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Quantum simulators could provide an alternative to numerical simulations for understanding minimal models of condensed matter systems in a controlled way. Typically, cold atom systems are used to simulate e.g. Hubbard models. In this paper, we discuss a range of exotic interactions that can be formed when cold Rydberg atoms are loaded into optical lattices with unconventional geometries; such as long-range electron-phonon interactions and extended Coulomb like interactions. We show how these can lead to proposals for quantum simulators for complex condensed matter systems such as superconductors. Continuous time quantum Monte Carlo is used to compare the proposed schemes with the physics found in traditional condensed matter Hamiltonians for systems such as high temperature superconductors.
We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involvi
Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail. Many platforms are being developed towards this goal, in particular bas
In the last twenty years, Rydberg atoms have become a versatile and much studied system for implementing quantum many-body systems in the framework of quantum computation and quantum simulation. However, even in the absence of coherent evolution Rydb
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using Forster resonances between collective many-body states controlled by an external electric field. Here we report on the first expe
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems,