Historical research guide · 0475 · 2018
Electromagnetic response of gravitational waves passing through an alternating magnetic field: A scheme to probe high-frequency gravitational waves
H. Zheng · L. F. Wei · H. Wen · F. Y. Li
In one minute
Gravitational waves and light are not separate subjects: send a gravitational wave through a strong magnetic field and part of it converts into electromagnetic waves, an effect Gertsenshtein and Zeldovich worked out in the 1960s. The trouble has always been that the converted signal goes as the square of the wave’s amplitude, and those amplitudes are already around ten to the minus twenty-one, so squaring puts the result out of reach. H. Zheng, Lianfu Wei, Hao Wen and Fangyu Li — the Chongqing and Sun Yat-sen group that has pursued this route for years — propose a fix. Alongside the strong steady magnet they add a weaker alternating one, then solve the Einstein-Maxwell equations exactly for a wave crossing the cavity. The interference between the passing wave and the alternating field gives a response linear in the wave’s amplitude rather than squared, arriving at three distinct frequencies. Better still, those signal photons carry wave impedances far from the 377 ohms of ordinary vacuum radiation, so the background can be filtered out by impedance matching. They tabulate the expected photon counts.
Connection
Chapter 10 is about coupling electromagnetism to gravity through fields and phase rather than through mass, and this paper is that coupling written as an instrument: magnets in, photons out, with a named frequency and a named impedance to look for. Chapter 11 wants a bench where gravity and electromagnetism meet under laboratory control, and a magnet whose sweep frequency you choose is exactly that — the same conversion runs both ways.
From the source
The Gertsenshtein-Zeldovich effect — the mutual conversion between electromagnetic waves and gravitational waves in a high stationary magnetic field — is the basis for detecting gravitational waves electromagnetically, but in the original configuration the detectable quantities are proportional to the square of the perturbative metric of the passing wave, which puts the induced signal out of experimental reach.Introduction, third paragraph
Adding a relatively weak alternating magnetic field to the strong stationary one makes the gravitational-wave-induced electromagnetic response linearly related to the amplitude of the passing wave rather than quadratic, which brings the signals within reach of current weak-light detection technique.Abstract; Introduction, final paragraph; Model and solutions, Equations 7 to 10
Solving the Einstein-Maxwell equation in the curved space-time for this configuration, the perturbed electromagnetic field carries three frequencies — the gravitational-wave frequency itself and that frequency plus or minus the magnet’s sweep frequency — so the signal is distinguishable from fields carrying no gravitational-wave information.Model and solutions, closing paragraph after Equation 10
Background electromagnetic noise obeys the flat space-time Maxwell equation and therefore always carries the vacuum wave impedance of 377 ohms, while the first-order gravitational-wave-induced signals carry impedances far above or far below that value, so wave-impedance matching can filter the uninformative zero-order photon flux out and leave only the signal photons for the detectors.Observable effects section, Equations 15 to 17; Figure 3
The expected signal is quantified: with a 10 tesla static field, a 0.005 tesla alternating field and a 30 metre cavity swept at 2 pi times ten million hertz, a wave of amplitude ten to the minus twenty-six yields about 2.83 times ten to the eleventh signal photons per second in the first channel and 6.76 times ten to the seventh in the second, the counts falling steeply as the frequency rises.Table I; Figure 2 and the paragraph following Equation 14
Because the sweep frequency of the applied alternating magnetic field is adjustable over a very large range, the configuration could actively search a band from about ten million hertz to a million million hertz once the cavity scale is experimentally achievable — and the authors state plainly that the setup is still imperfect for realistic experiments and that its sensitivity must be analysed in detail in the presence of noises and imperfect factors.Conclusions and discussions, second and third paragraphs; Table I
The way in
https://doi.org/10.1103/PhysRevD.98.064028How to cite it
H. Zheng, L. F. Wei, H. Wen, F. Y. Li (2018) Electromagnetic response of gravitational waves passing through an alternating magnetic field: A scheme to probe high-frequency gravitational waves doi:10.1103/PhysRevD.98.064028