FINALIST: Engineering and Imaging Nonlocal Spin Dynamics in an Optical Cavity*

Photon-mediated interactions between atoms coupled to an optical cavity are a powerful tool for engineering entangled states and many-body Hamiltonians. These applications motivate the construction of an optical cavity enabling coherent nonlocal spin interactions, with transverse optical access for high-resolution imaging and addressing of atomic sub-ensembles. Using this apparatus, we implement a nonlocal Heisenberg Hamiltonian, where the relative strength and sign of spin-exchange and Ising couplings are controllable parameters. This tunability enables the demonstration of an interaction-induced protection of spin coherence against single-atom dephasing terms. The optical access afforded by a near-concentric cavity facilitates local control and imaging of the magnetization for Hamiltonian tomography and spatially resolved detection of the spin coherence. Imaging also allows for the first observation of cavity-mediated spin mixing in a spin-1 system, a new mechanism for generating correlated atom pairs. Whereas the single-mode cavity most naturally mediates all-to-all couplings, I will also discuss progress in generalizing to control the distance-dependence of the interactions, with prospects in engineering the spatial structure of entanglement. I furthermore propose and analyze two specific protocols in quantum control enabled by strong and tunable atom-light interactions. I first introduce a protocol that enables entanglement-enhanced measurements near the Heisenberg limit while reducing technical requirements on detection. This is accomplished via an interaction-enhanced readout that relies on reversing the sign of global Ising interactions. Dispersive atom-light interactions also enable heralded schemes, in which a high-fidelity pure state is produced upon probabilistic detection of a single photon. In this context, I show how a time-shaped single-photon pulse can ``paint'' an arbitrary superposition of coherent spin states while avoiding infidelities due to finite cavity linewidth.