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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.
We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon
We study a parametrically-driven nanomechanical resonator capacitively coupled to a microwave cavity. If the nanoresonator can be cooled to near its quantum ground state then quantum squeezing of a quadrature of the nanoresonator motion becomes feasi
As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is
We theoretically investigate the implementation of the two-mode squeezing operator in circuit quantum electrodynamics. Inspired by a previous scheme for optical cavities [Phys. Rev. A $textbf{73}$, 043803(2006)], we employ a superconducting qubit cou
Squeezed light finds many important applications in quantum information science and quantum metrology, and has been produced in a variety of physical systems involving optical nonlinear processes. Here, we show how a nonlinear magnetostrictive intera