Stronger Limits on Hypothetical Yukawa Interactions in the 30–8000 nm Range

Abstract

We report the results of new differential force measurements between a test mass and rotating source masses of gold and silicon to search for forces beyond Newtonian gravity at short separations. The technique employed subtracts the otherwise dominant Casimir force at the outset and, when combined with a lock-in amplification technique, leads to a significant improvement (up to a factor of 10 3 ) over existing limits on the strength (relative to gravity) of a putative force in the 40-8000 nm interaction range. DOI: 10.1103/PhysRevLett.116.221102 Although the gravitational attraction between two point masses was the first force to be described, it remains, in comparison with other fundamental forces, poorly characterized. Unification theories, such as string theory, which introduce n compact extra spatial dimensions, predict deviations from Newtonian gravity over submillimeter scales [1,2]. Also, many extensions to the standard model predict the existence of new light bosons, the exchange of which would lead to new forces. In both cases, the existence of compact extra dimensions and the exchange of new light bosons, the non-Newtonian interaction between two point masses m 1 and m 2 separated by a distance r can be parametrized aswhere G is the Newtonian gravitational constant, α is the strength of the Yukawa-like correction arising from new physics, and λ is its characteristic range. In the case of compact extra dimensions, λ closely corresponds to the size of the extra dimension. For the exchange of a boson of massMotivated in part by these considerations a large number of experiments have been conducted to constrain the value of α (see, for example, the reviews [4,5]). While they have been successful in constraining jαj < 1 for λ > 50 μm [6], the limits on α are much less restrictive for λ < 10 μm. Constraints on α for small values of λ are much more difficult to achieve due to the small effective masses (i.e., mass within a distance r ∼ λ of the surface) interacting through the Yukawa-like contribution. Compounding the problem at submicron separations, the effects of vacuum fluctuations eventually become dominant after electrostatic contributions have been minimized. Hence, many of the limits in the λ ∈ ½10; 10000 nm range have been obtained by subtracting from the measured interaction the calculated contribution from the Casimir force [7][8][9][10] In the absence of electromagnetic contributions, a comparison of the forces exerted on a test mass by materials of different densities leads to constraints on α and λ in Eq. (1). Different materials differ not only in their densities but also in their response to vacuum fluctuations, and hence these effects must be suppressed when searching for the presence of putative new forces at submicron separations. The "isoelectronic" or "Casimir-less" technique introduced in Ref.[13] capitalizes on the fact that the response of a sample to vacuum fluctuations is mainly a surface effect, whereas any new force interacts with a portion within range ∼λ of its surface. In th...

Constraints on axionlike particles and non-Newtonian gravity from measuring the difference of Casimir forces

“…Our present constraints on the corrections to Newtonian gravity are weaker by up to a factor of 10.5 than that derived in Ref. [35], but stronger by up to a factor of 177 than the constraints derived in recent Ref. [36] exploiting measurements of the lateral force.…”

“…[35]. At larger λ the latter becomes stronger than the constraints of line 6 by up to a factor of 10.5.…”

“…The constraints derived [41] from the isoelectronic experiment of Ref. [35], where the Casimir force was nullified, are shown by the line 4. Finally, the line 5 demonstrates the constraints obtained [23] from the Cavendish-type experiment of Ref.…”

“…[30][31][32][33][34] in the interaction range below a micrometer. Recently, the major strengthening was achieved in the isoelectronic experiment, where the Casimir force, acting perpendicular to the test surfaces, was nullified [35] (see also the version of isoelectronic experiment based on measuring the difference of lateral forces [36]). …”

“…For the axion-like particles, which are lighter than 1 eV, even stronger constraints have been derived [41] from the isoelectronic experiment of Ref. [35]. According to the proposal of Ref.…”