STM-D-0646Paper2011Published and peer-reviewed

Observation of the thermal Casimir force

A. O. Sushkov · W. J. Kim · D. A. R. Dalvit · S. K. Lamoreaux

Abstract and summary · read the original at the source

In one page

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.

Why it matters hereChapter 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.

What it claims

01The 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
Settled physics
02The 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
Published and peer-reviewed
03Patches 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
What to watch
04Fitting 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
Published and peer-reviewed
05The 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
Published and peer-reviewed
06The 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
Published and peer-reviewed

Read it · abstract

Abstract

Quantum theory predicts the existence of the Casimir force between macroscopic bodies, due to the zero-point energy of electromagnetic field modes around them. This quantum fluctuation-induced force has been experimentally observed for metallic and semiconducting bodies, although the measurements to date have been unable to clearly settle the question of the correct low-frequency form of the dielectric constant dispersion (the Drude model or the plasma model) to be used for calculating the Casimir forces. At finite temperature a thermal Casimir force, due to thermal, rather than quantum, fluctuations of the electromagnetic field, has been theoretically predicted long ago. Here we report the experimental observation of the thermal Casimir force between two gold plates. We measured the attractive force between a flat and a spherical plate for separations between 0.7 µm and 7 µm. An electrostatic force caused by potential patches on the plates’ surfaces is included in the analysis. The experimental results are in excellent agreement (reduced chi-squared of 1.04) with the Casimir force calculated using the Drude model, including the T = 300 K thermal force, which dominates over the quantum fluctuation-induced force at separations greater than 3 µm. The plasma model result is excluded in the measured separation range.

The way in

https://doi.org/10.1038/nphys1909Published as Nature Physics 7, 230 (2011). The preprint is on arXiv as 1011.5219, filed November 2010 under arXiv’s non-exclusive distribution licence, which does not grant redistribution — so this page carries the summary, the claims and the authors’ own abstract, and sends the reader to the full text at the source. The work was supported by the DARPA Microsystems Technology Office Casimir Effect Enhancement project under SPAWAR contract N66001-09-1-2071.

How 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

Where it sits in the curriculum

What the vacuum is