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 such 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 $P\left(t\right)$ 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.

Figure 1

(Color online) (a) Schematic view of lumped Josephson junction embedded in an external cavity and its equivalent scheme. (b) Distributed Josephson junction subject to an external magnetic field with excited internal (Fiske) CMs and its equivalent scheme.

Figure 2

(Color online) The width of the switching current probability distribution as a function of magnetic field with (solid line) and without (dashed line) taking into account zero-point oscillations of CMs. Here, we have taken typical parameters for the junction as $I_{c0}=100\mu \mathrm{A}$ and $\hslash {\omega }_{p0}∕E_{J0}={10}^{-3}$; the junction size $L={\lambda }_J$.

Figure 3

(Color online) Time-dependent probability $P\left(t\right)$ of finding the junction in the zero-voltage state: without taking into account CMs (dotted line) and with taking into account quantum fluctuations induced by CMs (solid line) and coherent state of CMs (dashed line). The parameters are chosen as $\delta =5{10}^{-3}$, $I_c\left(H\right)∕I_c\left(0\right)=0.2$, $\hslash {\omega }_{p0}∕E_{J0}={10}^{-4}$, $\eta =1.5{10}^{-4}$, and the junction size $L=0.27{\lambda }_J$. For simplicity, we have taken ${\tau }_0={\tau }_{\mathrm{coh}}$.