A preliminary discussion of Dulkyn interferometer

The Dulkyn interferometer in Kazan is an active ring laser where the light propagates along two different paths. It has been developed with the idea that it could detect low frequency gravitational waves on Earth. Considering Dulkyn as a detector of periodic strains of order of h ~ 10−22 at low frequencies (10−3 Hz−10−5 Hz) we calculate that 30 W is the order of magnitude of the optical power necessary to beat the photon noise in the case of a long observation time (T = 4 months) and a reasonable signal to noise ratio (r = 3). We estimate that the displacement noise of the mirrors must not exceed 5×10−19m/$\sqrt{{Hz}}$. Dulkyn is also sensitive to accelerations and rotations. The acceleration noise does not seem to be troublesome ($\widetilde{g}\lesssim 0.1{m} {s}^{-2}/\sqrt{{Hz}}$), but the angular velocity noise must be less than 5×10−11 s−1/$\sqrt{{Hz}}$. The maximum strain (10−22) is obtained with free (pendulous) mirrors. Out of resonance, the strain is many orders of magnitude smaller when the mirrors are fixed on a rigid support. Such a case would rule out the possibility of a detection. As a conclusion we emphasize that the Dulkyn design does not bring any decisive improvement for the detection of low frequency gravitational waves on Earth