Recent developments on the Casimir torque
Benjamin Spreng · Tao Gong · Jeremy N. Munday
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In one page
Benjamin Spreng, Tao Gong and Jeremy Munday, at the University of California, Davis, survey the vacuum’s second mechanical signature. Everyone knows the Casimir force: two surfaces a fraction of a micrometre apart are pushed together by the electromagnetic fluctuations of empty space. Less famous is what happens when the surfaces care about direction — birefringent crystals, whose optical response depends on which way their axis points. Then the vacuum also twists them, trying to bring their axes into alignment, and the twist can be read as angular momentum handed from the vacuum modes to the plates. This review gathers the theory, the predictions and, above all, the hardware. It explains why the torque was so hard to measure — the trick that saves the force experiments, swapping one flat plate for a sphere, does not work when the material has an axis — how the first measurement finally succeeded in 2018 using a liquid crystal, and what the proposed benches look like: a disk floating on a repulsive Casimir force, a three-threaded pendulum, a levitated nanorod.
Why it matters hereChapter 2 rests on the vacuum being a real, structured medium, and the torque is the sharpest demonstration of that after the force itself: empty space does not merely pull two surfaces together, it turns them. Chapter 6 gets a shopping list, because this review is mostly about apparatus — three concrete benches with materials, dimensions and sensitivities, plus the finding that shaping a surface can beat choosing an exotic material by three orders of magnitude. The authors close by pointing out that the torque is far less explored than the force, theoretically and experimentally, which is an invitation. Their thermal calculation is at /library/stm-951ff458cb and a switchable-torque proposal at /library/stm-5a43d13a69.
What it claims
01The Casimir force exists between any pair of bodies separated by vacuum, generated by quantum fluctuations of the electromagnetic field, and dominates at submicron separations, which is why it has practical consequences for nano- and micro-electromechanical systems; in the nonretarded limit the same interaction is the van der Waals force.Section 1, Introduction, opening paragraph
Settled physics02When the two plates are made of anisotropic material the energy of the Casimir interaction depends on the mutual orientation of their optic axes, so a torque rotates them as well as a force pulling them together; where the force can be read as radiation pressure of the vacuum modes, the torque can be read as angular momentum transferred from the vacuum modes to the plates. The nonretarded torque was first predicted in the early 1970s and retardation was fully included in 1978.Section 1, Introduction, second and third paragraphs, citing references 7 to 10
Published and peer-reviewed03The torque was measured for the first time in 2018 between a liquid crystal and a solid birefringent plate — the liquid crystal 5CB against calcium carbonate, lithium niobate, titanium dioxide and yttrium orthovanadate, separated by isotropic layers — with the twist read optically against the elastic restoring torque of the liquid-crystal bulk; the measured torque follows the sine of twice the twist angle, and its magnitude and sign match theory for all four plate materials.Section 5, Experimental Verification; Figure 7(a) and 7(b)
Published and peer-reviewed04Anisotropic surfaces behave opposite to isotropic ones in a useful way: where retardation and an intervening medium weaken the ordinary Casimir interaction, they strengthen the torque — the torque between two titanium dioxide plates is enhanced once retardation is included, water as the intervening medium can roughly double it, and coating the surfaces with graphene can raise it by more than an order of magnitude.Section 3.1, Material response anisotropy; Figure 3(a), citing references 20 and 31
Published and peer-reviewed05Shape can stand in for material anisotropy and pays far better: two periodically corrugated plates give a torque per unit area of 5.2 times ten to the minus seven newtons per metre at a separation of 100 nanometres, three orders of magnitude above calcite against barium titanate, and lamellar gratings of 400-nanometre period, half filling factor and 200-nanometre corrugation height give 3.5 times ten to the minus eight newtons per metre at a twist angle near 12.5 degrees — and in these systems the torque stops following the simple sine law.Section 3.2, Morphological anisotropy, citing references 43 to 45
Published and peer-reviewed06Three benches are laid out with numbers: a quartz or calcite disk 40 micrometres across floating in ethanol about 100 nanometres above a barium titanate plate, held there by a repulsive Casimir force and free to turn like a frictionless bearing; a three-threaded torsion pendulum in vacuum whose rotational frequency of about 0.08 hertz sits below the microseismic background and whose minimum detectable torque is around ten to the minus fourteen newton metres per root hertz, well inside the grating prediction; and a silica nanorod 200 nanometres long and 40 nanometres across levitated above a birefringent plate by an optical tweezer, which works in air or vacuum.Sections 4.1, 4.3 and 4.4, Proposed Experiments; Figure 6
Designed, not yet built
The way in
https://doi.org/10.1142/S0217751X22410111LICENCE. Published as International Journal of Modern Physics A, volume 37, article 2241011, 24 pages — received 6 May 2022, accepted 25 May 2022, published 30 June 2022 — copyright World Scientific Publishing Company. Every page of the article carries the line ‘Re-use and distribution is strictly not permitted, except for Open Access articles’, and no Creative Commons statement appears on it, so this page reproduces none of the text. The claims below are read from the full article, from the authors’ own copy posted by the Munday group at the University of California, Davis, and every locator points into it. The work was supported by the National Science Foundation under grant PHY-1806768. Companion sheets on this site: the same group’s thermal calculation at /library/stm-951ff458cb and the altermagnet proposal at /library/stm-5a43d13a69.
How to cite it
Benjamin Spreng, Tao Gong, Jeremy N. Munday (2022) Recent developments on the Casimir torque. doi:10.1142/S0217751X22410111
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