**THE INTERPLAY OF ENTANGLEMENT
AND DISSIPATION IN MANY-BODY QUANTUM SYSTEMS**

__Michael
Foss-Feig__, __Kaden R. A. Hazzard__, Andrew J. Daley, James K. Thompson,
John J. Bollinger, and Ana Maria Rey

Understanding the behavior of strongly correlated quantum systems in the presence of dissipation is a fundamental challenge in modern physics. While dissipation generally tends to degrade correlations, it is now widely appreciated that it can also give rise to many-body physics not possible with strictly coherent dynamics, and can be used explicitly for the creation of entanglement. Regardless of whether one’s intention is to minimize or to harness dissipation, determining its effect on interacting many-body quantum systems is central to the fields of quantum simulation, quantum information, and quantum metrology. We present two complementary theoretical studies aimed at understanding both the limitations imposed by and the benefits afforded by dissipation in ultra-cold atomic gas experiments. First, we develop a comprehensive theoretical framework for predicting the effects of dissipation on the dynamics of the quantum Ising model. This model emerges naturally as a description of the spin degrees of freedom in a variety of solid state and atomic systems, and its coherent far-from-equilibrium dynamics has been used extensively for the generation of entanglement in these systems. Focusing in particular on trapped ion systems, we develop a complete description of the dynamical development of quantum correlations, and characterize the relative importance of the different possible sources of dissipation. To the best of our knowledge, this work provides the first closed form solution of an interacting spin-model (in more than one spatial dimension) with local dissipation. In addition to making concrete and experimentally relevant predictions, it should provide a useful benchmark for testing approximate techniques. Next, we consider the effects of reactive two-body collisions on ultracold atomic and molecular vapors. Such collisions are generally considered to be problematic in gases of reactive polar molecules and electronically excited alkaline earth atoms, limiting the lifetime of these otherwise promising experimental platforms. We show that this point of view is overly pessimistic: In particular, reactive two-body collisions drive two-component fermionic gases into entangled steady states. The entanglement, which comes in the form of Dicke states, could be useful for precision metrology experiments, and emerges naturally from initially spin incoherent gases that are well above the degeneracy temperature.