Nonstationary shot noise and its effect on the sensitivity of interferometers

We treat the shot noise of a light source modulated in power as a nonstationary random process. The spectrum of such modulated shot noise, although it is still white, is shown to contain correlations between different frequency components. In addition, the noise is not equally distributed in phase. These effects can deteriorate the shot-noise-limited sensitivity of modulated interferometers. Maximizing the signal-to-noise ratio (SNR) introduces constraints on both the modulation and demodulation waveforms. The sensitivities obtained with several commonly used modulation schemes are calculated, and new modulation strategies are proposed to realize good SNR. We apply the results to the case of laser interferometer gravitational wave detectors where it is essential to reach a shot-noise-limited sensitivity. By taking into account the additional noise contribution from the modulated shot noise, we reduce the 3-dB discrepancy between the measured sensitivity of the Garching prototype detector and the theoretical shot-noise limit to about 1.5 dB.