Measurement of non-monotonic Casimir forces between silicon nanostructures

Abstract

Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field 1 . Apart from controlling the Casimir force via the optical properties of the materials 2-11 , a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps 12-14 . Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators 15 , we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the Casimir force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.The prediction of the attraction between two neutral perfect conductors by Casimir 1 was obtained by considering the boundary conditions imposed by two planar surfaces on the quantum fluctuations of the electromagnetic field. Alternatively, the Casimir force is sometimes considered as an extension of the van der Waals force between fluctuating dipoles to solid bodies and in the regime of retardation. This attractive force increases monotonically when the distance between the two planes decreases. As the Casimir force becomes the dominant interaction between electrically neutral surfaces separated by nanoscale gaps, they are of practical importance in nanomechanical devices 16,17 . In experiments, one of the flat surfaces is often replaced by a spherical body 4-11 due to the difficulty in maintaining parallelism at small separations 18 . By introducing corrugations to one of the surfaces, recent experiments 19,20 have demonstrated the non-trivial geometry dependence of the Casimir force. Measuring the Casimir Device fabrication Supplementary Figure S1 | The fabrication procedure of the device (not to scale). a, A cross-sectional view of the silicon-on-insulator wafer. The silicon device layer, the buried oxide layer and the substrate are shown in blue, yellow and grey respectively. b, The silicon oxide etch mask (red) is created using the resist pattern from lithography. c, Silicon in the regions not protected by silicon oxide is removed by DRIE. d, HF selectively etches the silicon oxide isotropically, undercutting of the top silicon structure by ~ 2.7 µm. The middle silicon piece is thin enough to be suspended. The other two pieces have oxide underneath and therefore are anchored to the substrate.

Recent progress in engineering the Casimir effect – applications to nanophotonics, nanomechanics, and chemistry

“…In the decades that followed, several experiments confirmed Casimir's prediction [6][7][8][9][10], and methods have been developed to improve the measurement by taking into account surface roughness [11][12][13][14], electrostatic patch potentials [15][16][17][18][19][20][21], and thermal contributions [22,23]. Recently, experiments have begun to show other novel regimes where the strong deviations in the magnitude of the force or power law can be obtained through modification of the geometry [24][25][26][27][28][29][30][31] or optical properties [32][33][34][35][36][37][38][39].…”

Casimir pressure between metallic plates out of thermal equilibrium: Proposed test for the relaxation properties of free electrons

“…One of the most striking macroscopic effects of this kind is the Casimir force [3] resulting from the zero-point and thermal fluctuations. This force manifests itself in many branches of physics ranging from atomic physics, condensed matter physics to elementary particle physics, gravitation and cosmology [4], and is actively considered to be used in the next generation of microdevices with reduced dimensions [5][6][7][8][9][10][11].…”

Measurement of the Casimir Force between Two Spheres

“…The first begins with a sphereplate geometry, and textures one or both surfaces, so that the alignment advantages of the sphere-plate configuration are maintained while effects beyond the PFA are probed [17][18][19]. The second involves fabricating two interacting surfaces out of a single crystal to ensure the alignment of the surfaces [20,21]; however, measurements are limited to materials for which sufficient fabrication techniques exist. Geometries such as the needle-andhole [15] and sphere-sphere [22][23][24][25] (Fig.…”