Single photonic qutrit in a collective Rydberg polariton
We report on the coherent creation, control and read-out of a single photonic qutrit in a Rydberg ensemble. In each measurement, an optical photon is stored as a Rydberg polariton through electromagnetically induced transparency. Employing two microwave fields, the polariton is driven into an arbitrary superposition of three collective states, each encoded in a Rydberg state. The collective state is mapped into a photonic time-bin qutrit with the microwave field and read out sequentially. The complete sequence, including preparation, control, and read-out, is less than 1.8~$\mu$s, which mitigates decoherence significantly. We measure the coherence of the qutrit with non-destructive Ramsey interferometry, which is preferable for quantum information processing, and find good quantitative agreement with the theoretical model. The ability to write, process and read out the single photonic qutrit on microsecond time scales with microwave coupled Rydberg states demonstrates the coherent connectivity among the high Hilbert space of the qutrit.Our study is an important step in exploring qutrit based quantum information processes and quantum simulation of topological physics with microwave coupled Rydberg atom ensembles.