Stabilization of squeezing beyond 3 dB in a microwave resonator by reservoir engineering.

Squeezed states, whose fluctuations on one quadrature are below the zero point fluctuations (ZPF) at the expense of the other, are an instrumental resource for quantum sensing and information processing. Squeezing is usually generated by parametrically pumping a resonator. While any amount of squeezing can theoretically be obtained for the outgoing field, the intraresonator squeezing is limited to 3 dB below the ZPF. Indeed, input-output relations impose that the intraresonator fluctuations result from the average of the ingoing ZPF and outgoing squeezed fluctuations. Using reservoir engineering techniques [Kronwald PRA 88 (2013)], the 3 dB limit has recently been overcome in a mechanical resonator [Lei PRL 117 (2016)]. However, a proof of principle is still missing for electromagnetic modes.
In this work, we use two parametric pumps and a dump mode to engineer an effective coupling to an artificial squeezed reservoir. We perform in-situ Wigner tomography of the squeezed microwave mode using an ancillary superconducting qubit. We measure intraresonator squeezing as high as 6.73 +-0.03 dB, going well beyond the 3 dB limit.