Nearly quantum-limited Josephson-junction Frequency Comb synthesizer

Coherently-driven Kerr microresonators have rapidly emerged as the leading platform for frequency comb generation in the optical domain. These highly multimode devices generate stable broadband combs that have found varied applications, from spectroscopy and metrology to ultrashort pulse generation and cluster state formation for continuous variable quantum information. However, optical microresonators generally possess weak Kerr coefficients; consequently, triggering comb generation requires millions of photons to be circulating inside the cavity, thus suppressing the role of quantum fluctuations in the comb's dynamics. In this paper, we realize a version of coherently-driven Kerr-mediated microwave frequency combs based on a recent theoretical proposal, where the quantum vacuum's fluctuations are the primary limitation on comb coherence. Our minimal realization within the circuit QED (cQED) architecture consists of just two coupled modes, of which only one possesses a Kerr nonlinearity furnished by Josephson junctions. We achieve a comb phase coherence of up to 35$\mu$s, of the same order as most superconducting qubits and approaching the theoretical device quantum limit of 55$\mu$s. This is vastly longer than the modes' inherent lifetimes of tens of nanoseconds. The ability within cQED to engineer stronger nonlinearities than optical microresonators, together with operation at cryogenic temperatures, and the excellent agreement of comb dynamics with quantum theory indicates a promising platform for the study of complex quantum nonlinear dynamics.