Precision AFM Measurement of the Casimir Force with Sphere–Plate Geometry & Metamaterial Simulations
By Nivaan, Nived
Quantum vacuum fluctuations cause the Casimir force between neutral bodies at nanometer separations. Atomic force microscopy (AFM) in the sphere–plane configuration avoids the alignment challenges of parallel plates and enables precise measurements of F(z). We will perform a precision AFM study using a gold (Au)–coated silica microsphere (radius R ∼ 20–100 μm) epoxied to a tipless cantilever above an ultra-flat Au plate (e.g., template-stripped Au on Si or Au on freshly cleaved mica). This Au–Au baseline system maximizes signal strength, mitigates charging relative to dielectrics, and follows established AFM Casimir protocols.
On the theory side, we will implement Lifshitz calculations for Au–Au in air (and, time permitting, simple liquids), including finite conductivity, temperature, roughness, distance-offset, and residual electrostatic (patch) contributions. We will acquire ensembles of F(z) curves over ∼40–200 nm at multiple locations (with deliberate voltage offsets to validate electrostatic subtraction), and fit the data with parameters constrained by calibration, reporting confidence intervals and goodness-of-fit. Robustness checks will test expected scalings (e.g., F ∝ R) and instrument response (varying cantilever k). This validated baseline will support comparative measurements of accessible coatings (ITO, graphene-on-SiO2) and a liquid-cell extension against Lifshitz predictions.
This study can be utilized in several other applications. Our process and detailed logs will serve as useful guides for future studies detailing the Casimir Force and other Quantum Force Experiments. Additionally, the findings can be used to inform fields like nanotechnology design, where the Casimir Force and other phenomena influence stiction and device reliability. Finally, time permitting, we can use the same framework to study metamaterials and how the Casimir Force fluctuates and differs based on material composition. This will also be valuable to future advancements and developments in nanotechnology.