(ed.). Gravitational waves (IOP, 2001)(422s).

Introduction 105Figure 9.1. The simple Michelson.plane, moreover the Michelson is assumed ideal [10, 11] (contrast C = 1):δφ = π + α + gw . (9.3)Here α is the offset between the two interferometer arms and gw is the effect ofthe gravitational wave. The transmitted outgoing power P out has a simple relationwith the input power P in .P out = P in sin 2 α + gw2(9.4)for gw ≪ 1P out ≃ P in[sin 2 α 2 + 1 2 sin α gw]. (9.5)Equation (9.5) clearly states that P out is proportional to gw , the gravitationalwavesignal, and the fundamental limit of the measurement comes from thefluctuation of the incoming power, i.e. the fluctuation of the number of photons.For a coherent state of light, the number of photons fluctuates with Poissonianstatistics, and it can be shown that the signal-to-noise ratio (SNR), when C = 1,is:√P in tSNR =¯hω cos a gw (9.6)where ω is the circular frequency of the laser light, t is the time of the measureand ¯h is the Planck constant. The SNR is maximum when α = 0 and the interferometeris tuned to a dark fringe. The minimum phase shift detectable, per unittime, is evaluated assuming SNR = 1 mingw= √¯hωP in(9.7)