Spin-1 Bosons In Optical Lattice Research Articles

New Deep Superfluid Phases of Spin-1 Bosons in Optical Lattice

We analyse theoretically a spin-1 Bose gas loaded into a three-dimensional optical lattice in order to emerge different superfluid phases with external magnetic field. To achieve this, we generalize the mean-field perturbation theory up to the sixth hopping order for the underlying spin-1 Bose–Hubbard model. Our results indicate that the condensate density can be valid deep in the superfluid phase in comparison with that of the fourth hopping order. At zero temperature, new deep superfluid phases for an anti-ferromagnetic interaction are determined in the presence of the external magnetic field. Moreover, we find the second-order quantum phase transition between Mott insulator and superfluid phase for both ferromagnetic and anti-ferromagnetic interactions. Within the anti-ferromagnetic interaction, the transitions between respective superfluid phases can be of the first order.

Phase transitions and spin excitations of spin-1 bosons in optical lattice

We investigate ground state properties of spin-1 bosonic system trapped in optical lattice with extended standard basis operator (SBO) method. For both ferromagnetic ($U_2<0$) and antiferromagnetic ($U_2>0$) systems, we analytically figure out the symmetry properties in Mott-insulator and superfluid phases, which would provide a deeper insight into the MI-SF phase transition process. Then by applying self-consistent approach to the method, we include the effect of quantum and thermal fluctuations and derive the MI-SF transition phase diagram, which is in quantitative agreement with recent Monte-Carlo simulation at zero temperature, and at finite temperature, we find the underestimation of finite-temperature-effect in the mean-field approximation method. If we further consider the spin excitations in the insulating states of spin-1 system in external field, distinct spin phases are expected. Therefore, in the Mott lobes with $n=1$ and $n=2$ atoms per site, we give analytical and numerical boundaries of the singlet, nematic, partially magnetic and ferromagnetic phases in the magnetic phase diagrams.

Superfluid–Mott Insulator Transition of Spin-1 Bosons in Optical Lattice under Magnetic Field

We study the first- and second-order superfluid–Mott insulator transitions of spin-1 bosons in an optical lattice under a magnetic field by the Gutzwiller approximation. We find that, in contrast to previous perturbative studies, the phase boundary curve continuously changes as a function of magnetic field. We also find a sharp cusp structure on the phase boundary curve under some circumstances. When the phase boundary curve deviates from that obtained with the perturbative studies, the phase transition is a first-order one. We further clarify the specific features of the phase transition in the present system. The order parameters exactly at the boundary point, where the transition changes from first to second order, remain finite under a finite magnetic field and continuously vanish as the magnetic field approaches zero.