Networks of nonlinear superconducting transmission line resonators

TL;DR

This paper explores a network of nonlinear superconducting resonators with tunable Kerr nonlinearity, enabling scalable quantum simulation of many-body physics with potential for studying strongly correlated systems.

Contribution

It introduces a design for nonlinear superconducting resonator networks with tunable nonlinearity, suitable for quantum simulation of the Bose-Hubbard model.

Findings

Eigenmode spectrum shows anticrossings indicating strong coupling.

Nonlinearity can be tuned from 10 kHz to 4 MHz.

Array of such resonators can simulate strongly correlated quantum systems.

Abstract

We investigate a network of coupled superconducting transmission line resonators, each of them made nonlinear with a capacitively shunted Josephson junction coupling to the odd flux modes of the resonator. The resulting eigenmode spectrum shows anticrossings between the plasma mode of the shunted junction and the odd resonator modes. Notably, we find that the combined device can inherit the complete nonlinearity of the junction, allowing for a description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID instead of a single junction, the nonlinearity can be tuned between 10 kHz and 4 MHz while maintaining resonance frequencies of a few gigahertz for realistic device parameters. An array of such nonlinear resonators can be considered a scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The device would be capable of accessing the strongly correlated regime and be particularly well suited for investigating quantum many-body dynamics of interacting particles under the influence of drive and dissipation.