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arXiv:cond-mat/0205319 · Physical Review A

Magnetism in a lattice of spinor Bose-Einstein condensates

Kevin A. Gross, Christopher P. Search, Han Pu, Weiping Zhang, Pierre Meystre

Published Sep 6, 2002• 38 citations
arXivHTMLPDF

Abstract

We study the ground-state magnetic properties of ferromagnetic spinor Bose-Einstein condensates confined in deep optical lattices. In the Mott-insulator regime, the ``minicondensates'' at each lattice site behave as mesoscopic spin magnets that can interact with neighboring sites through both the static magnetic dipolar interaction and the light-induced dipolar interaction. We show that such an array of spin magnets can undergo a ferromagnetic or antiferromagnetic phase transition under the magnetic dipolar interaction depending on the dimension of the confining optical lattice. The ground-state spin configurations and related magnetic properties are investigated in detail.

DOI
10.1103/physreva.66.033603

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We study the ground-state magnetic properties of ferromagnetic spinor Bose-Einstein condensates confined in deep optical lattices. In the Mott-insulator regime, the ``minicondensates'' at each lattice site behave as mesoscopic spin magnets that can interact with neighboring sites through both the static magnetic dipolar interaction and the light-induced dipolar interaction. We show that such an array of spin magnets can undergo a ferromagnetic or antiferromagnetic phase transition under the magnetic dipolar interaction depending on the dimension of the confining optical lattice. The ground-state spin configurations and related magnetic properties are investigated in detail.
The spin dynamics of atomic Bose-Einstein condensates confined in a one-dimensional optical lattice is studied. The condensates at each lattice site behave like spin magnets that can interact with each other through both the light-induced dipole-dipole interaction and the static magnetic dipole-dipole interaction. We show how these site-to-site dipolar interactions can distort the ground-state spin orientations and lead to the excitation of spin waves. The dispersion relation of the spin waves is studied and possible detection schemes are proposed.
In this chapter, we discuss the magnetic solitons achieved in atomic spinor Bose-Einstein condensates (BECs) confined within optical lattice. Spinor BECs at each lattice site behave like spin magnets and can interact with each other through the static magnetic dipole-dipole interaction (MDDI), due to which the magnetic soliton may exist in blue-detuned optical lattice. By imposing an external laser field into the lattice or loading atoms in a red-detuned optical lattice, the light-induced dipole-dipole interaction (LDDI) can produce new magnetic solitons. The long-range couplings induced by the MDDI and ODDI play a dominant role in the spin dynamics in an optical lattice. Compared with spin chain in solid material, the nearest-neighbor approximation, next-nearest-neighbor approximation, and long-range case are discussed, respectively.
We study the spinor properties of S = 3 (52)Cr condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.
In this thesis we study various aspects of spinor Bose-Einstein condensates in optical superlattices using a Bose-Hubbard Hamiltonian that takes spin effects into account. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. In this way we derive the ground-state phase diagram of spinor bosons in superlattices. The system supports Mott-insulating as well as superfluid phases. The transitions between these phases are second-order for spinless bosons and second- or first-order for spin-1 bosons. Antiferromagnetic interactions energetically penalize high-spin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and first-order phase transitions. A change of magnetic fields can drive quantum phase transitions in the same way as a change in the tunneling amplitude does. Furthermore we study the physics of spin-1 atoms in superlattices deep in the Mott insulating phase when the superlattice decomposes into isolated double-well potentials. Assuming that a small number of spin-1 bosons is loaded in an optical double-well potential, we study single-particle tunneling that occurs when one lattice site is ramped up relative to a neighboring site. Spin-dependent effects modify the tunneling events in a qualitative and quantitative way. Depending on the asymmetry of the double well different types of magnetic order occur, making the system of spin-1 bosons in an optical superlattice a model for mesoscopic magnetism with an unprecedented control of the parameters. Homogeneous and inhomogeneous magnetic fields are applied and the effects of the linear and the quadratic Zeeman shifts are examined. We generalize the concept of bosonic staircases to connected double-well potentials. We show that an energy offset between the two sites of the unit cell in an extended superlattice induces a staircase of single-atom resonances in \nthe same way as in isolated double well. We also examine single-atom resonances in the superfluid regime and find clear fingerprints of them in the superfluid density. We also investigate the bipartite entanglement between the sites and construct states of maximal entanglement. The entanglement in our system is due to both orbital and spin degrees of freedom. We calculate the contribution of orbital and \nspin entanglement and show that the sum of these two terms gives a lower bound for the total entanglement.
We study the ground-state properties of spin-1 bosonic atoms trapped in a one-dimensional optical lattice with harmonic confinement. We have developed a highly efficient numerical method based on the Gutzwiller approximation to clarify the inhomogeneous magnetic phases induced by the harmonic confining potential. A quantum phase transition from a superfluid to a Mott insulator is examined for the respective cases with antiferromagnetic and ferromagnetic interactions. It is shown that the profile of local spins over the lattice sites changes as a function of the interaction strength forming the characteristic structures, which closely correlates with the average number of atoms at the sites. For antiferromagnetic cases, we find that there is a crossover from a superfluid polar condensate to Mott-insulator domains consisting of either a spin-singlet pair or a single spin at each site.