Observation of Back-Action Noise Cancellation in Interferometric and Weak Force Measurements

We experimentally demonstrate a cancellation of back-action noise in optical measurements. Back-action cancellation was first proposed within the framework of gravitational-wave detection by dual resonators as a way to drastically improve their sensitivity. We have developed an experiment based on a high-finesse Fabry-Perot cavity to study radiation-pressure effects in ultrasensitive displacement measurements. Using an intensity-modulated intracavity field to mimic the quantum radiation-pressure noise, we report the first observation of back-action cancellation due to a coherent mechanical response of the mirrors in the cavity to the radiation-pressure noise. We have observed a sensitivity improvement by a factor larger than 20 both in displacement and weak-force measurements.

Figure 1

Experimental setup. The high-finesse cavity is composed of two low-loss 1-inch mirrors. The frequency- and intensity-stabilized laser source is locked on the cavity resonance via an acousto-optic modulator (${\mathrm{AOM}}_1$). Two beams are sent into the cavity: a noise beam which is intensity-modulated by an electro-optic modulator (EOM) in order to apply a radiation-pressure noise on the mirrors, and a weaker probe beam whose reflected phase is measured by homodyne detection to monitor the mirror displacements. The signal in the measurement can either be an optical length variation of the cavity mimicked by a frequency modulation of the laser (signal generator 1), or a weak force applied through the radiation pressure of an intensity-modulated signal beam onto the front or end mirror of the cavity (signal generator 2 and modulator $\mathrm{AO}{\mathrm{M}}_2$). For simplicity, polarizing selective elements are not shown.

Figure 2

Top: thermal noise spectrum of the cavity in the vicinity of a particular doublet. Each peak is related to a specific vibration mode of one mirror. The dashed line is a double Lorentzian fit corresponding to the quadratic sum of individual mirrors’ thermal noises (dotted lines). Bottom: measurement of an optical length variation of the cavity produced by a modulation of the laser frequency. Curve a shows the monochromatic signal at different modulation frequencies, with the noise beam off. In presence of radiation-pressure noise (curve b), the signal is still observable in the dips associated with back-action cancellation. Dashed curves are theoretical fits of the signal and radiation-pressure noise, and dotted curves are the expected individual radiation-pressure noise spectra.

Figure 3

Measurement of a weak force applied at different frequencies by the signal beam, either to the front (peaks a around the first resonance) or end (peaks b around the second resonance) mirror. Curve c is obtained in the presence of radiation-pressure noise, with the force applied to the front mirror for frequency less than 710.6 kHz, and to the end mirror at higher frequency: the force is observable in the dips associated with back-action cancellation. Dashed curves are fits of both mirrors’ dynamical responses to the force.