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COMPARISON

BETWEEN EXPERIMENT AND THEORY

FOR THE THERMAL CASIMIR FORCE

G. L. KLIMCHITSKAYA

Department of Physics, North-West Technical University, St.Petersburg, Russia

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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

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1. Introduction

The magnitude of the thermal correction to the Casimir force between test bodiesmade of real materials, as predicted by theLifshitz theory and its generalizations,strongly depends on models of dielectricpermittivities 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 plateswith 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

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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 samecontributions to the Casimir force at T=0 and to its thermal correctionas the exact theory

(Bordag, Pirozhenko, PRD, 2010; Teo, PRD, 2011)

Only the correction of order d/R to the PFA results is possiblein the exact theory.

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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 thatIs 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)

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This is not always so!

The correct factor is:

outside the application regionof the PFA;

in the application regionof the PFA;

(Geyer, GLK, Mostepanenko, PRA, 2010)

For instance, according to the exact theory at separation of5 micrometers q increases from approximately 1.48 to 1.63 when d/R decreases from 2.5 to 0.5.

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outside the application regionof the PFA;

(Zandi, Emig, Mohideen, PRB, 2010)

Conclusion: inside its application region the PFA

works perfectly well.

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3. Experiments between metal test bodies using a micromachined oscillator

Decca et al, PRD (2003), Ann. Phys. (2005), PRD (2007), EJPC (2007)

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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.

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The errors are shown at a 67% confidence level.

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The number of degrees of freedom

The penetration depth of electromagnetic oscillations intoa metal:

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Plasma model approach:

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Plasma model approach:

Fit of the mean values of the pressure measured:

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Plasma model approach:

Fit of the mean values of pressure measured:

Fit of different sets of individual measurements:

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Drude model approach:

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Drude model approach:

Fit of the mean values of the pressure measured:

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Drude model approach:

Fit of the mean values of pressure measured:

Fit of different sets of individual measurements:

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Could patch effect compensate the difference betweenexperimental 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:1108.1761)

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.

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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.

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The characterization of the fit:

The theoretical force-distance dependence of the patches due tohypothetical large contaminants is irrelevant to the differencebetween the experimental data and the Drude model prediction.

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The difference between theexperimental data and theDrude 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).

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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.

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Difference of the Casimir force in the presence and absenceof laser light

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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., 2011.

4.3 The Casimir force between Au sphere and ITO plate

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Masuda, Sasaki, PRL 2009

5. Torsion balance experiments

5.1 Confirmation of the thermal correction predicted for ideal metals

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Sushkov, Kim, Dalvit,Lamoreaux, Nature Phys. 2011

5.2 Purported observation of the thermal Casimir force predicted by the Drude model

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5.2 Purported observation of the thermal Casimir force predicted by the Drude model

Sushkov, Kim, Dalvit,Lamoreaux, Nature Phys. 2011

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5.2 Purported observation of the thermal Casimir force predicted by the Drude model

Sushkov, Kim, Dalvit,Lamoreaux, Nature Phys. 2011

Fit using the Drude model:

f=19

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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 indefinitevalues of the Casimir force below 3 micrometers.

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The Casimir force between a perfectly spherical lens and a plate, both describedby the Drude mode is shownby the dashed line.

The red line shows the same force between a sphere withsome surface imperfection and a plate, both described by the plasma model.

Bezerra, GLK, Mohideen, Mostepanenko, Romero, PRB, 2011

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6. Conclusions

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

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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.

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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.

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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.

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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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