The measurement of weak continuous forces exerted on a mechanical oscillator is a fundamental problem in various physical experiments. It is fundamentally impeded by quantum back-action from the meter used to sense the displacement of the oscillator. In the context of interferometric displacement measurements, we here propose and demonstrate the working principle of a scheme for coherent back-action cancellation. By measuring the amplitude quadrature of the light reflected from a detuned optomechanical cavity inside which a stiff optical spring is generated, back-action can be canceled in a narrow band of frequencies. This method provides a simple way to improve the sensitivity in experiments limited by quantum back-action without injection of squeezed light or stable homodyne readout.

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• Optomechanics
• Quantum cavities
• Cavity resonators