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

We propose two 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 displacement noise of cavity mirrors as well as laser noise can be completely excluded in a proper linear combination of the cavities output signals. We show that in low-frequency approximation (gravitational wave length $\lambda-\text{gw}$ is much greater than distance $L$ between mirrors $\lambda_\text{gw}\gg L$) the decrease of response signal is about $(L/\lambda_\text{gw})^2$, i.e. signal is stronger than the one of the interferometer recently proposed by S. Kawamura and Y. Chen.