Casimir force measurement using dynamic holography
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Casimir Force Measurement Using Dynamic Holography V. M. Petrova, M. P. Petrova*, V. V. Bryksina, J. Petterb, and T. Tschudib a
Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia b Technische Universität Darmstadt, D-64289, Darmstadt, Germany *e-mail: [email protected] Received October 26, 2006
Abstract—The first holographic measurements are reported of the force between macroscopic objects mediated by zero-point electromagnetic fluctuations (Casimir force). A holographic interferometer is used to measure mirror oscillations with an amplitude of 1 pm. The objects under study are two thin metal films deposited on dielectric substrates. When one film is periodically oscillated, the first and second harmonics of the Casimir force acting on the other are detected. For the first time, an order-of-magnitude estimate is obtained for the Casimir force by using radiation pressure as a natural reference scale. The discrepancy between calculated and measured values of the Casimir force may be attributed to the small thickness and low conductivity of the metal films. PACS numbers: 05.40.-a, 03.70.+k, 77.22.-d, 81.07.-b DOI: 10.1134/S1063776107050032
1. INTRODUCTION According to quantum electrodynamics, a vacuum at zero temperature is filled with so-called zero-point electromagnetic fluctuations even in the absence of external radiation. Zero-point fluctuations can be represented as photons with frequencies ωk, ν, wavevectors k, and polarizations ν (ν can take one of two values) satisfying the dispersion relation ωk, ν = ck, where c is the speed of light in empty space. The total energy of the photons (zero-point energy) is 1 H = --2
∑ ω
k, ν .
(1)
k, ν
A formal explanation for the existence of zero-point fluctuations relies on the fact that transverse electric and magnetic field operators are mutually noncommutative. Even though the concept of zero-point fluctuations in quantum electromagnetic field theory was proposed as early as in the 1930s, only a few experimentally observable phenomena provide direct evidence of their existence, including the Lamb shift [1, 2] and the Casimir force [3]. The Lamb shift is a manifestation of the fact that the energy of charged particles, such as electrons in an atom, is renormalized by interaction with electromagnetic field, including zero-point fluctuations. The Casimir force between metal objects arises because the uniformity of zero-point fluctuations in empty space is violated by the presence of the objects. In particular, two infinite perfectly conducting metal plates separated by a distance Z make up a waveguide where only the waveguide modes can propagate, with wavevector magnitudes of at least k = π/Z. Accordingly, the photon energy density between the plates is lower
than outside, which implies that the outward radiation pressure on the plates is lower than the inward one. The resultant of these pressures gives rise to an attractive force between the plates called the Casimir force. In this configuration,
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