Synchronized Switching in a Josephson Junction Crystal

We consider a superconducting coplanar waveguide resonator where the central conductor is interrupted by a series of uniformly spaced Josephson junctions. The device forms an extended medium that is optically nonlinear on the single photon level with normal modes that inherit the full nonlinearity of the junctions but are nonetheless accessible via the resonator ports. For specific plasma frequencies of the junctions, a set of normal modes clusters in a narrow band and eventually becomes entirely degenerate. Upon increasing the intensity of a red detuned drive on these modes, we observe a sharp and synchronized switching from low-occupation quantum states to high-occupation classical fields, accompanied by a pronounced jump from low to high output intensity.

Figure 1

Central conductor of a CPWR of length $L$ interrupted by $N$ identical and uniformly distributed JJ with Josephson inductance $L_J$ and capacitance $C_J$.

Figure 2

Spectrum of CPWR with $v=0.98\times {10}^8\mathrm{m}/\mathrm{s}$ and $Z_0=50\mathrm{\Omega }$, interrupted by three identical and uniformly distributed JJs with $C_J=1\mathrm{pF}$ and $L=28\mathrm{mm}$, plotted over their plasma-frequency ${\omega }_p$ in units of the fundamental mode frequency $(\pi v)/L$ . Eigenmodes of the bare CPWR that do not couple to the JJs are omitted. The dashed box marks the degeneracy point ${\omega }_p=\overline{\omega }$, on which we focus our investigation.

Figure 3

Occupancies for the local modes $b_j$ (colored solid lines) plotted as a function of the drive strength $\mathrm{\Omega }$ (scale at left vertical axes) at the degeneracy point ${\omega }_p=\overline{\omega }$ (a) and for plasma frequencies ${\omega }_p$ slightly detuned from the degeneracy point (b) and (c). The gray dashed line shows the output intensities (scale at right vertical axes). Parameters: $v=0.98\times {10}^8\mathrm{m}/\mathrm{s}$, $Z_0=50\mathrm{\Omega }$, $C_J=1\mathrm{pF}$, and $N=8$.