Entanglement, quantum criticality, and coherent dynamics in many-atom and many-ion systems
Concepts from quantum information theory, such as "entanglement", are giving insight into long-standing problems in the physics of interacting particles, such as the nature of quantum critical states. At the same time, experiments on atomic and ionic systems, stimulated by the goal of quantum computing, are studying the quantum coherent dynamics of many-particle systems with much greater precision than previously possible. We first review the importance of entanglement for the theory of quantum critical ground states, primarily using one-dimensional models as an example: such ground states are infinitely more entangled than ordinary ground states, and a theory is presented for how this entanglement leads to universal errors ("finite-entanglement scaling") in any finite-entanglement representation, such as in a classical computer. We then discuss the zero-temperature coherent dynamics of many-particle states as studied in recent atomic physics experiments. We focus on the question of how thermalization/ equilibration occurs in fully coherent dynamics, using a combination of analytical and numerical methods. Current experiments offer the potential to settle many debates about equilibration and the foundations of statistical physics.