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Physical Review Letters

Observing the Einstein–de Haas Effect with Atoms in an Optical Lattice

Baoqing Sun, Li You

Published Oct 10, 2007• 15 citations
Publisher

Abstract

The conservation of magnetization, or atomic spin angular momentum, is broken for anisotropic dipolar interactions. As a result, the Einstein-de Haas effect, or the transfer of spin to spatial angular momentum, arises because the total angular momentum is conserved. We identify the regime for observing this with two 87Rb atoms in a single well, stimulated by the recent result for a condensate. The two-atom system is found to be more easily observed and confirmed with the addition of a periodically modulated magnetic field. Our result of utilizing a feeble dipolar interaction may find potential applications in precision measurements.

DOI
10.1103/physrevlett.99.150402

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The conservation of magnetization, or atomic spin angular momentum, is broken for anisotropic dipolar interactions. As a result, the Einstein-de Haas effect, or the transfer of spin to spatial angular momentum, arises because the total angular momentum is conserved. We identify the regime for observing this with two 87Rb atoms in a single well, stimulated by the recent result for a condensate. The two-atom system is found to be more easily observed and confirmed with the addition of a periodically modulated magnetic field. Our result of utilizing a feeble dipolar interaction may find potential applications in precision measurements.
We theoretically consider a spin polarized, optically trapped condensate of 87Rb atoms in F=1. We observe a transfer of atoms to other Zeeman states due to the dipolar interaction which couples the spin and the orbital degrees of freedom. Therefore the transferred atoms acquire an orbital angular momentum. This is a realization of the Einstein-de Haas effect in systems of cold gases. We find resonances which make this phenomenon observable even in very weak dipolar systems, when the Zeeman energy difference on transfer is fully converted to rotational kinetic energy.
The Einstein-de Haas effect is a phenomenon in which angular momentum is transferred from microscopic spins to mechanical rotation of a macroscopic rigid body. We report an observation of the Einstein-de Haas effect in a spinor-dipolar Bose-Einstein condensate, in which the intrinsic magnetic dipole-dipole interaction mediates coherent transfer of angular momentum from atomic spins to collective circulation of a quantum fluid. The depolarized spinor components displayed ring-shaped density distributions that were confirmed as quantized vortices through matter-wave interferometry, revealing a coherent conversion between spin and orbital angular momentum. This observation opens a pathway to exploring ground-state phases with broken chiral symmetry, spin textures, and mass circulation, as well as the Barnett effect in dipolar quantum gases.
We theoretically study a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in a F=1F=1F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in an mF=1{m}_{F}=1mF​=1, component we observe a significant transfer of atoms to other, initially empty Zeeman states exclusively due to dipolar forces. Because of conservation of a total angular momentum the atoms going to other Zeeman components acquire an orbital angular momentum and circulate around the center of the trap. This is a realization of the Einstein-de Haas effect in a system of cold gases. We show that the transfer of atoms via dipolar interactions is possible only when the energies of the initial and the final sates are equal. This condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. We found that there are many final states of different spatial density, which can be tuned selectively to the initial state. We show a simple model explaining high selectivity and controllability of weak dipolar interactions in the condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms.
We show that an analogue to the classical Einstein-de Haas effect can appear in ultracold dipolar Fermi gases. The anisotropic nature of dipole-dipole interactions can lead to a transfer of magnetization into orbital angular momentum. Remarkably, distinct from a Bose-Einstein condensate, this transfer is accompanied by twisting motion, where individual spin components rotate in opposite directions with larger orbital angular momenta than the full system, possibly leading to easier experimental observation of the effect. This feature is induced by the deformation of the Fermi surface and the direction of the twisting motion can be controlled by an s-wave scattering length or external magnetic field, possibly providing a method of measuring scattering lengths of strongly dipolar atomic species.
Einstein-de Haas effect for a 87^{87}87Rb atoms condensate
We consider a condensate of 87^{87}87Rb atoms in an F=1 hyperfine state confined in an optical dipole trap. Assuming the magnetic moments of all atoms are initially aligned along the magnetic field we observe, after the field's direction is reversed, a transfer of atoms to other Zeeman states due to the dipolar interaction. We find that there exist resonances which amplify the effect of dipolar interaction. When the resonance condition is satisfied the transfer of atoms to mF=0,−1m_F=0,-1mF​=0,−1 states might be of the order of the initial population of mF=1m_F=1mF​=1 component. While changing the magnetic moments during the transfer, the atomsacquire an orbital angular momentum and start to circulate around the center of the trap. This is a realization of the famous Einstein-de Haas effect in systems of cold gases. Due to the dipolar resonances, it becomes possible to observe this phenomenon even in a condensate of 87^{87}87Rb (F=1) atoms that have very small magnetic moment.
We propose an experiment which proves the possibility of spinning gaseous media via dipolar interactions in the spirit of the famous Einstein-de Haas effect for ferromagnets. The main idea is to utilize resonances that we find in spinor condensates of alkali atoms while these systems are placed in an oscillating magnetic field. A significant transfer of angular momentum from spin to motional degrees of freedom observed on resonance is a spectacular manifestation of dipolar effects in spinor condensates.