Linear temperature correction to the Casimir force

We compare theory and experiment in the Casimir force measurement between gold surfaces performed with the atomic force microscope. Both random and systematic experimental errors are found leading to a total absolute error equal to 8.5 pN at 95% confidence. In terms of the relative errors, experimental precision of 1.75% is obtained at the shortest separation of 62 nm at 95% confidence level (at 60% confidence the experimental precision of 1% is confirmed at the shortest separation). An independent determination of the accuracy of the theoretical calculations of the Casimir force and its application to the experimental configuration is carefully made. Special attention is paid to the sample-dependent variations of the optical tabulated data due to the presence of grains, contribution of surface plasmons, and errors introduced by the use of the proximity force theorem. Nonmultiplicative and diffraction-type contributions to the surface roughness corrections are examined. The electric forces due to patch potentials resulting from the polycrystalline nature of the gold films are estimated. The finite size and thermal effects are found to be negligible. The theoretical accuracy of about 1.69% and 1.1% are found at a separation 62 nm and 200 nm, respectively. Within the limits of experimental and theoretical errors very good agreement between experiment and theory is confirmed characterized by the root mean square deviation of about 3.5 pN within all measurement range. The conclusion is made that the Casimir force is stable relative to variations of the sample-dependent optical and electric properties, which opens new opportunities to use the Casimir effect for diagnostic purposes.

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“…[57] this contribution is postulated to be of the same value as for an ideal metal). The alternative thermal correction of Ref.…”

Section: Contributions Of the Thermal Corrections Residual Elec-tmentioning

confidence: 96%

Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision

2004

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“…Svetovoy and Lokhanin [20] proposed to use SDM prescription for the n = 0 term in the Lifshitz formula for real metals also. Later it was shown [21] that this prescription follows from a very general dimensional analysis of the classical contribution to the force if one demands continuous transition to the ideal metal case. The temperature correction happened to be small but observable at small separations between bodies.…”

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The Casimir free energy in high- and low-temperature limits

Svetovoy

Esquivel

2006

J. Phys. A: Math. Gen.

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The problem with the temperature dependence of the Casimir force is investigated. We analyse high-temperature limit analytically making calculations at real frequencies. The purpose is to answer the question why there is no continuous transition between real and ideal metals and why the result does not depend on the relaxation frequency. It is found that the contribution of evanescent s polarized fields is finite even for an infinitely small relaxation frequency (plasma model) and exactly cancels the contribution of propagating fields. For the ideal metal the evanescent fields do not contribute at all. The lowtemperature limit is analysed to establish behaviour of the entropy at T → 0. It is stressed that the nonlocal effects are important in this limit because the mean free path for electrons becomes larger than the field penetration depth. In this limit v F /a plays the role of the relaxation frequency, where v F is the Fermi velocity and a is the distance between plates. It is indicated that the Leontovich approximate impedance cannot be used for calculations because it is good for the description of propagating but not evanescent fields. It is found that due to nonlocality the Casimir entropy approaches zero at T → 0 when s polarization does not contribute to the classical part of the Casimir force.

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“…However, in all calculations [5,6,11] the role of Au/P d layer was ignored. Importance of this layer was stressed in [12] (see also [13]), where the upper limit on the force has been found using parameters of single-crystalline materials. This limit was smaller than the measured force in both experiments [5,6] and the discrepancy far exceeded the experimental errors.…”

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confidence: 99%

“…An error was admitted in extrapolation of the optical data for Au to low frequencies. At last, the finite temperature correction was neglected but it is important at small separations [12,15]. These are the main points we will discuss in this paper.…”

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Precise Calculation of the Casimir Force Between Gold Surfaces

Svetovoy

Lokhanin

2000

Mod. Phys. Lett. A

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We analyse the result of precise measurement of the Casimir force between bodies covered with gold. The values of the parameters used to extrapolate the gold dielectric function to low frequencies are very important and discussed in detail. The finite temperature effect is shown to exceed considerably the experimental errors. The upper limit on the force is found which is smaller than the measured force. Many experimental and theoretical uncertainties were excluded with gold covering and we conclude that, possibly, a new force has been detected at small separations between bodies.12.20. Ds, 12.20.Fv, 03.70.+k, 14.80 c a 4 has been found as change in the zero point energy between two parallel perfectly conducting plates separated by the distance a. For sphere and plate the expression above has to be modified with the proximity force theorem (PFT) [7] to the followingwhere R is the sphere radius. Real metals are not ideal conductors and there is an important correction to (1) taking into account their real properties. In the Lifshitz theory [8], which generalizes the Casimir approach, the force is represented in terms of the metal dielectric function ε (iω) at imaginary frequencies. This theory was applied for description of the experiments in [6,9]. Different but equivalent method has been developed in [10], where detailed calculations were made for Al, Au, and Cu metallization of the bodies using the handbook optical data for these metals. The result for Au is in good agreement with the torsion pendulum experiment [4]. For the atomic force microscope (AFM) experiment [5,6] Al metallization has been used. This metal is oxidized easily and charges can be trapped in the oxide. To prevent influence of these charges on the force, Al was covered with a thin layer (20 or 8 nm thick) of Au/P d. The conclusion has been made [6] that the result of the AFM experiment was in agreement with the theory. However, in all calculations [5,6,11] the role of Au/P d layer was ignored. Importance of this layer was stressed in [12] (see also [13]), where the upper limit on the force has been found using parameters of single-crystalline materials. This limit was smaller than the measured force in both experiments [5,6] and the discrepancy far exceeded the experimental errors. To exclude uncertainties connected with aluminum oxidation, Au/P d layer and clarify the origin of the discrepancy, it was proposed [12] to use Au metallization instead of Al. Very recently the AFM experiment with Au metallization has been carried out [14]. In this experiment the residual potential was reduced to a negligible level so as the surface roughness. The force was measured for smaller separations up to 62 nm with uncertainty 3.5 pN . In the previous experiments the photodiods response on the cantilever deflection was calibrated assuming that the plate-sphere system on the contact behaves as a rigid body. As the new experiment showed this natural assumption was not quite correct and different calibration method was proposed [14]. To all appearance the exc...

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Linear temperature correction to the Casimir force

Cited by 65 publications

References 24 publications

Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision

Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision

The Casimir free energy in high- and low-temperature limits

Precise Calculation of the Casimir Force Between Gold Surfaces

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