Rotation of a liquid crystal by the Casimir torque

We present a calculation of the Casimir torque acting on a liquid crystal near a birefringent crystal. In this system, a liquid crystal bulk is uniformly aligned at one surface and is twisted at the other surface by a birefringent crystal, e.g. barium titanate. The liquid crystal is separated from the solid crystal by an isotropic, transparent material such as SiO${}_2$. By varying the thickness of the deposited layer, we can observe the effect of retardation on the torque (which differentiates it from the close-range van der Waals torque). We find that a barium titanate slab would cause 5CB (4-cyano-4${}^{\mathrm{\prime }}$-pentylbiphenyl) liquid crystal to rotate by 10${}^{\circ }$ through its bulk when separated by 35 nm of SiO${}_2$. The optical technique for measuring this twist is also outlined.