Cavity-based single atom preparation and high-fidelity hyperfine state readout

We prepare and detect the hyperfine state of a single 87Rb atom coupled to a fiber-based high finesse cavity on an atom chip. The atom is extracted from a Bose-Einstein condensate and trapped at the maximum of the cavity field, resulting in a reproducibly strong atom-cavity coupling. We use the cavity reflection and transmission signal to infer the atomic hyperfine state with a fidelity exceeding 99.92% in a read-out time of 100 microseconds. The atom is still trapped after detection.