Title: Non-degenerate parametric resonance in tunable superconducting cavity,
Abstract: We develop a theory for non-degenerate parametric resonance in a tunable
superconducting cavity. We focus on nonlinear effects that are caused by
nonlinear Josephson elements connected to the cavity. We analyze parametric
amplification in a strong nonlinear regime at the parametric instability
threshold, and calculate maximum gain values. Above the threshold, in the
parametric oscillator regime the linear cavity response diverges at the
oscillator frequency at all pump strengths. We show that this divergence is
related to the continuous degeneracy of the free oscillator state with respect
to the phase. Applying on-resonance input lifts the degeneracy and removes the
divergence. We also investigate the quantum noise squeezing. It is shown that
in the strong amplification regime the noise undergoes four-mode squeezing, and
that in this regime the output signal to noise ratio can significantly exceed
the input value. We also analyze the intermode frequency conversion and
identify parameters at which full conversion is achieved.