Historical research guide · 0646 · 2011
Observation of the thermal Casimir force
A. O. Sushkov · W. J. Kim · D. A. R. Dalvit · S. K. Lamoreaux
In one minute
Alexander Sushkov, W. J. Kim, Diego Dalvit and Steve Lamoreaux hung a torsion pendulum inside a vacuum chamber, faced a flat gold plate at a gold-coated lens, and measured the pull between them at thirty separations from 0.7 to 7 micrometres — 383 sweeps, eight days of data. At close range the attraction between two uncharged metal plates comes from the zero-point field, the Casimir force Hendrik Casimir predicted in the late 1940s. Further apart something else takes over: the same electromagnetic field’s thermal fluctuations at room temperature, a force that falls away more slowly, as one over the square of the separation, and that dominates beyond about three micrometres. This is the first observation of that thermal Casimir force between two macroscopic bodies. It also answers a long-running question about how to describe gold at very low frequencies — the data match the Drude description with the 300 kelvin thermal term almost exactly, and the alternative plasma description does not fit the measured range.
Connection
Chapter 2 says the vacuum is a real medium whose structure is measured, not inferred, and this is one of the cleanest measurements of it: the field between two plates is doing two separate things at once, and this experiment separates them by distance. It is also the working reminder that the ‘zero’ in zero-point energy means zero thermal temperature — put the plates far enough apart at room temperature and the thermal part of the field is the larger of the two.
From the source
The attractive force between two uncharged, non-magnetic macroscopic bodies has two distinct sources — the zero-point fluctuations of the electromagnetic field, which give the Casimir force that vanishes in the classical limit, and the thermal population of those same field modes, which gives a finite-temperature force long predicted but never before observed between two macroscopic objects.Abstract and introduction, Eqs. 1 to 3
The measurement is made with a torsion pendulum in a vacuum chamber at five times ten to the minus seven torr, with a flat plate facing a spherical lens of 15.6 centimetre radius, both carrying an optically thick 700 angstrom gold layer over 100 angstroms of titanium, sampled at thirty logarithmically spaced separations from 0.7 to 7 micrometres across 383 sweeps totalling eight days of data.Results, Figure 1; Methods
Patches of varying surface potential are present even on chemically inert metal prepared in an ultra-clean environment, so their electrostatic contribution is modelled rather than measured — the fit carries just two adjustable parameters, an rms patch potential and a constant force offset — and the authors state what an independent measurement would need: millivolt potential sensitivity at micron spatial resolution, where the best custom Kelvin probes reach micron resolution at only 30 millivolts.Results, paragraph following Figure 2
Fitting the corrected data against four candidate models gives a reduced chi-squared of 1.04 for the Drude model including the 300 kelvin thermal force, with an rms patch potential of 5.4 plus or minus 0.1 millivolts and a force offset of minus 3.0 plus or minus 0.4 piconewtons, while the same fit returns 23 for the Drude model at zero temperature, 32 for the plasma model at 300 kelvin and 43 for the plasma model at zero temperature.Results, Figure 3 and the paragraph following it
The thermal Casimir force falls off as temperature divided by the square of the separation, while the zero-point force falls roughly as one over the cube, so beyond about three micrometres at room temperature the thermal term is the larger of the two — appearing in the data as a constant offset of 97 piconewton micrometres squared — and in that region the force is largely independent of the material properties of the plates.Figure 3 caption; Results, final paragraph
The theoretical curves are not free of measurement either: the Casimir force is computed in the Lifshitz formalism from ellipsometry taken between 191 and 1700 nanometres on gold plates prepared identically to the ones under test, extrapolated to zero frequency by each candidate model, with the explored plasma-frequency and dissipation ranges producing a theoretical spread of up to 3 percent.Methods, ellipsometric measurements
The way in
https://doi.org/10.1038/nphys1909How to cite it
A. O. Sushkov, W. J. Kim, D. A. R. Dalvit, S. K. Lamoreaux (2011) Observation of the thermal Casimir force doi:10.1038/nphys1909