PARAMETRIC GRAVITY WAVE DETECTOR

Abstract

Since 1978 superconducting coupled cavities have been proposed as a sensitive detector of gravitational waves. The interaction of the gravitational wave with the cavity walls, and the resulting motion, induces the transition of some energy from an initially excited cavity mode to an empty one. The energy transfer is maximum when the frequency of the wave is equal to the frequency difference of the two cavity modes. In 1984 Reece, Reiner and Melissinos built a detector of the type proposed, and used it as a transducer of harmonic mechanical motion, achieving a sensitivity to fractional deformations of the orderx/x � 10 18 . In this paper the working principles of the detector are discussed and the last experimental results summarized. New ideas for the development of a realistic gravitational waves detector are considered; the outline of a possible detector design and its expected sensitivity are also shown. In this paper we shall discuss the mechanism of the interaction of a gravitational wave with a detector based on two coupled electromagnetic cavities. In previous works this issue was discussed using the concept of a dielectric tensor associated with the gravitational wave. 1 The interaction was analyzed in the reference frame where the resonator walls were at rest even in presence of a gravitational perturbation. Here we shall analyze the interaction in the proper reference frame attached to the detector and we shall therefore consider both the coupling between the wave and the mechanical structure of the detector and the perturbation induced on the field stored inside the resonator due to the time-varying boundary conditions. The proposed detector exploits the energy transfer induced by the gravitational wave between two levels of an electromagnetic resonator, whose frequencies ω1 and ω2 are both much larger than the characteristic angular frequency of the g.w. and satisfy the resonance condition ω2 − ω1 = . The interaction between the g.w. and the detector is characterized by a transfer of energy and of angular momentum. Since the elicity of the g.w. (i.e. the angular momentum along the direction of propagation) is 2, it can induce a transition between the two levels provided their angular momenta differ by 2; this can be achieved by putting the two cavities at right angle or by a suitable polarization of the electromagnetic field axis inside the resonator. In the scheme suggested by Bernard et al. the two levels are obtained by coupling two identical high frequency cavities. 2,3 The angular frequency ω1 is the frequency of the level symmetrical in the fields of the two cavities, and ω2 is that of the antisymmetrical one. The frequency difference between the symmetric and the antisymmetric level is determined by the coupling and can be adjusted by a careful resonator design. Since the detector sensitivity is proportional to the square of the resonator quality factor, superconducting cavities must be used for maximum sensitivity.