Scheme to Probe Optomechanical Correlations between Two Optical Beams Down to the Quantum Level

The quantum effects of radiation pressure are expected to limit the sensitivity of second-generation gravitational-wave interferometers. Though ubiquitous, such effects are so weak that they have not been experimentally demonstrated yet. Using a high-finesse optical cavity and a classical intensity noise, we have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be used to retrieve weak correlations at the quantum level and has applications both in high-sensitivity measurements and in quantum optics.

Figure 1

Principle of the direct observation of optomechanical correlations. Both an intense signal beam and a weaker meter beam are sent into a resonant high-finesse cavity with a moving mirror. Intensity fluctuations of the signal beam are imprinted by radiation pressure onto the position fluctuations of the moving mirror, and, subsequently, onto the phase fluctuations of the meter beam. The two reflected beams then display intensity-phase correlations, retrieved with both a photodiode and a homodyne detection.

Figure 2

Experimental setup. The laser beam is split in two orthogonally polarized beams, which are both sent into the moving mirror cavity. A resonant electro-optical modulator (REOM) is used to lock the laser onto the optical resonance via a Pound-Drever-Hall technique. The residual birefringence of the cavity is compensated by the frequency shift of two acousto-optic modulators (AOM), also used to stabilize the intensities of both beams after their spatial filtering by the mode cleaner cavity. A second EOM modulates the intensity of the signal beam to mimic quantum radiation-pressure noise. For simplicity, most polarizing elements are not shown.

Figure 3

Phase-space trajectories of the intensity noise of the signal beam (left) and the phase noise of the meter beam (right), in the case $\sqrt{S_x^{\mathrm{rad}}/S_x^T}\simeq 5$. The phase noise is calibrated as displacements of the moving mirror.

Figure 4

Probability distributions in phase space of the signal intensity fluctuations $\delta I_s^{\mathrm{out}}$ (left) and of the conditional fluctuations $\delta I_{s|m}$ deduced from the meter measurement (right). Note the sharper peak, related to the lower conditional variance, and the factor 5 between the two vertical scales.

Figure 5

Estimated optomechanical correlation coefficient $C_{I_s,{\phi }_m}$ with respect to the number $N$ of independent 200-ms runs averaged. Dashed lines delineate the expected $1/\sqrt{N}$ statistical uncertainty region.