Selective Decoupling and Hamiltonian Engineering in Dipolar Spin Networks.

We present a protocol to selectively decouple, recouple, and engineer effective interactions in mesoscopic dipolar spin networks. In particular, we develop a versatile protocol that relies upon magic angle spinning to perform Hamiltonian engineering. By using global control fields in conjunction with a local actuator, such as a diamond nitrogen vacancy center located in the vicinity of a nuclear spin network, both global and local control over the effective couplings can be achieved. We show that the resulting effective Hamiltonian can be well understood within a simple, intuitive geometric picture, and corroborate its validity by performing exact numerical simulations in few-body systems. Applications of our method are in the emerging fields of two-dimensional room temperature quantum simulators in diamond platforms, as well as in molecular magnet systems.

Emulating solid-state physics with a hybrid system of ultracold ions and atoms.

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.