Signal photon flux and background noise in a coupling electromagnetic detecting system for high-frequency gravitational waves

Abstract

A coupling system among Gaussian-type microwave photon flux, a static magnetic field, and fractal membranes (or other equivalent microwave lenses) can be used to detect high-frequency gravitational waves (HFGWs) in the microwave band. We study the signal photon flux, background photon flux, and the requisite minimal accumulation time of the signal in the coupling system. Unlike the pure inverse Gertsenshtein effect (G effect) caused by the HFGWs in the gigahertz band, the electromagnetic (EM) detecting scheme proposed by China and the U.S. HFGW groups is based on the composite effect of the synchroresonance effect and the inverse G effect. The key parameter in the scheme is the first-order perturbative photon flux (PPF) and not the second-order PPF; the distinguishable signal is the transverse first-order PPF and not the longitudinal PPF; the photon flux focused by the fractal membranes or other equivalent microwave lenses is not only the transverse first-order PPF but the total transverse photon flux, and these photon fluxes have different signal-to-noise ratios at the different receiving surfaces. Theoretical analysis and numerical estimation show that the requisite minimal accumulation time of the signal at the special receiving surfaces and in the background noise fluctuation would be $\ensuremath{\sim}{10}^{3}--{10}^{5}$ seconds for the typical laboratory condition and parameters of ${h}_{\mathrm{rms}}\ensuremath{\sim}{10}^{\ensuremath{-}26}--{10}^{\ensuremath{-}30}/\sqrt{\mathrm{Hz}}$ at 5 GHz with bandwidth $\ensuremath{\sim}1\text{ }\text{ }\mathrm{Hz}$. In addition, we review the inverse G effect in the EM detection of the HFGWs, and it is shown that the EM detecting scheme based only on the pure inverse G effect in the laboratory condition would not be useful to detect HFGWs in the microwave band.