State-resolving cavity readout and cooling of atom arrays in a finite magnetic field

Alkali atom arrays switch between two magnetic field regimes in a typical experimental sequence: finite B-field for storage and high-fidelity quantum information processing, and 0 B-field for cooling and detection. The switching time for fields is significantly longer than other timescales, constraining how frequently important operations like mid-circuit readout and continuous reloading can be performed. We present the experimental realization of cavity-enhanced readout and EIT cooling of a 87Rb atom array in a 8G B-field, rendering long field switching times unnecessary. Our readout is state-resolving and minimizes measurement induced loss to <1%  by adaptively terminating the measurement when the detection threshold is surpassed. Our system demonstrates the utility of optical cavities for fast, adaptive control methods and lays groundwork for measurement-based error correction techniques.