gapped mode, corresponding to the breaking of a singlet pair. For the ferromagnetic Mott insulator, the Gutzwiller mean-field theory only yields particle-hole-like modes but no Goldstone mode associated with long-range spin order. To overcome this limitation, we supplement the Gutzwiller theory with a Schwinger boson mean-field theory which captures superexchange-driven fluctuations. In addition to the gapped particle-hole-like modes, we obtain a gapless quadratically dispersing ferromagnetic spin-wave Goldstone mode. We discuss the evolution of the singlet gap, particle-hole gap, and the effective mass of the ferromagnetic Goldstone mode as the superfluid-Mott phase boundary is approached from the insulating side. We discuss the relevance and validity of Gutzwiller mean-field theories to spinful systems, and potential extensions of this framework to include more exotic physics which appears in the presence of spin-orbit coupling or artificial gauge fields.
In this paper,the excitation spectra of quasiparticles and quasiholes in Mott-insulator phase of 7Li atoms which have an attractive two-body interaction in an optical lattice are discussed when the repulsive three-body interaction is considered.It is concluded that with the increase of the repulsive three-body interaction,the energy of quasiparticles is increased and the energy of quasiholes is decreased. For a low filling factor of atoms,the energy of quasiholes is decreased slightly.With the increase of the filling factor of atoms,the energy of quasiholes is decreased remarkably.
The Bose–Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. We propose a mean-field theory based on a constraint SU(3) pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phase transition. By calculating the elementary excitation spectra and the average particle number fluctuation in the Brillouin zone center, we find that the energy gaps vanish continuously around ( J XY / J z ) c ≈0.175 and ( J XY / J z ) c ≈0.094 for 2D and 3D cubic lattices respectively, where the superfluid order parameters come up from zero and the Mott insulator state changes into a superfluid state.