arXiv:cond-mat/0305513 · Physical Review A

Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field

Anatoly A. Svidzinsky, S. T. Chui

Published Oct 10, 2003• 24 citations

Abstract

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.

DOI: 10.1103/physreva.68.043612

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arXiv:cond-mat/0305513 · Physical Review A

Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field

Anatoly A. Svidzinsky, S. T. Chui

Published Oct 10, 2003• 24 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.68.043612

Related papers

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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.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.

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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.

n=1

and

n=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

^{52}\mathrm{Cr}

atoms and suggest possible experiments to detect different phases in such systems.

^{3}\mathrm{He}

. Moreover, for typical experimental setups, we estimate the critical temperature (entropy) for different ordered phases and our results suggest that direct experimental observation of these phases is promising.

{F}_{g}=1

{F}_{e}=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.