Spin dynamics of pairs of submerged 4f shell atoms in cylindrically symmetric harmonic traps: Connecting multi channel models to effective analytical approaches

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Abstract

We study spin-dynamics and quantum magnetism with ultracold highly-magnetic atoms. In particular, we focus on the interactions among rare-earth atoms localized in a site of an optical-lattice potential, modeled as a cylindrically symmetric harmonic oscillator in the presence of a weak external magnetic field. The interactions between the atoms are modeled using multi-channel Hamiltonian containing multiple spin-spin and anisotropic spin-orbit interactions with strengths that depend on the separation between the atoms. We studied the eigenenergies of the atom pair in a site for different lattice-site geometries and magnetic field strengths. In parallel, we compared these energies to those found from a simplified approach, where the complex-collisional physics is replaced by a two-length-scale pseudo-potential containing a contact and the magnetic dipole-dipole interaction. The eigenenergies within this model can be computed analytically within the Born approximation as well as non-perturbatively for stronger contact interactions. We have shown that the pseudo-potential model can accurately represent the multi-channel Hamiltonian in certain parameter regimes of the shape or geometry of the site of an optical lattice. The pseudo-potential forms the starting point for many-body, condensed matter simulations involving many atom pairs in different sites of an optical lattice.

Physics and Atomic / molecular / quantum

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