QFEXT11 COMPARISON BETWEEN EXPERIMENT AND THEORY FOR THE THERMAL CASIMIR FORCE G. L. KLIMCHITSKAYA Department of Physics, North-West Technical University, St.Petersburg, Russia

QFEXT11 CONTENT 1. Introduction 2. Is the PFA exact enough for theory-experiment comparison? 3. Experiments between metal test bodies using a micromachined oscillator 4. Experiments with semiconductor and dielectric test bodies 5. Torsion balance experiments 6. Conclusions

QFEXT11 1. Introduction The magnitude of the thermal correction to the Casimir force between test bodies made of real materials, as predicted by the Lifshitz theory and its generalizations, strongly depends on models of dielectric permittivities used for the description of these materials.

Models of the frequency-dependent dielectric permittivity Permittivity of dielectric plates, as determined by core electrons Permittivity of dielectric plates with dc conductivity included The Drude model permittivity for metallic plates The plasma model permittivity for metallic plates The Lifshitz theory with or for perfect crystal lattices violates the Nernst theorem QFEXT11

2. Is the PFA exact enough for theory-experiment comparison? The region of experimental parameters: For ideal metals in the zeroth order in d/R the PFA gives the same contributions to the Casimir force at T=0 and to its thermal correction as the exact theory (Bordag, Pirozhenko, PRD, 2010; Teo, PRD, 2011) Only the correction of order d/R to the PFA results is possible in the exact theory.

QFEXT11 For plasma and Drude metals the exact computations of the Casimir force were done for d/R>0.1. Deviations in ratios q of the Casimir forces calculated using the plasma and Drude models in the framework of the exact theory and PFA decreases from 9.2% to 2.5% when d/R decreases from 5 to 0.1. Claim: at large separations the Drude model leads to a force that Is smaller by a factor q=3/2 than the force with the plasma model (instead of a factor q=2 as follows from the PFA). (Canaguier-Durand, Maia Neto, Lambrecht, Reynaud, PRL, 2010)

QFEXT11 This is not always so! The correct factor is: outside the application region of the PFA; in the application region of the PFA; (Geyer, GLK, Mostepanenko, PRA, 2010) For instance, according to the exact theory at separation of 5 micrometers q increases from approximately 1.48 to 1.63 when d/R decreases from 2.5 to 0.5.

QFEXT11 outside the application region of the PFA; (Zandi, Emig, Mohideen, PRB, 2010) Conclusion: inside its application region the PFA works perfectly well.

QFEXT11 3. Experiments between metal test bodies using a micromachined oscillator Decca et al, PRD (2003), Ann. Phys. (2005), PRD (2007), EJPC (2007)

QFEXT11 The errors are shown at a 95% confidence level. The red band shows the prediction of the plasma model. The green band corresponds to the Drude model.

QFEXT11 The errors are shown at a 67% confidence level.

QFEXT11 The number of degrees of freedom The penetration depth of electromagnetic oscillations into a metal:

QFEXT11 Plasma model approach:

QFEXT11 Plasma model approach: Fit of the mean values of the pressure measured:

QFEXT11 Plasma model approach: Fit of the mean values of pressure measured: Fit of different sets of individual measurements:

QFEXT11 Drude model approach:

QFEXT11 Drude model approach: Fit of the mean values of the pressure measured:

QFEXT11 Drude model approach: Fit of the mean values of pressure measured: Fit of different sets of individual measurements:

QFEXT11 Could patch effect compensate the difference between experimental data and the Drude model prediction? (I) Patch effect due to polycrystallite structure in Speake-Trenkel model (PRL, 2003) is negligibly small (Chen et al., PRA, 2004; Decca et al., Ann. Phys., 2005) (II) Recently an alternative “quasi-local” model of patches was suggested (Behunin, Intravaia, Dalvit, Maia Neto, Reynaud, arXiv: ) In this model: --- patch effect due to polycrystallite structure is by orders of magnitude larger than in the Speake-Trenkel model and much exceeds the difference between experimental data and the Drude model prediction; --- it is claimed that the patch effect due to hypothetical large contaminants can be equal to this difference.

QFEXT11 The parameters of these contaminants (the maximum size and the root-mean-square voltage) are determined from the fit to the difference between the experimental data and the Drude model prediction. This fit has the two defects: --- the Drude model prediction was computed using too simplified model of the dielectric permittivity and the surface roughness was not taken into account; --- in the fit, instead of the variance of the mean, the experimental error determined at a 95% confidence level was used.

