Historical research guide · 0669 · 2017
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
In one minute
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.
Connection
Chapter 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.
From the source
The 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
The 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’
At 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
The 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
The 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
The 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
The way in
https://doi.org/10.1038/nphoton.2016.254How 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