Displacement-noise-free gravitational-wave detection with two Fabry-Perot cavities

We propose two detuned Fabry-Perot cavities, each pumped through both the mirrors, positioned in line as a toy model of the gravitational-wave (GW) detector free from displacement noise of the test masses. It is demonstrated that the noise of cavity mirrors can be completely excluded in a proper linear combination of the cavities output signals. This model is illustrated by a simplified round trip model (without Fabry-Perot cavities). We show that in low-frequency region the obtained displacement-noise-free response signal is stronger than the one of the interferometer recently proposed by S. Kawamura and Y. Chen.