Historical research guide · 0750 · 2013
High-frequency gravitational waves having large spectral densities and their electromagnetic response
Fang-Yu Li · Hao Wen · Zhen-Yun Fang
In one minute
A gravitational wave crossing a strong magnetic field turns partly into light. That is the inverse Gertsenshtein effect, and Li Fang-Yu, Wen Hao and Fang Zhen-Yun of Chongqing University take it as the starting point for a detector. Their target is the high-frequency end of the spectrum — a hundred megahertz up to a terahertz — where relic waves from the early universe, oscillating branes, plasma driven by intense radiation and even collider events are all expected to leave something, and where the big interferometers simply do not listen. The team works through five schemes and prices each one: the bare conversion effect, the same effect helped by a coherent radio beam, a flat superconducting cavity, a closed cylindrical superconducting cavity, and their own synchro-resonance system, in which a Gaussian microwave beam meets the wave inside a nine-tesla field. Their conclusion is that the last of these can in principle reach amplitudes near ten to the minus thirty-two, and that what stands in the way is engineering rather than physics.
Connection
Chapter 10 rests on electromagnetism and gravity being two sides of one coupling, and the Gertsenshtein effect is that coupling written down as a published, calculable, two-way conversion: field into wave, wave into field. Chapter 11 gets the hardware — superconducting cavities with quality factors in the hundreds of billions, used as gravitational antennas — and chapter 4 gets the reminder that a metric disturbance is something you can build an instrument for. Read it beside the same group’s signal-photon-flux calculation at /library/stm-c15757c634, Beckwith and Robertson on relic high-frequency waves at /library/stm-c1ad7838f6, and the international review of megahertz-to-gigahertz searches at /library/stm-96e41ddb23.
From the source
The Gertsenshtein effect and its inverse follow from the Einstein-Maxwell equations: an electromagnetic wave crossing a transverse static magnetic field generates gravitational waves, and a gravitational wave crossing the same field generates an electromagnetic wave — and for a laboratory-sized interaction region the relevant band is roughly 10⁸ Hz to 10¹² Hz.Section 2.1; Eq. 1
The signal photon flux from the inverse Gertsenshtein effect grows in proportion to the gravitational-wave frequency, so a high-frequency graviton has a larger interaction cross-section with a static magnetic field than a low-frequency one, and the minimal detectable amplitude falls as the inverse of the frequency, of the field strength, of the interaction length and of the square root of the receiving area.Section 2.1; Eqs. 3 and 4
With a detectable minimum power of about 10⁻²² W in a 1 Hz bandwidth, a 9 T field, a 3 m interaction length and a 0.36 m² receiving surface, the bare inverse Gertsenshtein scheme reaches a minimal detectable amplitude of 1.8 times 10⁻²¹ at 3 GHz and 1.8 times 10⁻²⁴ at 3 THz — within reach of the brane-oscillation prediction of about 10⁻²², and far from the 10⁻²⁹ to 10⁻³⁰ expected of relic waves.Section 2.1; Eqs. 5; brane oscillation limit from ref. 11
Adding a coherent plane electromagnetic wave lifts the signal to first order in the wave amplitude instead of second, a ratio of about 10¹¹ in photon flux for the worked parameters — but the background beam shares the signal’s direction and distribution, so after the noise is accounted for the sensitivity gain is only one to two orders of magnitude.Section 2.2; Eqs. 7 to 10; Figure 1
Superconducting cavities do better on the same field: a planar open cavity of 0.05 m³ with quality factor 10⁷ at 9 T and 3 GHz reaches 3.9 times 10⁻²³ for a non-stochastic wave, and a closed cylindrical cavity of radius 0.35 m and length 89 cm with quality factor 10¹¹ reaches 3.0 times 10⁻²⁶ — with the caveat that cavity signal energy depends on the wave’s amplitude rather than its frequency.Sections 2.3 and 2.5; Eqs. 16 and 30; Concluding remark IV
In the synchro-resonance system the perturbative photon flux is transverse and differs from the background beam in distribution, direction, polarisation and decay rate, so it can be separated by choosing the position and orientation of the receiving surface; with 9 T, a 10 W Gaussian beam, a 2 m interaction length, an operating temperature near 0.14 K and 10⁶ s of integration the scheme reaches about 5.7 times 10⁻³², and the authors argue the remaining barriers are engineering and technology rather than a limit of principle.Section 2.6; Eqs. 37 and 38; Figures 3 and 4; Section 3, points I to III and V
The way in
https://doi.org/10.1088/1674-1056/22/12/120402How to cite it
Fang-Yu Li, Hao Wen, Zhen-Yun Fang (2013) High-frequency gravitational waves having large spectral densities and their electromagnetic response doi:10.1088/1674-1056/22/12/120402