Precision measurement of the Casimir-Lifshitz force in a fluid

The Casimir force, which results from the confinement of the quantum-mechanical zero-point fluctuations of electromagnetic fields, has received significant attention in recent years for its effect on micro- and nanoscale mechanical systems. With few exceptions, experimental observations have been limited to interacting conductive bodies separated by vacuum or air. However, interesting phenomena, including repulsive forces, are expected to exist in certain circumstances between metals and dielectrics when the intervening medium is not vacuum. In order to better understand the effect of the Casimir force in such situations and to test the robustness of the generalized Casimir-Lifshitz theory, we have performed precision measurements of the Casimir force between two metals immersed in a fluid. For this situation, the measured force is attractive and is approximately 80% smaller than the force predicted by Casimir for ideal metals in vacuum. We present experimental results and find them to be consistent with Lifshitz’s theory.

Figure 1

(Color online) Schematic representation of the experimental setup (not to scale). A polystyrene sphere is attached to a cantilever and coated with gold. An AFM with fluid cell is used to measure surface forces as the sphere approaches the bottom plate. Inset shows a schematic of the relative motion of the cantilever with respect to the laser, which is determined and removed.

Figure 2

(Color online) Raw deflection data versus piezo displacement (thin lines) at various approach speeds, and corresponding fit (thick black line) to the hydrodynamic force ($4.5\mu \mathrm{m}∕\mathrm{s}$ tip velocity) used for determination of the force constant and absolute surface separation. Residual shows no systematic error in the least-squares curve fit.

Figure 3

(Color online) Experimental results (circles) with three different calculations based on theory: Lifshitz’s theory for two perfectly smooth gold surfaces separated by ethanol (dotted line), Lifshitz’s theory for gold surfaces in ethanol with surface roughness corrections (solid line), and Lifshitz’s theory for gold surfaces in vacuum with roughness corrections (dashed line). Inset: data from $35\text{to}50\mathrm{nm}$ showing the deviation from theory below $50\mathrm{nm}$. The data points and error bars represent averages and standard deviations, respectively, for 11 measurements.