Under a strong quantum measurement, the motion of an oscillator is disturbed by the measurement back-action, as required by the Heisenberg uncertainty principle. When a mechanical oscillator is continuously monitored via an electromagnetic cavity, as in a cavity optomechanical measurement, the back-action is manifest by the shot noise of incoming photons that becomes imprinted onto the motion of the oscillator. Following the photons leaving the cavity, the correlations appear as squeezing of quantum noise in the emitted field. Here we observe such ponderomotive squeezing in the microwave domain using an electromechanical device made out of a superconducting resonator and a drumhead mechanical oscillator. Under a strong measurement, the emitted field develops complex-valued quantum correlations, which in general are not completely accessible by standard homodyne measurements. We recover these hidden correlations, using a phase-sensitive measurement scheme employing two local oscillators. The utilization of hidden correlations presents a step forward in the detection of weak forces, as it allows to fully utilize the quantum noise reduction under the conditions of strong force sensitivity.
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