Customized silicon cantilevers for Casimir force experiments using focused ion beam milling

Castillo-Garza, R.; Chang, Chia‐Cheng; Yan, Dong; Mohideen, U.

doi:10.1088/1742-6596/161/1/012005

Cited by 8 publications

(8 citation statements)

References 35 publications

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“…For example, let us consider the tip of an atomic force microscope: At separations, d ≈ 0.3 μm, where the tip may be well approximated as a metal cone, our results predict a force that is a fraction of a piconewton. Such forces are at the limit of current sensitivities (45) and will likely become accessible with future improvements. Current experiments are performed on spheres of relatively large radius R, where the force is greater by a factor of (R∕d) (a typical R is 100 μm).…”

Section: Discussionmentioning

confidence: 99%

Analytical results on Casimir forces for conductors with edges and tips

Maghrebi

Rahi

Emig

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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Casimir forces between conductors at the submicron scale are paramount to the design and operation of microelectromechanical devices. However, these forces depend nontrivially on geometry, and existing analytical formulae and approximations cannot deal with realistic micromachinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically wedges and cones. The Casimir interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of microelectromechanical devices. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe. We find an unexpectedly large temperature dependence of the force in the cone tip which is of immediate relevance to experiments.fluctuations | quantum electrodynamics T he inherent appeal of the Casimir force as a macroscopic manifestation of quantum "zero-point" fluctuations has inspired many studies over the decades that followed its discovery (1). Casimir's original result (2) for the force between perfectly reflecting mirrors separated by vacuum was quickly extended to include slabs of material with specified (frequency-dependent) dielectric response (3). Quantitative experimental confirmation, however, had to await the advent of high-precision scanning probes in the 1990s (4-7). Recent studies have aimed to reduce or reverse the attractive Casimir force for practical applications in micron-sized mechanical machines, where Casimir forces may cause components to stick and the machine to fail. In the presence of an intervening fluid, experiments have indeed observed repulsion due to quantum (8) or critical thermal (9) fluctuations. Metamaterials, fabricated designs of microcircuitry, have also been proposed as candidates for Casimir repulsion across vacuum (10).Although there have been many studies of the role of materials (dielectrics, conductors, etc.), the treatment of shapes and geometry has remained comparatively less investigated. Interactions between nonplanar shapes are typically calculated via the proximity force approximation (PFA), which sums over infinitesimal segments treated as locally parallel plates (11). This approximation represents a serious limitation because the majority of experiments measure the force between a sphere and a plate with precision that is now sufficient to probe deviations from PFA in this and other geometries (12, 13). Practical applications are likely to explore geometries further removed from parallel plates. Several numerical schemes (14, -16), and even an analog computer (17), have recently been developed for computing Casimir forces in general geometries. However, analytical formulae for quick...

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Section: Discussionmentioning

confidence: 99%

Analytical results on Casimir forces for conductors with edges and tips

Maghrebi

Rahi

Emig

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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show abstract

“…For example, let us consider the tip of an atomic force microscope (AFM): At separations, d ≈ 0.2µm, where the tip may be well approximated as a metal cone, our results predict a force that is a fraction of a pico-Newton. Such forces are at the limit of current sensitivities [33], and will likely become accessible with future improvements. Current experiments are performed on spheres of relatively large radius R, where the force is greater by a factor of (R/d) (a typical R is 100µm).…”

Section: Overview and Discussionmentioning

confidence: 99%

Casimir force between sharp-shaped conductors

Maghrebi,

Rahi,

Emig

et al. 2010

Preprint

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Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.

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“…Numerous efforts have been recently made to develop high sensitivity cantilevers able to measure forces of weak amplitude [35]. We propose to observe mesoscopic FIF using an atomic force microscope, in a setup similar to [10] where Casimir-Lifshitz forces of a few piconewtons have been measured between a gold plate and a sphere coated with gold in a liquid.…”

Section: L1(µm)mentioning

confidence: 99%

Fluctuating Forces Induced by Nonequilibrium and Coherent Light Flow

2020

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Introductory Paragraph Casimir physics covers a wealth of phenomena where forces between macroscopic objects are induced by long range fluctuations [1] of either classical or quantum origin. Fluctuations of the quantum electrodynamic (QED) vacuum epitomize this type of physics [2], but such fluctuation induced forces (FIF) arise in a wide range of systems [3][4][5][6][7].Here we present an unexpected example of FIF caused by classical light propagating in a scattering medium. In weakly disordered media, light intensity has long ranged spatial fluctuations (speckle) associated to mesoscopic coherent effects resulting from elastic multiple scattering. These intensity fluctuations lead to measurable FIF on top of the disorder average radiation forces.Quite remarkably, spatially coherent light fluctuations can be thoroughly described using a Langevin equation, where a properly tailored noise accounts for mesoscopic coherent effects. This non intuitive result allows to interpret mesoscopic FIF as resulting from a non equilibrium light flow. The strength of the FIF depends on a single dimensionless parameter g -the analog of conductance in electronic systems, henceforth called conductancewhich encapsulates both the geometry and the scattering properties of the random medium.The scarcity of measurable and temperature independent non equilibrium phenomena makes the present proposal particularly relevant to experimental inspections. Indeed, since light induced fluctuating forces depend on the easily tunable parameter g, coherent multiple light scattering offers setups where FIF are significantly enhanced compared to other known situations [8][9][10][11][12][13]. This should have interesting and a wide variety of applications such as new types of sensors in soft condensed matter, biophysics [14] and quantum technologies. Precise Statement of ResultsThe mechanical actions of radiation forces have been well studied, e.g on dielectric bodies placed in vacuum. In random media, these forces result from multiple light scattering and they are expressed by phenomenological light currents obtained from an effective Langevin equation. On average, radiation forces depend on the transmission coefficient and the group velocity. But a yet unanticipated result is the existence of significant fluctuations of radiation forces around the average value, analogous to hydrodynamics fluctuating forces which occur in strongly non equilibrium systems [4]. However, unlike systems hitherto considered, here the radiation forces fluctuations originate from un-derlying coherent mesoscopic effects associated to elastic multiple scattering.To understand the origin of these FIF, we first note that, on average, light propagation in a scattering medium is well described by a diffusion approximation [15,16]. Light intensity at a point results from the superposition of classical diffusion paths built out of the pairing of two phase coherent multiple scattering amplitudes of opposite phases. This phase information, hidden in the average light intensity, can b...

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Customized silicon cantilevers for Casimir force experiments using focused ion beam milling

Cited by 8 publications

References 35 publications

Analytical results on Casimir forces for conductors with edges and tips

Analytical results on Casimir forces for conductors with edges and tips

Casimir force between sharp-shaped conductors

Fluctuating Forces Induced by Nonequilibrium and Coherent Light Flow

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