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STM-D-0669Paper2017Published and peer-reviewed

Measurement of non-monotonic Casimir forces between silicon nanostructures

L. Tang · M. Wang · C. Y. Ng · M. Nikolic · C. T. Chan · A. W. Rodriguez · H. B. Chan

Abstract and summary · read the original at the source

In one page

Ho Bun Chan’s group at the Hong Kong University of Science and Technology, with Alejandro Rodriguez at Princeton, did something the field had wanted for years: they shaped the vacuum. The Casimir force between two flat plates always pulls, and pulls harder as they close. Theory says that if you give the surfaces the right shape, the force can instead rise, fall, reverse and rise again. Nobody had measured that, because holding two sculpted surfaces in alignment a few hundred nanometres apart is close to impossible. Their answer was to stop trying: they etched both surfaces, an array of T-shaped protrusions facing an opposing array, out of a single silicon chip, so alignment came free with the lithography. A comb actuator moves one side, a vibrating silicon beam reads the force. The measured force gradient changes sign twice, and at one position the vacuum stiffens the beam — a Casimir spring, built from nothing but fluctuations.

Why it matters hereChapter 2 says the vacuum is a real structured medium, and this is the experiment where the structure becomes an engineering variable: change the shape of the boundary and the force changes sign. Chapter 6’s vacuum-energy devices are built on exactly that move — asymmetry in a vacuum gap turned into work — and this paper shows that the geometry-dependent part of the Casimir force is measurable, calculable and now fabricable on a chip.

What it claims

  1. 01The Casimir force between two silicon surfaces carrying opposing arrays of T-shaped protrusions depends non-monotonically on displacement: the measured force gradient changes sign at two separate positions, near 0.6 and 0.8 micrometres. To the authors’ knowledge, non-monotonic Casimir forces had not been measured in any previous experiment.Abstract; Fig. 4 and the first of the three features discussed after it

    Published and peer-reviewed
  2. 02The alignment problem that had blocked these geometries is solved by making both bodies at once. The whole structure is etched from the device layer of a single silicon-on-insulator wafer, so the two facing arrays — 31 units of protrusions on the detector beam and 32 on the movable electrode — are automatically aligned by the lithography; an integrated comb actuator sets the separation and a doubly-clamped beam 1.5 micrometres wide and 100 micrometres long reads the force gradient from its shift in resonant frequency.Fig. 2 and its caption; the paragraph beginning ‘For conventional force measurement schemes’

    Published and peer-reviewed
  3. 03At the displacement where the tops of the protrusions line up, the beam’s resonant frequency rises above its unperturbed value: the quantum fluctuations of the electromagnetic field add mechanical confinement, a Casimir spring closely analogous to the optical spring produced by real photons in optomechanical systems, though much weaker here than the silicon spring itself.Fig. 4, second discussed feature; Fig. 1d, position II

    Published and peer-reviewed
  4. 04The measurement is compared against a first-principles calculation with no fitting parameters — the boundary-element fluctuating-surface-currents method in SCUFF-EM, meshing the geometry digitized from the electron micrograph and including the finite conductivity of silicon — and the calculation reproduces every main feature: the two maxima, the minimum and the sharp rise. At the 4 kelvin measurement temperature the thermal correction is negligible, the zeroth Matsubara term contributing under 0.3 per cent of the force.The paragraph beginning ‘We minimize the electrostatic contribution’; Fig. 4 caption; Methods

    Published and peer-reviewed
  5. 05The result respects the Rahi and colleagues stability theorem rather than testing it: for bodies separated by vacuum whose optical response is a dielectric function with negligible magnetic susceptibility, Casimir equilibria can only be unstable. The restoring behaviour measured here acts along the detection direction only; the configuration remains unstable to displacements perpendicular to it, where the mechanical springs supporting the electrode and combs supply the restoring force.Fig. 4, third discussed feature

    Settled physics
  6. 06The authors present this as a first step: the same on-chip scheme can measure lateral Casimir forces between structures of other novel shapes, and realizing the geometries predicted to give repulsive Casimir forces — a glide-symmetric arrangement, or an elongated metallic particle approaching a metallic plane with a circular hole — would open the possibility of reducing stiction and levitating nanomechanical devices.Introduction, final paragraph; Summary paragraph

    What to watch

Read it · abstract

Abstract

Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field. Apart from controlling the Casimir force via the optical properties of the materials, a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps. Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators, we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the Casimir force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.

The way in

https://doi.org/10.1038/nphoton.2016.254Published in Nature Photonics under the Springer text-and-data-mining licence. The preprint is on arXiv as 1701.02351 with no Creative Commons statement on the paper or the listing, so this sheet carries the summary, the claims and the authors’ own abstract and sends the reader to the source. The work is from the Hong Kong University of Science and Technology with Princeton University.

How to cite it

L. Tang, M. Wang, C. Y. Ng, M. Nikolic, C. T. Chan, A. W. Rodriguez, H. B. Chan (2017) Measurement of non-monotonic Casimir forces between silicon nanostructures. doi:10.1038/nphoton.2016.254

Where it sits in the curriculum

What the vacuum isEnergy from the vacuum

Provenance: Retrieved 2026-09-08 · sha256 1af205812850 · Summary by The Spacetime Metric editorial rail (AI draft from the source text, 2026-09-07)← The library