Dissipative stabilization of squeezing beyond \SI{3}{dB} in a microwave mode

While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implement a reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bound on the squeezing at about 6.7±0.2 dB below the zero-point level. Further, we show how to correct for resonator evolution during the Wigner tomography and obtain a squeezing as high as 8.2±0.8 dB. Moreover, this level of squeezing is achieved with a purity of −0.4±0.4 dB.