Accurate theory for drive-activated nonlinear processes in the SNAIL parametric amplifier

The presence of spurious nonlinear interactions in parametric amplifiers often leads to detrimental effects such as gain saturation. In this talk, we present a perturbative approach aimed at analytically characterizing unwanted interactions and predicting parameter regimes in which their effect is minimized, and apply it to a specific degenerate parametric amplifier. We derive for arbitrary pump strengths the effective Hamiltonian, accounting for drive-induced renormalizations of its energy scales. In particular, this theory captures the nonlinear AC Stark shift, drive-activated Kerr nonlinearity and a collection of other terms ensuing from the expansion of the Josephson potential. Our predictions agree qualitatively with recent experimental results on the SNAIL parametric amplifier [N. Frattini et al., Phys. Rev. Appl. 10, 054020 (2018); V. Sivak et al., ibid. 11, 054060 (2019)].