Historical research guide · 1112 · 2019
Chiral Casimir forces: Repulsive, enhanced, tunable
Qing-Dong Jiang · Frank Wilczek
In one minute
Two flat mirrors in vacuum pull towards each other because the quantum fluctuations of the electromagnetic field between them are not the same as the ones outside. A well-known theorem says you cannot turn that pull into a push if the two bodies are mirror images of each other — and that theorem has discouraged a lot of work. Qing-Dong Jiang and Frank Wilczek find the loophole in it. The proof quietly assumes that left-handed and right-handed circularly polarised light travel the same way through whatever sits between the plates. Fill the gap with a chiral material — an optically active liquid, or any medium in a magnetic field — and the two handednesses travel at different speeds, the theorem’s key step fails, and the force becomes something you can engineer. Their calculation gives a Casimir force that oscillates with separation between attraction and repulsion, can be made stronger than the plain metallic force, and can be turned up and down with an external magnet.
Connection
Chapter 2 treats the vacuum as a medium whose modes you can reshape, and this is the cleanest statement of what that buys you: change the handedness of the medium and the sign of a quantum-vacuum force changes with it. Chapter 6 keeps the record of useful work drawn from vacuum fluctuations, and a force whose direction you control with a knob is where that record starts.
From the source
The no-go theorem that objects made of the same isotropic material always attract across a reflection-symmetric gap has a loophole: its proof needs one operator combination to be Hermitian, and that step fails whenever the medium in the gap gives left-circular and right-circular photons different phase velocities.Section ‘Identifying the loophole’, Equation 6 and the paragraph following Equation 7
With a chiral medium between two identical plates the Casimir energy picks up a cosine of twice the optical rotation angle, so the force oscillates with separation between attraction and repulsion instead of always pulling.Equation 11; Figure 3(a), where the shaded band marks the repulsive regime
In a Faraday medium the rotation angle is the Verdet constant times the magnetic field times the gap, so an external magnet becomes the control knob: it moves the force between attraction and repulsion and can also push its magnitude above the ordinary metallic Casimir force.Section (i) Faraday materials; Equation 11 and Figure 3(b)
An optically active liquid does the same job with no magnet at all, and without breaking time-reversal symmetry: replacing the Verdet-constant-times-field product with specific rotation times mass concentration reproduces the same Casimir energy.Section (ii) Optically active materials, following Equation 11
The proposal comes with laboratory numbers rather than a hope: a Verdet constant of five times ten to the fourth radians per metre per tesla, taken from measurements on organic molecules and liquids, fields of four and ten tesla, and plate separations of six and eight micrometres, with the frequency dependence of the rotation and imperfect mirror reflectivity both carried through.Text preceding Equation 11; Figures 3 and 4
Because the effect is tied to material properties that are measured independently — the Verdet constant and the specific rotation — the prediction is directly checkable, and the authors note that the finite-temperature extension gives larger forces with the same qualitative behaviour, which is the version an experiment would meet first.Summary paragraph; supplemental materials
The way in
https://doi.org/10.1103/physrevb.99.125403How to cite it
Qing-Dong Jiang, Frank Wilczek (2019) Chiral Casimir forces: Repulsive, enhanced, tunable doi:10.1103/physrevb.99.125403