Einstein–de Haas Effect in Dipolar Bose-Einstein Condensates

Abstract

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...

Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets

“…The MDDI is known to yield the spatial structure of magnetizations [28][29][30][31]. On the other hand, the quadratic Zeeman energy determines the easy axis of the magnetization.…”

Parametric amplification of matter waves in dipolar spinor Bose-Einstein condensates

“…Contrary to the short-range interactions the DDI may violate, in principle, the conservation of the total spin projection (they may induce the equivalent of the Einstein-de Haas effect [25,26]). However, the associated change in LZE is typically, even for very low magnetic fields, orders of magnitude larger than any energy in the system and hence these spin-violating processes can be safely considered as suppressed.…”

“…II the homogeneous LZE plays typically no role in the spinor dynamics (only at very low magnetic fields B < 1 mG the DDI could induce the equivalent of the Einstein-de Haas effect [25,26], and in this case the residual LZE could play a role). However, magnetic-field gradients cannot be gauged out, and may play a relevant role in the spinor physics [27].…”

Ferromagnetic resonance in spinor dipolar Bose-Einstein condensates

“…In particular, we are interested in magnetic dipole-dipole interactions (MDDI) in spinor BECs, which have been actively studied. The interaction between spins has a characteristic symmetry of rotation and spin, which is expected to result in a new quantum phase [10][11][12] and Einstein-de Haas effects [13]. Experimentally, Griesmaier et al realized spinor dipolar condensates using 52 Cr atoms, which have a larger magnetic moment than alkali atoms [14].…”