Utility investigation of artificial time delay in displacement-noise-free interferometers

Laser interferometer gravitational wave detectors are usually limited by displacement noise in their lower frequency band. Recently, theoretical proposals have been put forward to construct schemes of interferometry that are insusceptible to displacement noise as well as classical laser noise. These so-called displacement-noise-free interferometry (DFI) schemes take advantage of the difference between gravitational waves and displacement noise in their effects on light propagation. However, since this difference diminishes in lower frequencies (i.e., Ω<c/L_D, with L_D the size of the detector), shot-noise-limited sensitivity of DFI schemes deteriorates dramatically in these frequencies—exactly the regime in which they are supposed to be superior, thereby limiting their applicability. In this paper, we explore the obvious possibility of increasing the effective size of the detector in the time domain, by introducing artificial time delays (T_D≫L_D/c) into the interferometry scheme, with the hope of improving low-frequency sensitivity. We found that sensitivity can only be improved by schemes in which fluctuations in the artificial time delays are not canceled.