Dissipative stabilization of squeezing beyond 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 $6.7 \pm 0.2$ 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 $8.2 \pm 0.8$ dB. Moreover, this level of squeezing is achieved with a purity of $-0.4 \pm 0.4$ dB.