Reduction and possible elimination of coating thermal noise using a rigidly controlled cavity with a QND technique

Brownian motion of the coating layers on a test mass is one of the limiting noise sources for high precision measurements such as gravitational-wave detection [1] or cold damping experiments [2]. Thermal noise is also the most significant source of the environmental decoherence that prevents us to observe quantum behavior of a macroscopic object [3]. Reduction of classical noise is a key for various subjects in the modern Physics. Several ideas to reduce thermal noise have been proposed [4], among which the mechanical separation of coating layers proposed by Khalili [5] is the easiest and the most sensational one, especially for an interferometer with high-reflective, multi-layer-coated mirrors. The mechanical separation can be realized by using two mirrors with fewer coatings locked to the anti-resonance so that the reflectivity of the anti-resonant cavity is as high as a single mirror with more coatings. Figure 1 shows the configuration of a typical gravitationalwave detector with the end test mass (ETM) replaced by the anti-resonant cavity. The differential mode of the two resonant arm cavities is measured at the dark port of the Michelson interferometer while the common mode and the dc component of the incident light return to the other side, reflected back by the power-recycling mirror (PRM). The reflectivity of the compound mirror in the case without optical losses is given by