Magnetism in a lattice of spinor Bose-Einstein condensates

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

doi:10.1103/physreva.66.033603

Cited by 37 publications

(32 citation statements)

References 40 publications

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“…1. For sufficiently small separations z a, where a is lattice constant, we reproduce the earlier predicted [20,21] canted antiferromagnetic phase, AFM K , with the ordering vector K. For z > a, we find an antiferromagnetic phase, AFM M , with a larger unit cell and ordering wave vector at the M point of the Brillouin zone of the bipartite lattice. For intermediate interlayer distances, we find a stable ferromagnetic phase (FM), separated from the antiferromagnetic ones by incommensurate spin-wave states (ISW).…”

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confidence: 82%

Phase transitions in dipolar gases in optical lattices

2012

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We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence of easy-plane magnetically ordered phases separated by incommensurate spin-wave states. A recent breakthrough in the cooling of dipolar gases in optical lattices [1], following a decade of intensive research [2][3][4][5][6][7][8][9], has opened a door into the earlier inaccessible manybody physics of lattice systems with anisotropic long-range interaction. Although bulk crystalline dipolar systems are abundant in nature [10,11], their experimental investigation has been hindered by the extremely low temperatures required for the observation of ordering transitions [12] and the absence of continuously variable parameters. Recently, artificial twodimensional dipolar systems, such as lithographically created nanomagnet arrays, have been realized [13,14]. However, it is the advent of optical lattices with tunable lattice structure containing ultracold dipolar gases that has created numerous possibilities for studies of previously unexplored phase transitions-both classical and quantum-between ordered and disordered phases of this fundamental many-body system.In this paper, we analyze a series of magnetic phase transitions in a classical dipolar gas in deep optical lattices (square, Fig. 1 and triangular, Fig. 2) obtained from bipartite monolayer lattices by vertical separation, z, of the two sublattices. One way to realize such systems would be loading the ferromagnetic spinor Bose-Einstein minicondensates in the nodes [15] of a deep bilayer optical lattice created with the help of a painted potential technique [16], which would allow for a high degree of control over the shapes of optical lattices and interlayer separation.We find that, upon the variation of z, each system experiences a sequence of easy-plane magnetically ordered phases separated by incommensurate spin-wave states, which could be detected with the help of Bragg diffraction of light [17][18][19]. The phase diagram for the square lattice on the z-T plane is shown in Fig. 1. For sufficiently small separations z a, where a is lattice constant, we reproduce the earlier predicted [20,21] canted antiferromagnetic phase, AFM K , with the ordering vector K. For z > a, we find an antiferromagnetic phase, AFM M , with a larger unit cell and ordering wave vector at the M point of the Brillouin zone of the bipartite lattice. For intermediate interlayer distances, we find a stable ferromagnetic phase (FM), separated from the antiferromagnetic ones by incommensurate spin-wave states (ISW). At the critical temperature T c , all of the ordered phases feature a degeneracy in the orientation of magnetization, characterized in Fig. 1 by angle θ , or θ A and θ B for AFM M . Away from T c , such a degeneracy is lifted, and Fig. 1 shows the optimal orientation of the order parameter for the low-temperature states. The structure of the i...

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Phase transitions in dipolar gases in optical lattices

2012

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“…This distortion can propagate and hence generate spin waves along the atomic spin chain. For an optical lattice created by bluedetuned laser beams, the atoms are trapped in the dark-field nodes of the lattice and the light-induced dipole-dipole interaction is very small [8]. However, this small light-induced dipole-dipole interaction induces the amplitude and size of the soliton varying with time periodically as we will show in the following section.…”

Section: Latticementioning

confidence: 99%

“…The asymptotic form of two-soliton solution in limits t → −∞ and t → ∞ is similar to that of the one-soliton solution (8). In order to analyze the asymptotic behavior of two-soliton…”

