arXiv:cond-mat/0607463 · Physical Review Letters

Quantum Insulating States of F=2 Cold Atoms in Optical Lattices

Fei Zhou, Gordon Walter Semenoff

Published Nov 2, 2006• 47 citations

Abstract

In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an octopole coupling between two neighboring lattice sites. Depending on scattering lengths and numbers of particles per site the ground states are either rotationally invariant dimer or trimer Mott insulators or insulating states with various spin orders. Three spin-ordered insulating phases are ferromagnetic, cyclic, and nematic Mott insulators. We estimate the phase boundaries for states with different numbers of atoms per lattice site.

DOI: 10.1103/physrevlett.97.180411

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arXiv:cond-mat/0607463 · Physical Review Letters

Quantum Insulating States of F=2 Cold Atoms in Optical Lattices

Fei Zhou, Gordon Walter Semenoff

Published Nov 2, 2006• 47 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.97.180411

Related papers

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arXiv:cond-mat/0612044Physical Review BJul 5, 20079 citations

We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as

{}^{23}\mathrm{Na},

in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three-dimensional lattices, insulating phases with an odd number of particles per site are always nematic. For insulating states with an even number of particles per site, there is always a spin-singlet phase, and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry but preserves time reversal symmetry, and has gapless spin-wave excitations. The spin-singlet phase does not break spin symmetry and has a gap to all excitations. In one-dimensional lattices, insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.

{c}_{0}/t

{(c}_{0}

is the spin-independent on-site interaction and t is the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is a different phase boundary between superfluid and Mott-insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.

S=1

chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.

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.