Engineered Open Systems and Quantum Simulations with Atoms and Ions

The enormous experimental progress in atomic, molecular, and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even many-body ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the well-established concept of engineering of many-body Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in many-body quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems of atoms and ions. This comprises digital quantum simulations in a general open system setting, as well as engineering and understanding new classes of systems far away from thermodynamic equilibrium. In the context of digital quantum simulation, we first outline the basic concepts and illustrate them on the basis of a recent experiment with trapped ions. We also discuss theoretical work proposing an intrinsically scalable simulation architecture for spin models with high-order interactions such as Kitaev's toric code, based on Rydberg atoms stored in optical lattices. We then turn to the digital simulation of dissipative many-body dynamics, pointing out a route for the general quantum state preparation in complex spin models, and discuss a recent experiment demonstrating the basic building blocks of a full-fledged open-system quantum simulator. In view of creating novel classes of out-of-equilibrium systems, we focus on ultracold atoms. We point out how quantum mechanical long-range order can be established via engineered dissipation, and present genuine many-body aspects of this setting: in the context of bosons, we discuss dynamical phase transitions resulting from competing Hamiltonian and dissipative dynamics. In the context of fermions, we present a purely dissipative pairing mechanism, and show how this could pave the way for the quantum simulation of the Fermi-Hubbard model. We also propose and analyze the key properties of dissipatively targeted topological phases of matter.