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Journal of the Physical Society of Japan

Superfluid–Mott Insulator Transition of Spinor Bose Gases with External Magnetic Fields

Nobutaka Uesugi, Miki Wadati

Published May 15, 2003• 12 citations
Publisher

Abstract

We study the superfluid–Mott insulator (SF–MI) transition of a spin-1 boson system in an optical lattice, especially the responce of the system to an external magnetic field. Using the mean field theory, we obtain the phase diagram of SF–MI transition at zero temperature. For antiferromagnetic bosons, the Mott insulator region is stabilized when the number of particles per site is even. We find that only by changing the external magnetic field, the SF–MI transition is realized. On the other hand, the ferromagnetic case perfectly recovers the spin frozen case, that is already performed in experiments.

DOI
10.1143/jpsj.72.1041

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We study the superfluid–Mott insulator (SF–MI) transition of a spin-1 boson system in an optical lattice, especially the responce of the system to an external magnetic field. Using the mean field theory, we obtain the phase diagram of SF–MI transition at zero temperature. For antiferromagnetic bosons, the Mott insulator region is stabilized when the number of particles per site is even. We find that only by changing the external magnetic field, the SF–MI transition is realized. On the other hand, the ferromagnetic case perfectly recovers the spin frozen case, that is already performed in experiments.
We study the superfluid--Mott insulator (SF-MI) transition of spin-1 bosons interacting antiferromagnetically in an optical lattice. Starting from a Bose-Hubbard tight-binding model for spin-1 bosons, we obtain the zero-temperature phase diagram by a mean-field approximation. We find that the MI phase with an even number of atoms per site is a spin singlet state, while the MI phase with an odd number of atoms per site has spin 1 at each site in the limit of t=0t=0t=0, where ttt is the hopping matrix element. We also show that the superfluid phase is a polar state as in the case for a spin-1 Bose condensate in a harmonic trap. It is found that the MI phase is strongly stabilized against the SF-MI transition when the number of atoms per site is even, due to the formation of singlet pairs. We derive the effective spin Hamiltonian for the MI phase with one atom per site and briefly discuss the spin order in the MI phase.
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 analyze theoretically the emergence of different superfluid phases of spin-1 bosons in a three-dimensional cubic optical lattice by generalizing the recently developed Ginzburg–Landau theory for the Bose–Hubbard model to a spinor Bose gas. In particular at zero temperature, our theory distinguishes within its validity range between various superfluid phases for an anti-ferromagnetic interaction with an external magnetic field. In addition, we determine that the superfluid–Mott insulator phase transition is of second order and that the transitions between the respective superfluid phases with anti-ferromagnetic interaction can be both of first and second order.
We analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons in the presence of an external magnetic field, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. In particular at zero temperature, we determine both the Mott and the superfluid phases for the competition between the anti-ferromagnetic interaction and the linear Zeeman effect within the validity range of the Ginzburg-Landau theory. Moreover, we find that the phase transition between the superfluid and Mott insulator phases is of second order and that the transitions between the respective superfluid phases for anti-ferromagnetic interaction can be both of first and second order.
Abstract Cluster mean field theory for the two-dimensional spin-1 Bose–Hubbard model is applied to study superfluid (SF) to Mott insulator (MI) phase transitions and various magnetic phases that arise in the presence of spin-dependent anti-ferromagnetic and ferromagnetic interactions. This study clearly shows the nematic behavior of SF and odd-density MI phases, and a continuous phase transition between them for anti-ferromagnetic interaction. The even-density MI shows a nematic or singlet phase depending upon the strength of the interaction, and a continuous crossover between them. The SF to singlet MI transition is discontinuous. The dependence of cluster size on the critical on-site interaction ( U 0 C ) for SF to MI transitions is also studied. In the case of anti-ferromagnetic interaction, it is found that U 0 C for the SF to odd-density MI transition decreases with cluster size; however, no such changes are observed for the SF to singlet MI transition. In the case of ferromagnetic interactions, SF to MI transitions are continuous, and Mott lobes become enlarged with cluster size. Second order Rényi entanglement entropy (EE) is calculated in different phases. The results show that Rényi EE is large in the nematic MI phase.
We study the insulator-superfluid transition of spin-1 bosons in an optical lattice in a uniform magnetic field. Based on a mean-field approximation we obtained a zero-temperature phase diagram. We found that depending on the particle number the transition for bosons with antiferromagnetic interaction may occur into different polar superfluid phases with spins aligned along or opposite to the field direction. This is qualitatively different from the field-free transition for which the mean-field theory predicts a unique polar superfluid state for any particle number.