Quantum cavity modes in spatially extended Josephson systems

We report a theoretical study of the macroscopic quantum dynamics in spatially extended Josephson systems. We focus on a Josephson tunnel junction of finite length placed in an externally applied magnetic field. In such a system, electromagnetic waves in the junction are excited in the form of cavity modes manifested by Fiske resonances, which are easily observed experimentally. We show that in the quantum regime various characteristics of the junction as its critical current $I_c$, width of the critical current distribution $\sigma$, escape rate $\Gamma$ from the superconducting state to a resistive one, and the time-dependent probability $P(t)$ of the escape are influenced by the number of photons excited in the junction cavity. Therefore, these characteristics can be used as a tool to measure the quantum states of photons in the junction, e.g. quantum fluctuations, coherent and squeezed states, entangled Fock states, etc.