Section: Elastic Soliton Collision For Spinor Bec In An Optical Lmentioning

confidence: 99%

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

Li¹,

He²,

Li³

et al. 2005

Phys. Rev. A

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“…The ground state of the 52 Cr atom has a total electronic spin of three and a nuclear spin of zero, and therefore the 52 Cr BEC has seven internal degrees of freedom. The interplay between dipolar and spinor interactions makes the order parameter of this system highly non-trivial [11,12,13]. Moreover, the dipole interaction couples the spin and orbital angular momenta so that an initial magnetization of the system causes the gas to rotate mechanically (Einstein-de Haas effect [14]) or, conversely, solid-body rotation of the system leads to its magnetization (Barnett effect [15]).…”

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Einstein–de Haas Effect in Dipolar Bose-Einstein Condensates

2006

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The general properties of the order parameter of a dipolar spinor Bose-Einstein condensate are discussed based on the symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions, a phenomenon reminiscent of the Einstein-de Haas effect in ferromagnets.PACS numbers: 03.75. Mn,03.75.Nt,03.75.Kk,03.75.Lm The realization of a Bose-Einstein condensate (BEC) of 52 Cr [1, 2] marks a major development in degenerate quantum gases in that the interparticle interaction via magnetic dipoles in this BEC is much larger than those in other spinor BECs of alkali atoms. The long-range nature and anisotropy of the dipolar interaction pose challenging questions concerning the stability and superfluidity of the BEC [3,4,5,6,7,8,9,10]. The ground state of the 52 Cr atom has a total electronic spin of three and a nuclear spin of zero, and therefore the 52 Cr BEC has seven internal degrees of freedom. The interplay between dipolar and spinor interactions makes the order parameter of this system highly non-trivial [11,12,13]. Moreover, the dipole interaction couples the spin and orbital angular momenta so that an initial magnetization of the system causes the gas to rotate mechanically (Einstein-de Haas effect [14]) or, conversely, solid-body rotation of the system leads to its magnetization (Barnett effect [15]).This Letter investigates the Einstein-de Haas and Barnett effects in a spin-3 BEC system. We discuss the symmetry of the order parameter of a dipolar spinor BEC and study the dynamic formation of spin textures using numerical simulations of the seven-component nonlocal mean-field theory, which takes into account short-range (van der Waals) interactions and magnetic dipole-dipole interactions subject to a trapping potential and an external magnetic field.We first consider general properties of the order parameter by discussing two fundamental symmetries of the dipolar interaction between the magnetic dipole moments µ 1 = gµ Bŝ1 and µ 2 = gµ Bŝ2 , where g is the electron gfactor, µ B is the Bohr magneton, andŝ 1 andŝ 2 are the spin operators. The interaction between the magnetic dipoles located at r 1 and r 2 is described bŷwhere r 12 ≡ r 1 − r 2 , e 12 ≡ r 12 /r 12 , and c dd = µ 0 (gµ B ) 2 /4π with µ 0 being the magnetic permeability of the vacuum. The dipole interaction is invariant under simultaneous rotation in spin and coordinate spaces about an arbitrary axis, say the z-axis, so that the projected total angular momentum operatorŜ z +L z on that axis commutes withv dd , whereŜ =ŝ 1 +ŝ 2 is the total spin operator andL is the relative orbital angular momentum operator. Another symmetry of the dipolar interaction is the invariance under the transformation P z e −iπŜz , where P z : (x, y, z) → (x, y, −z) and. Thus, the eigenvalues of the following operators are conserved by the dipole interaction:A crucial observation is that these operators also commute with the short-range interactions. Thus if the confining potential is axi...

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Magnetism in a lattice of spinor Bose-Einstein condensates

Cited by 37 publications

References 40 publications

Phase transitions in dipolar gases in optical lattices

Phase transitions in dipolar gases in optical lattices

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

Einstein–de Haas Effect in Dipolar Bose-Einstein Condensates

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