Probing many body physics with cold atom quantum simulators

Cold atomic systems constitute a near perfect platform for quantum simulation, where a well controlled quantum system is experimentally tuned to behave according to a many body interacting Hamiltonian. In this talk, I will discuss a few examples of quantum simulation experiments with ultracold trapped ions in a radio-frequency (Paul) trap and Bosonic neutral atoms in an optical lattice. The trapped ion system is most suitable for studying long range spin Hamiltonians including frustration, that might result in a highly degenerate ground state manifold and entanglement. I will present experimental results from a quantum simulation of a frustrated antiferromagnetic quantum Ising model with trapped Yb-171+ ions, where we tune the range of interactions continuously and directly measure the spin correlation functions. I will also describe a quantum gas microscope set up that is used to project a two dimensional optical lattice onto a Bose Einstein Condensate of Rb-87 atoms and detect the atoms with single site resolution, for exploring many body physics involving Bose-Hubbard model and quantum phase transitions.