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Journal of the Physical Society of Japan

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

T. Kimura, Shunji Tsuchiya, Makoto Yamashita, Susumu Kurihara

Published Jul 10, 2006• 9 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.75.074601

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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.
We study spin-1 bosons in an optical lattice under a magnetic field with the Gutzwiller approximation for the Bose-Hubbard model. Phase boundary curves between superfluids and Mott insulators depend continuously on the magnetic field, and this provides better results than those obtained with the perturbative mean-field approximation. The phase boundary curve as a function of magnetic field has a sharp cusp structure under certain circumstances. In superfluid phases, both the spin magnetizations and fluctuations in the total number of bosons show strong magnetic field dependence, which is related to the fact that both first-and second-order transitions appear on the phase boundary curve according to the magnetic field.
The superfluid--Mott-insulator transition of spin-2 boson atoms with repulsive interaction in an optical lattice in a magnetic field is presented. By using the mean-field theory, the Mott ground states and phase diagrams of the superfluid--Mott-insulator transition at zero temperature are revealed. An applied magnetic field leads to splitting of some phase boundaries. For all the initial Mott ground states containing multiple spin components, different spin components take on different phase boundaries. It is found that in this system phase boundaries with different magnetization can be moved in different ways by changing only the intensity of the applied magnetic field.
We investigate the superfluid--Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an Fg=1{F}_{g}=1Fg​=1 to Fe=1{F}_{e}=1Fe​=1 internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well as within the framework of perturbation theory.
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.
The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $\ensuremath{\theta}$ between the polarization vectors ($\mathrm{lin}\text{\ensuremath{-}}\ensuremath{\theta}\text{\ensuremath{-}}\mathrm{lin}$ configuration), driving an Fg=1{F}_{g}=1Fg​=1 to Fe=1{F}_{e}=1Fe​=1 internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\ifmmode\pm\else\textpm\fi{}1$. Due to the coupling the system can be described as a two-component one. At $\ensuremath{\theta}=0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid--Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $\ensuremath{\theta}$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.