Historical research guide · 0585 · 2016
Interaction of gravitational waves with superconductors
N. A. Inan · J. J. Thompson · R. Y. Chiao
In one minute
A gravitational wave stretches and squeezes everything it passes through, including a superconductor. Nader Inan, Jay Thompson and Raymond Chiao work out what a superconductor does back. They rewrite weak-field general relativity so that the wave has an electric-like and a magnetic-like part, exactly as an electromagnetic wave does, and find that the magnetic-like part is pushed out of the superconductor the way an ordinary magnetic field is — a gravitational version of the Meissner effect. Then they treat the two things inside the metal separately. The lattice of ions, modelled as quantum oscillators, responds strongly; the Cooper pairs, locked into one coherent quantum state, barely respond at all — about ten thousand times less. Because the ions are positive and the pairs negative, the wave pulls them apart and leaves a charge separation behind. Their other result is the interesting one for this site: the wave modulates the zero-point energy of the lattice phonons, which is a dynamical Casimir effect made of sound.
Connection
Chapter 11 asks whether coherent quantum matter can couple to gravity strongly enough to use, and this paper gives that question a full theoretical machine — London equations, Meissner effect, penetration depth and shear modulus, all written for gravity instead of electromagnetism. It also feeds chapter 3, because the quantity doing the work here is the zero-point energy of the lattice, modulated by a passing ripple in the metric.
From the source
Applying the Helmholtz decomposition to linearised general relativity gives a gauge-invariant formulation in which the transverse-traceless part of the metric perturbation describes gravitational waves inside matter, not only plane waves in vacuum as the transverse-traceless gauge alone allows.Section 1, Introduction
A gravitational wave incident on a superconductor obeys a London-like constituent equation set by a gravitational shear modulus, which yields a gravitational plasma frequency and a gravitational penetration depth in the same form as their electromagnetic counterparts.Sections 2 and 3, Equation 6
In the DC limit the magnetic-like gravitational tensor field is expelled from the superconductor in a gravitational Meissner-like effect, and the expulsion holds for all frequencies down to DC, with the upper frequency bound set by the BCS energy gap, above which the Cooper pairs break and superconductivity is destroyed.Section 4, Equation 16
The zero-point energy of the ionic lattice phonons is modulated by the gravitational wave, which is a dynamical Casimir effect of the acoustic kind — the authors name it a dynamical gravito-phonon Casimir effect — and it predicts a rise in the occupation number of the lattice phonon modes, the quantum analogue of a Weber-bar effect in which incoming gravitational wave energy is converted into sound energy in the lattice.Section 6, following Equation 34
For niobium, the zero-point energy density term dominates the gravitational shear modulus of the lattice, giving about 2.8 times ten to the eighth joules per cubic metre against a sum-of-modes term near 9 times ten to the minus twelfth, so the lattice ions are on the order of 10⁴ times more responsive to a gravitational wave than the Cooper pair density.Section 6, Equations 37 and 38
Because the lattice and the Cooper pairs move differently, the relative strain between them is about one percent of the gravitational wave strain, and since lattice ions are positively charged and Cooper pairs negatively charged, a gravitational wave induces a macroscopic charge separation with no classical analogue — confined to the London penetration depth, since the wave itself decays exponentially deeper in.Section 7, Conclusion, Equations 39 and 40
The way in
https://doi.org/10.1002/prop.201600066How to cite it
N. A. Inan, J. J. Thompson, R. Y. Chiao (2016) Interaction of gravitational waves with superconductors doi:10.1002/prop.201600066