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
ng many-body interactions and constraints. The central building block of the simulation scheme is constituted by a mesoscopic Rydberg gate that permits the entanglement of several atoms in an efficient, robust and quick protocol. In addition, optical pumping on ancillary atoms provides the dissipative ingredient for engineering the coupling between the system and a tailored environment. As an illustration, we discuss how the simulator enables the simulation of coherent evolution of quantum spin models such as the two-dimensional Heisenberg model and Kitaevs toric code, which involves four-body spin interactions. We moreover show that in principle also the simulation of lattice fermions can be achieved. As an example for controlled dissipative dynamics, we discuss ground state cooling of frustration-free spin Hamiltonians.
We demonstrate theoretically a parallelized C-NOT gate which allows to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond timescale. Our scheme relies on the strong and long-ra
nged interaction between Rydberg atoms triggering Electromagnetically Induced Transparency (EIT). By this we can robustly implement a conditional transfer of all ensemble atoms among two logical states, depending on the state of the control atom. We outline a many body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.
We experimentally and theoretically investigate the dephasing rates of the coherent evolution of a resonantly driven pseudo spin emersed in a reservoir of pseudo spins. The pseudo spin is realized by optically exciting 87 Rb atoms to a Rydberg state.
Hence, the upper spin states are coupled via the strong van der Waals interaction. Two different experimental techniques to measure the dephasing rates are shown: the rotary echo technique known from nuclear magnetic resonance physics and electromagnetically induced transparency. The experiments are performed in a dense frozen Rydberg gas, either confined in a magnetic trap or in an optical dipole trap. Additionally, a numerical simulation is used to analyse the dephasing in the rotary echo experiments.
