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arXiv:cond-mat/0209676 · Physical Review A

Superfluid–Mott insulator transition of spin-1 bosons in an optical lattice

Shunji Tsuchiya, Susumu Kurihara, T. Kimura

Published Oct 28, 2004• 80 citations
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Abstract

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 $t=0$, where $t$ 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.

DOI
10.1103/physreva.70.043628

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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.
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 examine the superfluid-Mott insulator (SF-MI) transition of antiferromagnetically interacting spin-1 bosons trapped in a square or triangular optical lattice. We perform a strong-coupling expansion up to the third order in the transfer integral t between the nearest-neighbor lattices. As expected from previous studies, an MI phase with an even number of bosons is considerably more stable against the SF phase than it is with an odd number of bosons. Results for the triangular lattice are similar to those for the square lattice, which suggests that the lattice geometry does not strongly affect the stability of the MI phase against the SF phase.
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We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.
We study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two-dimensional optical trap. We chart out the phase diagrams for Mott states with n=1n=1n=1 and n=2n=2n=2 atoms per lattice site. It is shown that the long-range dipolar interaction stabilizes a state where the chains of the ferromagnetically aligned spins run along the longer trap direction while the spin ordering is staggered between nearby chains, leading to an antiferromagnetic ordering along the shorter trap direction. We also obtain the mean-field phase boundary for the superfluid-insulator transition in these systems and study the nature of spin ordering in the superfluid state near the transition. We show that, inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first-order antiferromagnetic-ferromagnetic spin ordering transition. We discuss implications of our results for 52Cr^{52}\mathrm{Cr}52Cr atoms and suggest possible experiments to detect different phases in such systems.