Networks of nonlinear superconducting transmission line resonators

Abstract

We investigate a network of coupled superconducting transmission line\nresonators, each of them made nonlinear with a capacitively shunted Josephson\njunction coupling to the odd flux modes of the resonator. The resulting\neigenmode spectrum shows anticrossings between the plasma mode of the shunted\njunction and the odd resonator modes. Notably, we find that the combined device\ncan inherit the complete nonlinearity of the junction, allowing for a\ndescription as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID\ninstead of a single junction, the nonlinearity can be tuned between 10 kHz and\n4 MHz while maintaining resonance frequencies of a few gigahertz for realistic\ndevice parameters. An array of such nonlinear resonators can be considered a\nscalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The\ndevice would be capable of accessing the strongly correlated regime and be\nparticularly well suited for investigating quantum many-body dynamics of\ninteracting particles under the influence of drive and dissipation.\n