Multi-Photon Resonances in Josephson Junction-Cavity Circuits

TL;DR

This paper investigates multi-photon resonances in Josephson junction-cavity circuits, revealing complex dynamical transitions, bistability, and oscillations in steady states driven by nonlinear interactions and effective rate models.

Contribution

It demonstrates the occurrence of multiple dynamical transitions and bistability in multi-photon resonances within circuit QED systems, introducing a simple rate model to describe these phenomena.

Findings

Identification of two closely spaced dynamical transitions for multi-photon resonances.

Observation of bistable behaviour and oscillations in steady state weights.

Development of an effective rate model capturing the system's complex dynamics.

Abstract

We explore the dissipative dynamics of nonlinearly driven oscillator systems tuned to resonances where multiple excitations are generated. Such systems are readily realised in circuit QED systems combining Josephson junctions with a microwave cavity and a drive achieved either through flux or voltage bias. For resonances involving 3 or more photons the system undergoes a sequence of two closely spaced dynamical transitions (the first one discontinuous and the second continuous) as the driving is increased leading to steady states that form complex periodic structures in phase space. In the vicinity of the transitions the system displays interesting bistable behaviour: we find that coherent effects can lead to surprising oscillations in the weight of the different dynamical states in the steady state of the system with increasing drive. We show that the dynamics is well-described by a simple effective rate model with transitions between states localised at different points in the phase space crystal. The oscillations in the weights of the dynamical states is reflected in corresponding oscillations in a time-scale that describes transitions between the states.