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Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using atomic force microscope in a frequency shift technique

We present measurement results for the gradient of the Casimir force between an Au-coated sphere and an Au-coated plate obtained by means of an atomic force microscope operated in a frequency shift technique. This experiment was performed at a pressure of 3x10^{-8} Torr with hollow glass sphere of 41.3 mcm radius. Special attention is paid to electrostatic calibrations including the problem of electrostatic patches. All calibration parameters are shown to be separation-independent after the corrections for mechanical drift are included. The gradient of the Casimir force was measured in two ways with applied compensating voltage to the plate and with different applied voltages and subsequent subtraction of electric forces. The obtained mean gradients are shown to be in mutual agreement and in agreement with previous experiments performed using a micromachined oscillator. The obtained data are compared with theoretical predictions of the Lifshitz theory including corrections beyond the proximity force approximation. An independent comparison with no fitting parameters demonstrated that the Drude model approach is excluded by the data at a 67% confidence level over the separation region from 235 to 420 nm. The theoretical approach using the generalized plasma-like model is shown to be consistent with the data over the entire measurement range. Corrections due to the nonlinearity of oscillator are calculated and the application region of the linear regime is determined. A conclusion is made that the results of several performed experiments call for a thorough analysis of the basics of the theory of dispersion forces.Comment: 35 pages, 14 figures, 1 table; to appear in Phys. Rev.

Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder $(\epsilon_1, \mu_1)$ and of that which makes up the surroundings $(\epsilon_2, \mu_2)$ obey the relation $\epsilon_1\mu_1= \epsilon_2\mu_2$. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in complete agreement with that obtained by DeRaad and Milton who employed a Green's function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in previous version corrected, giving a zero Casimir energy for a tenuous cylinde

Experimental approaches to the difference in the Casimir force through the varying optical properties of boundary surface

We propose two novel experiments on the measurement of the Casimir force acting between a gold coated sphere and semiconductor plates with markedly different charge carrier densities. In the first of these experiments a patterned Si plate is used which consists of two sections of different dopant densities and oscillates in the horizontal direction below a sphere. The measurement scheme in this experiment is differential, i.e., allows the direct high-precision measurement of the difference of the Casimir forces between the sphere and sections of the patterned plate or the difference of the equivalent pressures between Au and patterned parallel plates with static and dynamic techniques, respectively. The second experiment proposes to measure the Casimir force between the same sphere and a VO${}_2$ film which undergoes the insulator-metal phase transition with the increase of temperature. We report the present status of the interferometer based variable temperature apparatus developed to perform both experiments and present the first results on the calibration and sensitivity. The magnitudes of the Casimir forces and pressures in the experimental configurations are calculated using different theoretical approaches to the description of optical and conductivity properties of semiconductors at low frequencies proposed in the literature. It is shown that the suggested experiments will aid in the resolution of theoretical problems arising in the application of the Lifshitz theory at nonzero temperature to real materials. They will also open new opportunities in nanotechnology.Comment: 23 pages of the text, 2 tables, and captions of 12 figures (to appear in Phys. Rev. A

Fluctuations of the Retarded Van der Waals Force

The retarded Van der Waals force between a polarizable particle and a perfectly conducting plate is re-examined. The expression for this force given by Casimir and Polder represents a mean force, but there are large fluctuations around this mean value on short time scales which are of the same order of magnitude as the mean force itself. However, these fluctuations occur on time scales which are typically of the order of the light travel time between the atom and the plate. As a consequence, they will not be observed in an experiment which measures the force averaged over a much longer time. In the large time limit, the magnitude of the mean squared velocity of a test particle due to this fluctuating Van der Waals force approaches a constant, and is similar to a Brownian motion of a test particle in an thermal bath with an effective temperature. However the fluctuations are not isotropic in this case, and the shift in the mean square velocity components can even be negative. We interpret this negative shift to correspond to a reduction in the velocity spread of a wavepacket. The force fluctuations discussed in this paper are special case of the more general problem of stress tensor fluctuations. These are of interest in a variety of areas fo physics, including gravity theory. Thus the effects of Van der Waals force fluctuations serve as a useful model for better understanding quantum effects in gravity theory.Comment: 14 pages, no figure

Constraints on non-Newtonian gravity from the Casimir force measurements between two crossed cylinders

Constraints on the Yukawa-type corrections to Newtonian gravitational law are obtained resulting from the measurement of the Casimir force between two crossed cylinders. The new constraints are stronger than those previously derived in the interaction range between 1.5 nm and 11 nm. The maximal strengthening in 300 times is achieved at 4.26 nm. Possible applications of the obtained results to the elementary particle physics are discussed.Comment: An error in the text and in the figure had been corrected. To appear in Phys. Rev.

Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to Sonoluminescence

We show that the Casimir, or zero-point, energy of a dilute dielectric ball, or of a spherical bubble in a dielectric medium, coincides with the sum of the van der Waals energies between the molecules that make up the medium. That energy, which is finite and repulsive when self-energy and surface effects are removed, may be unambiguously calculated by either dimensional continuation or by zeta function regularization. This physical interpretation of the Casimir energy seems unambiguous evidence that the bulk self-energy cannot be relevant to sonoluminescence.Comment: 7 pages, no figures, REVTe

Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of a nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate is suggested which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur

Casimir type effects for scalar fields interacting with material slabs

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. For the single layer system we develop a rigorous calculation method and derive explicitly the propagator of the theory, S-matrix elements and the Casimir self-energy of the slab. Detailed investigation of particular limits of self-energy is presented, and connection to know cases is discussed. The calculation method is found applicable to the two mirrors case as well. By means of it we derive the corresponding Casimir energy and analyze it. For particular values of the parameters of the model the obtained results recover the Lifshitz formula. We also propose a procedure to obtain unambiguously the finite Casimir \textit{self}-energy of a single slab without reference to any renormalizations. We hope that our approach can be applied to calculation of Casimir self-energies in other demanded cases (such as dielectric ball, etc.)Comment: 22 pages, 3 figures, published version, significant changes in Section 4.

Casimir and van der Waals force between two plates or a sphere (lens) above a plate made of real metals

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated accounting for the finite conductivity of the metals. The simple formalism of surface modes is briefly presented which allows the possibility to obtain the generalization of Lifshitz results for the case of two semi-spaces covered by the thin layers. Additional clarifications of the regularization procedure provides the means to obtain reliable results not only for the force but also for the energy density. This, in turn, leads to the value of the force for the configuration of a sphere (lens) above a plate both of which are covered by additional layers. The Casimir interaction between Al and Au test bodies is recalculated using the optical tabulated data for the complex refractive index of these metals. The computations turn out to be in agreement with the perturbation theory up to the fourth order in relative penetration depth of electromagnetic zero point oscillations into the metal. The disagreements between the results recently presented in the literature are resolved. The Casimir force between Al bodies covered by the thin Au layers is computed and the possibility to neglect spatial dispersion effects is discussed as a function the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure non-retarded van der Waals force law between Al and Au bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2--4) nm. New, more exact, values of the Hamaker constant for Al and Au are determined.Comment: 5 figure