Fractional Shapiro steps in a Cavity-Coupled Josephson ring condensate

The Josephson effect presents a fundamental example of macroscopic quantum coherence as well as a crucial enabler for metrology (e.g. voltage standard), sensing (e.g. Superconducting Quantum Interference Device) and quantum information processing (Josephson qubits). Recently, there has been a major renewal of interest in the effect, following its observation in Bose, Fermi, and dipolar atomic condensates, in exciton-polariton condensates, and in momentum space. We present theoretically a nondestructive, \textit{in situ} and real time protocol for observing the AC and DC Josephson effects including integer (recently observed in cold atoms) and fractional (hitherto unobserved in cold atoms) Shapiro steps, using a ring condensate coupled to an optical cavity. Our analysis presents a metrology standard that does not require measurmement of atomic number and that challenges the conventional wisdom that quantum computations cannot be observed without being destroyed. Our results have implications for the fields of atomtronics, sensing, metrology and quantum information processing.