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In this work we show that a tunable coupling between microwave resonators canbe engineered by means of simple Josephson junctions circuits, such as dc- andrf-SQUIDs. We show that by controlling the time dependence of the coupling itis possible to switch on and off and modulate the cross-talk, boost theinteraction towards the ultrastrong regime, as well as to engineer red and bluesideband couplings, nonlinear photon hopping and classical gauge fields. Wediscuss how these dynamically tunable superconducting circuits enable keyapplications in the fields of all optical quantum computing, continuousvariable quantum information and quantum simulation - all within the reach ofstate of the art in circuit-QED experiments.

Tunable coupling engineering between superconducting resonators: from sidebands to effective gauge fields