Vacuum squeezing in resonant SNAIL parametric amplifier operated near the Kerr-free point*

Squeezed states are an important resource in certain quantum measurements and computing architectures. Single-mode squeezed states of traveling microwave photons are commonly created by quantum-limited parametric amplifiers operated in phase-sensitive mode. One major impediment to creating a highly squeezed state is the distortion of the state at high gain due to Kerr (fourth-order) nonlinearity, which is innate to most Josephson junction-based parametric amplifiers. One exception is the SNAIL parametric amplifier (SPA), which can be designed and flux-biased to reach a point where the Kerr nonlinearity reaches zero and third-order nonlinearity is still significant. We will report experimental results on the degree of squeezing of a resonant three-wave-mixing SPA operated in the vicinity of its Kerr-free point. To date, we have observed approximately 1dB of squeezing at our detection electronics, and will discuss calibration of the measurement setup to infer the level of vacuum squeezing at the SPA.