Casimir-Lifshitz forces and torques

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Quantum electromagnetic field fluctuations result in the well-documented Casimir-Lifshitz force between macroscopic objects. If the objects are anisotropic, theory predicts a corresponding Casimir-Lifshitz torque that causes the objects to rotate and align. In this work, we report the first measurements of the Casimir-Lifshitz torque, which confirm the predictions first made decades ago. The experimental design uses a nematic liquid crystal separated from a birefringent crystal by an isotropic Al2O3 layer with a thickness <nm. The molecular orientation of the liquid crystal is fixed with a rubbed counterplate, and, by varying the rubbing and Al2O3 thickness, we measured the Casimir-Lifshitz torque as a function of angle and distance.

Along the way, we developed a simpler formulation for calculating the Casimir-Lifshitz interaction in planar systems, which facilitated further theoretical study of the Casimir-Lifshitz torque. Using this method, we outline the conditions for a repulsive Casimir-Lifshitz force between birefringent materials that would allow for an angularly-dependent sign of the force. We also report an unexpected enhancement of the torque from two sources: an intermediate dielectric medium and the finite speed of light.