Gravitational waves reaching a Michelson interferometer are expected to induce a very small change in the length of its arms causing a phase shift between them, but it is very difficult to observe the extremely small phase shift signals produced. In the present letter we show that the gravitational waves signal could be amplified by orders of magnitude by using very special conditions for a coherent-squeezed Michelson interferometer in which the coherent state enters one port of the interferometer and the squeezed vacuum enters in the other port. We treat the case where without the gravitational induced phase shift the very strong coherent state goes out of one output port while the squeezed vacuum goes out the other output port (the ``dark'' port). While the phase shift produced by the gravitation waves does not give any significant change in the strong coherent output, the light intensity in the ``dark'' port is amplified with decreased fluctuations as the squeezing increases.
Extension of the input-output relation for a Michelson interferometer to arbitrary coherent-state light sources: --- Gravitational-wave detector and weak-value amplification ---
Bidirectional Internal Squeezing for Gravitational-Wave Detectors
Institute of Quantum Information and Matter, California Institute of Technology（量子信息与物质研究所，加州理工学院）；Division of Physics, Mathematics and Astronomy, California Institute of Technology（物理、数学与天文学系，加州理工学院）
