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.

and self-organized on a Si substrate. Planar silicon wafers of (111) orientation (just, r = 5 X cm) were used. Silicon wafers were cleaned thoroughly and a thin oxide layer (< 1 nm) was prepared by chemical means. NPs were introduced onto this silicon wafer covered with the thin oxide layer at room temperature (RT) by dip coating [1] from an ethanol suspension, aided by an ultrasonic bath. The samples were then loaded into an UHVC and annealed at various temperatures, monitoring the nature of the surface species in situ by employing Auger as well as photoelectron spectroscopic techniques (only XPS results were presented here). XPS measurements were made using a VG Microtech instrument. The samples were initially degassed at 250 C for several hours and the final annealing was performed at temperatures in the range of 800±850 C for 10± 15 min. After cooling the sample to RT, the measurements were performed. We have employed a variety of techniques such as small-angle X-ray scattering, X-ray diffraction, scanning electron microscopy, Auger mapping, energy dispersive X-ray (EDX) analysis, extended X-ray absorption fine structure, and AFM (DI instrument) to characterize the system. STM measurements were performed independently in a separate instrument (Omicron). Optical characterization of the samples were carried out by PL, SNOM (solid-state laser source of nominal wavelength of 405 nm and a Hamamatsu photomultiplier tube detector in an Omicron setup), and TL [5].

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular silicon gratings. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.