We present experimental and theoretical studies of the off-resonant and strongly nonlinear regime of Josephson transmission lines (JTLs) with galvanically coupled nonlinear elements. The transition from the weakly to the strongly nonlinear regime of a JTL induced by increasing the input power of the pump is probed by two-tone spectroscopy. Measurements of the phase of the transmission coefficient for a weak probe signal reveal a large increase and pronounced oscillations in the phase-length variation as a function of the microwave power of the pump. Experimental observations are explained on the basis of the developed theoretical approach suitable for the description of the nonlinear response of strongly driven JTLs. Using the derived nonlinear wave equation, we show that the behavior of the phase-length variation is associated with the oscillatory dependence of the Josephson inductances on the microwave power. It is demonstrated that the dissipation-induced propagation losses increase in the strongly nonlinear regime and also lead to smearing of the phase-length oscillations. The developed theoretical analysis is in good agreement with experimental observations.

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• Circuit quantum electrodynamics
• Josephson effect
• Nonlinear waveguides
• Quantum information processing
• Metamaterials
• SQUID
• Superconducting devices
• Microwave techniques