Stiction, Adhesion Energy and the Casimir Effect in Micromechanical Systems

We measure the adhesion energy of gold using a micromachined doubly-clamped beam. The stress and stiffness of the beam are characterized by measuring the spectrum of mechanical vibrations and the deflection due to an external force. To determine the adhesion energy we induce stiction between the beam and a nearby surface by capillary forces. Subsequent analysis yields a value $\gamma =0.06$ J/m$^{2}$ that is a factor of approximately six smaller than predicted by idealized theory. This discrepancy may be resolved with revised models that include surface roughness and the effect of adsorbed monolayers intervening between the contacting surfaces in these mesoscopic structures.Comment: RevTex, 4 pages, 4 eps figure

New experimental limits on non-Newtonian forces in the micrometer-range

We report measurements of the short-range forces between two macroscopic gold-coated plates using a torsion pendulum. The force is measured for separations between 0.7 $\mu$m and 7 $\mu$m, and is well described by a combination of the Casimir force, including the finite-temperature correction, and an electrostatic force due to patch potentials on the plate surfaces. We use our data to place constraints on the Yukawa-type "new" forces predicted by theories with extra dimensions. We establish a new best bound for force ranges 0.4 $\mu$m to 4 $\mu$m, and, for forces mediated by gauge bosons propagating in $(4+n)$ dimensions and coupling to the baryon number, extract a $(4+n)$-dimensional Planck scale lower limit of $M_*>70$ TeV.Comment: 4 pages, 2 figure

The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities

The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The present paper is a continuation of an earlier investigation [Phys. Rev. E {\bf 63}, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index n=infinity). Here, analogous results are presented for dielectrics, for some chosen values of n. Our basic calculational method stems from quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l down to l=1. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as a physical input, invoke the actual dispersion relations. The result of our analysis, based upon the adoption of the Drude dispersion relation at low frequencies, is that the zero-frequency TE mode does not contribute for a real metal. Accordingly, F turns out in this case to be only one half of the conventional value at high temperatures. The applicability of the Drude model in this context has however been questioned recently, and we do not aim at a complete discussion of this issue here. Existing experiments are low-temperature experiments, and are so far not accurate enough to distinguish between the different predictions. We also calculate explicitly the contribution from the zero-frequency mode for a dielectric. For a dielectric, this zero-frequency problem is absent.Comment: 23 pages, LaTeX, 7 ps figures; expanded discussion, especially in Sec. 5. To appear in Phys. Rev.

On the sensitivity of condensed-matter P- and T-violation experiments

Experiments searching for parity- and time-reversal-invariance-violating effects that rely on measuring magnetization of a condensed-matter sample induced by application of an electric field are considered. A limit on statistical sensitivity arises due to random fluctuations of the spins in the sample. The scaling of this limit with the number of spins and their relaxation time is derived. Application to an experiment searching for nuclear Schiff moment in a ferroelectric is discussed.Comment: 6 pages, no figure

Johnson-Nyquist noise and the Casimir force between real metals at nonzero temperature

It is well known since a long time that all lossy conductors at finite temperature display an electronic noise, the Johnson-Nyquist noise, arising from the thermal agitation of electric charges inside the conductor. The existence of this noise implies that two nearby discharged conductors at finite temperature should repel each other, as a result of the electrodynamic interaction between the Johnson-Nyquist currents in either conductor and the eddy currents they induce in the other. It is suggested that this force is at the origin of the recently discovered large repulsive correction to the thermal Casimir force between two lossy metallic plates. Further support for this physical picture is obtained by studying a simple system of two linear noisy antennas. Using elementary concepts from circuit theory, we show that the repulsive force engendered by the Johnson-Nyquist noise results in the same kind of thermodynamic inconsistencies found in the Casimir problem. We show that all inconsistencies are however resolved if account is taken of capacitive effects associated with the end points of the antennas. Our findings therefore suggest that capacitive effects resulting from the finite size of the plates, may be essential for a resolution of the analogous problems met in the thermal Casimir effect.Comment: 9 pages, 1 encapsulated figure. Contributed to 8th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT07), Leipzig, Germany, 17-21 Sep 200

Radiative corrections to the Casimir force and effective field theories

Radiative corrections to the Casimir force between two parallel plates are considered in both scalar field theory of one massless and one massive field and in QED. Full calculations are contrasted with calculations based on employing ``boundary-free'' effective field theories. The difference between two previous results on QED radiative corrections to the Casimir force between two parallel plates is clarified and the low-energy effective field theory for the Casimir effect in QED is constructed.Comment: 17 pages, revte

The Energy Density in the Casimir Effect

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.Comment: 16 pages, 4 figures; 3 references and some new material in Sect. 4.4 adde

Computation of Casimir forces for dielectrics or intrinsic semiconductors based on the Boltzmann transport equation

The interaction between drifting carriers and traveling electromagnetic waves is considered within the context of the classical Boltzmann transport equation to compute the Casimir-Lifshitz force between media with small density of charge carriers, including dielectrics and intrinsic semiconductors. We expand upon our previous work [Phys. Rev. Lett. {\bf 101}, 163203 (2008)] and derive in some detail the frequency-dependent reflection amplitudes in this theory and compute the corresponding Casimir free energy for a parallel plate configuration. We critically discuss the the issue of verification of the Nernst theorem of thermodynamics in Casimir physics, and explicity show that our theory satisfies that theorem. Finally, we show how the theory of drifting carriers connects to previous computations of Casimir forces using spatial dispersion for the material boundaries.Comment: 9 pages, 2 figures; Contribution to Proceedings of "60 Years of the Casimir Effect", Brasilia, June 200

Measurement of the Casimir force between dissimilar metals

The first precise measurement of the Casimir force between dissimilar metals is reported. The attractive force, between a Cu layer evaporated on a microelectromechanical torsional oscillator, and an Au layer deposited on an Al$_2$O$_3$ sphere, was measured dynamically with a noise level of 6 fN/$\sqrt{\rm{Hz}}$. Measurements were performed for separations in the 0.2-2 $\mu$m range. The results agree to better than 1% in the 0.2-0.5 $\mu$m range with a theoretical model that takes into account the finite conductivity and roughness of the two metals. The observed discrepancies, which are much larger than the experimental precision, can be attributed to a lack of a complete characterization of the optical properties of the specific samples used in the experiment.Comment: 6 pages, 4 figure

Searching for physics beyond the Standard Model through the dipole interaction

The magnetic dipole interaction played a central role in the development of QED, and continued in that role for the Standard Model. The muon anomalous magnetic moment has served as a benchmark for models of new physics, and the present experimental value is larger than the standard-model value by more than three standard deviations. The electric dipole moment (EDM) violates parity ({$P$}) and time-reversal ({$T$}) symmetries, and in the context of the $CPT$ theorem, the combination of charge conjugation and parity ($CP$). Since a new source of {$CP$} violation outside of that observed in the $K$ and $B$ meson systems is needed to help explain the baryon asymmetry of the universe, searches for EDMs are being carried out worldwide on a number of systems. The standard-model value of the EDM is immeasurably small, so any evidence for an EDM would signify the observation of new physics. Unique opportunities exist for EDM searches using polarized proton, deuteron or muon beams in storage rings. This talk will provide an overview of the theory of dipole moments, and the relevant experiments. The connection to the transition dipole moment that could produce lepton flavor violating interactions such as $\mu^+ \rightarrow e^+ \gamma$ is also mentioned.Comment: Invited Plenary talk at the 19th International Spin Physics Symposium, Juelic