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We study a spin dynamics of two magnetic Chromium atoms trapped in a singlesite of a deep optical lattice in a resonant magnetic field. Dipole-dipoleinteractions couple spin degrees of freedom of the two particles to theirmotion in the site. The motion is quantized, therefore a trap geometry combinedwith two-body contact s-wave interactions influence a spin dynamics through theenergy spectrum of the two atom system. Anharmonicity and anisotropy of thesite results in a `fine' structure of two body eigenenergies. The structure canbe easily resolved by a weak magnetic dipole-dipole interactions. As an examplewe examine the effect of anharmonicity and anisotropy of the binding potentialon the Einstein-de Haas effect. We show that the weak dipolar interactionsprovide a perfect tool for a precision spectroscopy of the energy spectrum ofthe interacting few particle system.

Spin dynamics of two bosons in an optical lattice site: a role of anharmonicity and anisotropy of the trapping potential