QFEXT11 The data for the patch pressure (red line) were kindly provided by R. O. Behunin and D. A. R. Dalvit.

QFEXT11 The characterization of the fit: The theoretical force-distance dependence of the patches due to hypothetical large contaminants is irrelevant to the difference between the experimental data and the Drude model prediction.

QFEXT11 The difference between the experimental data and the Drude model prediction: -- as calculated by Behunin et al. (upper crosses); -- calculated using the tabulated optical data (Palik) extrapolated by the Drude model with account of surface roughness (lower crosses).

QFEXT11 4. Experiments with semiconductor and dielectric test bodies 4.1 Optical modulation of the Casimir force between Au sphere and Si plate Chen, GLK, Mostepanenko, Mohideen, Opt. Express, 2007; PRB, 2007.

QFEXT11 Difference of the Casimir force in the presence and absence of laser light

QFEXT11 Obrecht, Wild, Antezza, Pitaevskii, Stringari, Cornell, PRL (2007); Klimchitskaya, Mostepanenko, JPA (2008) 4.2 Frequency shift of center-of-mass oscillations due to the Casimir-Polder force

Chang, Banishev, GLK, Mostepanenko, Mohideen, Phys. Rev. Lett., The Casimir force between Au sphere and ITO plate QFEXT11

Masuda, Sasaki, PRL Torsion balance experiments 5.1 Confirmation of the thermal correction predicted for ideal metals

QFEXT11 Sushkov, Kim, Dalvit, Lamoreaux, Nature Phys Purported observation of the thermal Casimir force predicted by the Drude model

QFEXT Purported observation of the thermal Casimir force predicted by the Drude model Sushkov, Kim, Dalvit, Lamoreaux, Nature Phys. 2011

QFEXT Purported observation of the thermal Casimir force predicted by the Drude model Sushkov, Kim, Dalvit, Lamoreaux, Nature Phys Fit using the Drude model: f=19

QFEXT11 Fit using the Drude model: Fit using the plasma model: GLK, Bordag.Fischbach, Krause, Mostepanenko, Int. J. Mod. Phys. A, 2011 f=4

Different types of surface imperfections demand use of more sophisticated forms of the PFA Unavoidable imperfections on lens surfaces make indefinite values of the Casimir force below 3 micrometers. QFEXT11

The Casimir force between a perfectly spherical lens and a plate, both described by the Drude mode is shown by the dashed line. The red line shows the same force between a sphere with some surface imperfection and a plate, both described by the plasma model. Bezerra, GLK, Mohideen, Mostepanenko, Romero, PRB, 2011

QFEXT11 6. Conclusions 1. The PFA is well applicable to all performed experiments with smooth surfaces.

QFEXT11 6. Conclusions 1. The PFA is well applicable to all performed experiments with smooth surfaces. 2. The thermal Casimir force, as predicted by the Drude model, is in contradiction with a number of experiments.

QFEXT11 6. Conclusions 1. The PFA is well applicable to all performed experiments with smooth surfaces. 2. The thermal Casimir force, as predicted by the Drude model, is in contradiction with a number of experiments. 3. The suggested quasi-local patches are incapable to explain the difference between data and the Drude model prediction.

QFEXT11 6. Conclusions 1. The PFA is well applicable to all performed experiments with smooth surfaces. 2. The thermal Casimir force, as predicted by the Drude model, is in contradiction with a number of experiments. 3. The suggested quasi-local patches are incapable to explain the difference between data and the Drude model prediction. 4. The purported observation of the thermal Casimir force, as predicted by the Drude model, is not an independent measurement, but a fit using fitting parameters.

QFEXT11 6. Conclusions 1. The PFA is well applicable to all performed experiments with smooth surfaces. 2. The thermal Casimir force, as predicted by the Drude model, is in contradiction with a number of experiments. 3. The suggested quasi-local patches are incapable to explain the difference between data and the Drude model prediction. 4. The purported observation of the thermal Casimir force, as predicted by the Drude model, is not an independent measurement, but a fit using fitting parameters. 5. At separations above 3 micrometers the experimental data are in agreement not with the Drude model, but with the plasma model. Below 3 micrometers a seeming agreement of the data with the Drude model can be explained by a disregard of surface imperfections.

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