**Quantum Simulation**

## Analogical quantum simulators |
The description of quantum systems of many particles poses a formidable challenge. For this reason, complex materials such as high Tc superconductors or some exotic quantum magnets are not fully understood. An alternative to standard methods for numerical simulation is to use a quantum simulator. This is a quantum system where interactions can be tuned and quantum states intialized and detected to emulate the physics of a quantum material. Our work includes the theoretical study of quantum simulators with trapped ions, ultracold atoms and superconducting qubits.
Ch. Schneider, D. Porras, T. Schaetz, Reports on Progress in Physics 75, 024401 (2012). |

## Trapped ion simulators |
We have shown how to use trapped ion crystals to simulate quantum magnets (Ising and Heisenberg models), as well as systems of interacting bosons, spin-boson models, and Jahn-Teller systems. We have predicted some of the properties of synthetic trapped ion magnets with theoretical tools such as mean-field theory, exact diagonalization and Matrix Product State methods.
D. Porras and J.I. Cirac, Physical Review Letters 92, 207901 (2004). A. Fridenauer et al., Nature Physics 4, 757 (2008). |

## Shaken quantum lattices |
.A quantum lattice is a regular network where a particle can move by hopping between different neighbour sites. Quantum optical setups such as ultracold atoms in optical lattices and trapped ions can be described by quantum lattice models. By periodically driving ("shaking") a quantum lattice a variety of interesting features emerge, such as effective magnetic fields and topological properties. Periodic drivings are thus a useful piece of the quantum simualtion toolbox
A. Bermudez and D. Porras, Physical Review Letters 107, 150501 (2011). A. Bermudez and D. Porras, New Journal of Physics 17, 103021 (2015) . S. Fernandez-Lorenzo, J.J. Garcia-Ripoll and D. Porras, New Journal of Physics 18, 023030 (2016). |