Engineered frequency combs in a multimode Josephson network

We investigate the dynamics of a microwave-driven Josephson junction capacitively coupled to an arbitrary multimode linear network. Under specific symmetry conditions, we show that the classical phase diagram simplifies, and may be determined semi-analytically for an arbitrarily large network. The resulting system admits unstable regimes with emergent frequency combs akin to its single mode counterpart [1], with the latter being recently realized in superconducting circuits [2]. The multimode network enables further control over comb properties via its tunable parameters. The coherence of the combs is found to be determined by the intrinsic nonlinearity of the Josephson junction, but is also controllable via network parameters. We also clarify the connection and identify important differences between the network here which consists of a single Kerr nonlinear mode that ultimately delocalizes over the linear network due to the coupling, and standard multimode Kerr combs that have been well-studied in optical systems. The system provides a highly-engineerable platform for frequency comb generation, especially suited to realization within the superconducting circuit architecture.

[1] S. Khan, H. E. Türeci, Phys. Rev. Lett. 120, 153601 (2018)
[2] Pinlei Lu et. al., in preparation