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arXiv:1512.00631 · Europhysics Letters (EPL)

Two dipolar atoms in a harmonic trap

Rafał Ołdziejewski, Wojciech Górecki, Kazimierz Rza̧żewski

Published May 1, 2016• 8 citations
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Abstract

Two identical dipolar atoms moving in a harmonic trap without an external magnetic field are investigated. Using the algebra of angular momentum we reduce the problem to a simple numerics. We show that the internal spin-spin interactions between the atoms couple to the orbital angular momentum causing an analogue of the Einstein-de Haas effect. We show a possibility of adiabatically pumping our system from the s -wave to the d -wave relative motion. The effective spin-orbit coupling occurs at anti-crossings of the energy levels.

DOI
10.1209/0295-5075/114/46003

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Two identical dipolar atoms moving in a harmonic trap without an external magnetic field are investigated. Using the algebra of angular momentum we reduce the problem to a simple numerics. We show that the internal spin-spin interactions between the atoms couple to the orbital angular momentum causing an analogue of the Einstein-de Haas effect. We show a possibility of adiabatically pumping our system from the s -wave to the d -wave relative motion. The effective spin-orbit coupling occurs at anti-crossings of the energy levels.
I will discuss the spin dynamics of two magnetic atoms trapped in an external trap. Assuming that initially the atoms are in their orbital ground state I will discuss in details all possible elementary processes of spin flipping. Dipole-dipole interactions couple spin degrees of freedom of the two particles to their quantized orbital motion. Because of conservation of the total angular momentum if a magnetization of the system changes the system acquires an orbital angular momentum and atoms circulate around the center of the trap. I show that spin dynamics driven by dipolar interactions is possible only when the energies of the initial and the final sates are equal. In a case of weak magnetic moments of atoms this condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. I will illustrate the resonant dynamics comparing the theoretical predictions to some results of experiments on Chromium 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.
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 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.
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.