Abstract
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.
Highlights
One of the most striking predictions of quantum mechanics is that even in the ground state of an harmonic oscillator, any quadrature measurement is noisy
This is achieved through the use of an ancillary superconducting qubit, which enables in situ Wigner tomography of the squeezed intracavity microwave mode
Our device consists in a Josephson ring modulator [35] coupling one mode, which we would like to stabilize in a squeezed state, and a second auxiliary mode strongly coupled to a transmission line
Summary
One of the most striking predictions of quantum mechanics is that even in the ground state of an harmonic oscillator, any quadrature measurement is noisy. Steady-state squeezing can occur in stationary or propagating modes For the latter, it is typically achieved by parametrically pumping a resonator coupled to a single port. A more attractive approach is to use reservoir-engineering techniques [17], where tailored driving results in the cavity being coupled to effective squeezed dissipation [18,19,20] These methods can surpass the 3-dB limit, and do not involve transporting an externally prepared squeezed state. Squeezed state instead of inferring the resonator state from the measured output mode This is achieved through the use of an ancillary superconducting qubit, which enables in situ Wigner tomography of the squeezed intracavity microwave mode. Our stabilization technique could be extended beyond simple squeezed states to other continuous variable states such as cat or grid states [26,27,28,29,30,31] by taking advantage of the large nonlinearities that can be engineered in circuit-QED
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