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arXiv:1802.01638 · Physical review. B./Physical review. B

Quantum many-body dynamics of the Einstein–de Haas effect

Johan H. Mentink, Mikhail I. Katsnelson, Mikhail Lemeshko

Published Feb 20, 2019• 47 citations
arXivHTMLPDF

Abstract

What is the shortest possible timescale of the Einstein--de Haas effect? Addressing this problem theoretically poses a monumental challenge, for it involves an infinite number of coupled quantum angular momenta. Here, the authors formulate for the first time the problem in a rotationally invariant way, thereby enabling its solution in terms of angulon quasiparticles. Intriguingly, the first calculations reveal already that transfer between electron spin, orbital, and lattice degrees of freedom can occur on the femtosecond time scale.

DOI
10.1103/physrevb.99.064428

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What is the shortest possible timescale of the Einstein--de Haas effect? Addressing this problem theoretically poses a monumental challenge, for it involves an infinite number of coupled quantum angular momenta. Here, the authors formulate for the first time the problem in a rotationally invariant way, thereby enabling its solution in terms of angulon quasiparticles. Intriguingly, the first calculations reveal already that transfer between electron spin, orbital, and lattice degrees of freedom can occur on the femtosecond time scale.
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.
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.
We study the reciprocal Barnett and Einstein--de Haas effects in an exactly solvable quantum spin--rotor model that conserves the total angular momentum. For a single spin-1/21/21/2, the model describes rotation-dependent spin polarization, coherent transfer of angular momentum between the spin and the rotor, and the accompanying spin--rotor entanglement. At a recoil-compensation point, all angular-momentum sectors become synchronized, allowing complete spin reversal and a one-quantum shift of an arbitrary rotor wave packet. We then extend the model to two spins coupled to the same rotor, where the shared rotational degree of freedom participates dynamically in the generation of spin--spin entanglement. The singlet forms a dark state, while the triplet sector remains coupled to the mechanical motion. At a special parameter point, the rotor returns to its original dynamical branch and disentangles from the spins, leaving behind a maximally entangled two-spin state locally equivalent to a Bell state.