Historical research guide · 0817 · 2009
Signal photon flux and background noise in a coupling electromagnetic detecting system for high-frequency gravitational waves
Fangyu Li · Nan Yang · Zhenyun Fang · Robert M. L. Baker · Gary V. Stephenson · Hao Wen
In one minute
A gravitational wave crossing a strong magnetic field turns partly into light. That is the Gertsenshtein effect, and it is the oldest idea for catching gravitational waves with electronics rather than mirrors. Fangyu Li’s group at Chongqing University, with Robert Baker and Gary Stephenson, work out what a detector built on it would actually see around five gigahertz, the band where relic waves from the early universe are expected to peak. Their scheme is not the plain conversion, which they show is hopelessly faint on its own: they add a Gaussian microwave beam for the passing wave to beat against, so the signal grows in proportion to the wave’s amplitude instead of its square. The careful part is the noise. Signal photons and background photons spread differently across the apparatus, and there is one surface — the beam’s own symmetry plane — where the background transverse flux vanishes while the signal peaks. Focus that with fractal membranes and, they estimate, hours of counting would show it.
Connection
Chapter 10 says electromagnetism and gravity couple through fields and phase rather than through mass, and this paper is that coupling written as an instrument budget: how many photons, against how much background, on which surface, for how long. Chapter 11 wants a bench where the two meet under laboratory control, and a three-tesla magnet with a ten-watt beam is one. The same group’s later alternating-magnet scheme is on this site at /library/stm-949ba88682, and the twenty-five-author survey of the whole megahertz-to-gigahertz band is at /library/stm-96e41ddb23.
From the source
A detecting scheme based only on the pure inverse Gertsenshtein effect would not be useful for detecting high-frequency gravitational waves in the microwave band under laboratory conditions: for a field of 10 tesla over a path of 10 metres the converted power is of order ten to the minus forty watts, which is about seven times ten to the minus seventeen photons per second.Section II, Detecting scheme based on the inverse Gertsenshtein effect, Equations 7 and 8
The electromagnetic detecting scheme proposed by the China and US high-frequency gravitational wave groups is based on the composite effect of the synchro-resonance effect and the inverse Gertsenshtein effect, in which the key parameter is the first-order perturbative photon flux and not the second-order flux.Abstract; Section IV, opening
The distinguishable signal is the transverse first-order perturbative photon flux, which reaches its maximum at the longitudinal symmetrical surface of the Gaussian beam — exactly the surface where the transverse background photon flux vanishes identically, a fundamental characteristic of Gaussian beams — so the signal-to-noise ratio depends strongly on which receiving surface is used and can be optimised by choosing it.Section IV, Equations 45 and 46 and the two numbered points following them
With typical parameters of a static magnetic field of 3 tesla, an interaction length of 6 metres, a 10 watt Gaussian beam at 5 gigahertz and a receiving surface of about one hundredth of a square metre, the requisite minimal accumulation time of the signal in the background noise fluctuation would be of order one thousand to one hundred thousand seconds for wave amplitudes between ten to the minus twenty-six and ten to the minus thirty at one hertz bandwidth.Section IV, numerical estimation, Equations 60 to 65; Section V, Brief summary
The photon flux focused by the fractal membranes or other equivalent microwave lenses is not only the transverse first-order perturbative flux but the total transverse photon flux, and the two have different signal-to-noise ratios at different receiving surfaces, so the focusing optics and the choice of surface are part of the measurement rather than an afterthought.Abstract; Section IV, discussion of the fractal membranes
Relic gravitational waves expected from quintessential inflationary models and from some string cosmology scenarios peak in the gigahertz band with root-mean-square dimensionless amplitudes of about ten to the minus thirty to ten to the minus thirty-four, which is why the microwave band is the one worth instrumenting.Section I, Introduction, reason 1; Table 1, Some possible HFGW sources and relevant parameters
The way in
https://doi.org/10.1103/PhysRevD.80.064013How to cite it
Fangyu Li, Nan Yang, Zhenyun Fang, Robert M. L. Baker, Gary V. Stephenson, Hao Wen (2009) Signal photon flux and background noise in a coupling electromagnetic detecting system for high-frequency gravitational waves doi:10.1103/PhysRevD.80.064013