Abstract:
Finite temperature Green's function technique is used to calculate the energies and damping rates of elementary excitations of the homogeneous, dilute, spin-1 Bose gases below the Bose-Einstein condensation temperature both in the density and spin channels. For this purpose the self-consistent dynamical Hartree-Fock model is formulated, which takes into account the direct and exchange processes on equal footing by summing up certain classes of Feynman diagrams. The model is shown to fulfil the Goldstone theorem and to exhibit the hybridization of one-particle and collective excitations correctly. The results are applied to the gases of ^{23}Na and ^{87}Rb atoms.

Abstract:
In this paper we investigate the properties of Bose gases with Raman-induced spin-orbit(SO) coupling. It is found that the SO coupling can greatly modify the single particle density-of-state, and thus lead to non-monotonic behavior of the condensate depletion, the Lee-Huang-Yang correction of ground-state energy and the transition temperature of a non-interacting Bose-Einstein condensate. The presence of the SO coupling also breaks the Galilean invariance, and this gives two different critical velocities, corresponding to the movement of the condensate and the impurity respectively. Finally, we show that with SO coupling, the interactions modify the BEC transition temperature even at Hartree-Fock level, in contrast to the ordinary Bose gas without SO coupling. All results presented here can be directly verified in the current cold atom experiments using Raman laser-induced gauge field.

Abstract:
Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases.

Abstract:
We consider Raman scattering of coupled two leg spin ladders in the Fleury-Loudon regime. We derive the dependence of the intensity with polarization of the incoming light and temperature and discuss the effect of interaction of the elementary excitations on the shape of the spectrum. We show that Raman scattering spectrum is sensitive to the effective dimensionality of the coupled ladder system, making Raman scattering useful to discriminate true ladder systems from quasi two dimensional spin gap systems.

Abstract:
We explain quantitatively why resonant Raman scattering spectroscopy, an extensively used experimental tool in studying elementary electronic excitations in doped low dimensional semiconductor nanostructures, always produces an observable peak at the so-called "single particle" excitation although the standard theory predicts that there should be no such single particle peak in the Raman spectra. We have thus resolved an experimental puzzle which dates back more than twenty-five years.

Abstract:
Possible types of elementary excitations in the symmetric spin-orbital model on the a square lattice are analyzed using a spherically symmetric self-consistent approach. The excitation spectra are calculated. The behavior of the corresponding correlation functions depending on the temperature and parameters of the model is studied. A schematic phase diagram is plotted. It is shown that the thermodynamics of the system is mainly determined by elementary excitations with the entangled spin and orbital degrees of freedom.

Abstract:
We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins 1 and 1/2 antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.

Abstract:
We study elementary excitations of spin-1 bosons with antiferromagnetic interaction in an optical lattice by applying the Gutzwiller approximation to the spin-1 Bose-Hubbard model. There appear various excitations associated with spin degrees of freedom in the Mott-insulator (MI) phase as well as in the superfluid (SF) phase. In this system, the ground state in the MI phase is known to exhibit a remarkable effect of even-odd parity of particle filling, in which even fillings stabilize the MI state due to formation of spin-singlet pairs. We find that excitation spectra in the MI phase exhibit characteristic features that reflect the even-odd parity effect of the ground state. We clarify evolution of elementary excitations across the quantum critical point of the SF-MI transition.

Abstract:
We have numerically solved the low-energy excitation spectra of ferromagnetic Bose-Einstein condensates subject to dipolar interparticle interactions. The system is assumed to be harmonically confined by purely optical means, thereby maintaining the spin degree of freedom of the condensate order parameter. Using a zero-temperature spin-1 model, we solve the Bogoliubov excitations for different spin textures, including a spin-vortex state in the absence of external magnetic fields and a rapidly rotating polarized spin texture in a finite homogeneous field. In particular, we consider the effect of dipolar interactions on excitations characteristic of ferromagnetic condensates. The energies of spin waves and magnetic quadrupole modes are found to increase rapidly with the dipolar coupling strength, whereas the energies of density oscillations change only slightly.

Abstract:
Using hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large N, is compared with other corrections due to finite size, non-linearity and finite temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean field correction is the leading contribution and amounts to about 1%. The role of the deformation of the trap is also discussed.