Dissipative cooling of spin chains by a bath of dipolar particles

Abstract

We consider a spin chain of fermionic atoms in an optical lattice, interacting with each other by superexchange interactions. We theoretically investigate the dissipative evolution of the spin chain when it is coupled by magnetic dipole-dipole interaction to a bath consisting of atoms with a strong magnetic moment. Dipolar interactions with the bath allow for a dynamical evolution of the collective spin of the spin chain. Starting from an uncorrelated thermal sample, we demonstrate that the dissipative cooling produces highly entangled low energy spin states of the chain in a timescale of a few seconds. In practice, the lowest energy singlet state driven by super-exchange interactions is efficiently produced. This dissipative approach is a promising alternative to cool spin-full atoms in spinindependent lattices. It provides direct thermalization of the spin degrees of freedom, while traditional approaches are plagued by the inherently long timescale associated to the necessary spatial redistribution of spins under the effect of super-exchange interactions. Recent proposals [23,24,27,31] involve the use of light as a bath, and spontaneous emission as the dissipative process. In the present work, we explore binary atomic mixtures [3, 28, 32], one species acting as many-body quantum system, the other as bath. Namely, the quantum system is a spin chain of fermionic atoms, and it is coupled to a Bose-Einstein condensate of a different species. The low energy many-body states of the spin chain are driven by nearest-neighbor super-exchange interactions. Magnetic dipole interaction between fermions and bath lead to spin flips in the chain, associated with spontaneous phonon emission in the BEC. Thus, spin-thermalization can arise, due to the spin-orbit coupling conveyed by dipole-dipole interactions, an effect which is connected to the Einstein-de Haas effect [33]. As we show here, spin-orbit coupling offers a possibility to directly cool the collective spin degrees of freedom in a spin chain. Such a collective coupling of the spin chain to phonons in the BEC can be seen as an analog of superradience in quantum optics, with the spontaneous collective emission of phonons instead of photons. We point out that the possibility to couple to the total spin of the chain is particularly relevant to the quantum simulation of the spin-full lattice Hubbard model with ultra-cold atoms. Indeed, in most experiments the collective spin is a conserved quantity which is OPEN ACCESS RECEIVED

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