Achieving a Strongly Temperature-Dependent Casimir Effect

Abstract

We propose a method of achieving large temperature T sensitivity in the Casimir force that involves measuring the stable separation between dielectric objects immersed in a fluid. We study the Casimir force between slabs and spheres using realistic material models, and find large >2 nm=K variations in their stable separations (hundreds of nanometers) near room temperature. In addition, we analyze the effects of Brownian motion on suspended objects, and show that the average separation is also sensitive to changes in T. Finally, this approach also leads to rich qualitative phenomena, such as irreversible transitions, from suspension to stiction, as T is varied. DOI: 10.1103/PhysRevLett.105.060401 PACS numbers: 12.20.Ds, 42.50.Lc Casimir forces between macroscopic objects arise from thermodynamic electromagnetic fluctuations, which persist even in the limit of zero temperature due to quantummechanical effects (the Bose-Einstein distribution of the photon fluctuations) [1]. In most vacuum-separated geometries, such as parallel metal plates, the force is attractive and decaying as a function of plate-plate separation [1], becoming readily observable at micron and submicron separations. For a nonzero temperature T, the force is predicted to change as a consequence of the changing photon thermal distribution, but this change is typically negligible near room temperature and submicron separations [2,3] and is only a few percent for $100 K changes in T at 1-2 m separations where Casimir forces are barely observable [2][3][4]. Therefore, despite theoretical interest in these T effects [2,5], it has proven difficult for experiments to unambiguously observe T corrections to the Casimir force [4]. Other attempts to measure T Casimir corrections have focused on nonequilibrium situations that differ conceptually from forces due purely to equilibrium fluctuations [6]. A clear experimental verification of a T Casimir correction would be important in order to further validate the foundation of Lifshitz theory for Casimir effects [2,3].In this Letter, we propose a method for obtaining strongly temperature-dependent Casimir effects by exploiting geometries involving fluid-separated dielectric objects (with separations in the hundreds of nanometers). In fluid-separated geometries, the Casimir force can be repulsive [1,7], and can even lead to stable suspensions of objects due to force-sign transitions from material dispersion [8,9] or gravity [9,10]. We show that, by a proper choice of materials or geometries, this stable separation d can depend dramatically on T (2 nm=K is easily obtainable), and there can even be transitions where d jumps discontinuously at some T. Essentially, a stable separation arises from a delicate cancellation of attractive and repulsive contributions to the force from fluctuations at different frequencies, and this cancellation is easily altered or upset by the T corrections. This appears to be the first prediction of a strong T-dependent Casimir phenomenon at submicron separations where Casimir effect...

Temperature dependent graphene suspension due to thermal Casimir interaction

“…As the temperature is elevated, the force changes due to changes in the photon thermal distribution, but such effects are usually small at submicron scales and room temperature, and they are difficult to observe [9,10]. Recently, it has been proposed to utilize objects suspended in a fluid, in which the corrections due to thermal fluctuations in the Casimir force can be observed [11,12]. This method is particularly intriguing since it relies on the balance between attractive and repulsive contributions to the force arising from the dielectric response of the materials.…”

Casimir microsphere diclusters and three-body effects in fluids

“…Because the integrand f (ξ) is smooth and typically varies on a scale much slower than 1/λ T , where λ T = 7.6 µm at room temperature T = 300 K, the finite-T correction to the zero-temperature Casimir force is often negligible [3]. However, in fluids, as is the case here, larger temperature effects have been obtained [9] by dispersion-induced oscillations in f (ξ), and so we must check our previous zero-temperature predictions against finite-T calculations. For the Tef-Si-Substrate case considered here, we find that T > 0 corrections to the T = 0 forces are no more than 2% over the entire range of separations considered here, and hence they can be neglected.…”

“…III, we also consider temperature corrections to the Casimir interactions. Although a careful choice of materials can lead to a large temperature dependence stemming from the thermal change in the photon distribution [9,13,14], we find that such thermal-photon effects are negligible (< 2%) for the materials considered here. However, we show that substantial modifications to the objects separations occur due to Brownian motion of the micro-spheres.…”

“…Such micro-sphere interactions are predicted to possess a variety of unusual Casimir effects, including repulsive forces, [6][7][8] a strong interplay with material dispersion [4], and strong temperature dependences [9], and may have applications in microfluidic particle suspensions [10,11]. A typical situation considered in this paper is depicted in Fig.…”

“…These basic ideas were exploited in our previous work [4] to design sphere-sphere and sphere-plate geometries exhibiting a stable non-touching configuration. The effects of material dispersion are further modified by an interplay with geometric effects (which set additional length-scales beyond that of the separation), as well as by nonzerotemperature effects which set a Matsubara length-scale 2πkT / [14] that can further interact with dispersion in order to yield strong temperature corrections [9]. Experimentally, stable suspensions are potentially appealing in that one would be measuring static displacements rather than force between micro-scale objects.…”