量子涨落在双折射板上引起的力矩
On the torque on birefringent plates induced by quantum fluctuations
摘要：
我们提出了详细的数值计算两个平行的双折射板的平面光学各向异性的量子波动引起的机械扭矩，分离的真空或液体（乙醇）。发现扭矩随$\sin(2θ)$变化，其中$θ$表示两个光轴之间的角度，并且其大小随着板分离$d$的减小而迅速增加。对于由石英或方解石制成的40 μ m直径的盘，保持平行于在$d\simeq 100$ nm处的钡钛板，最大扭矩（在$θ={π\over 4}$处）为$\simeq 10^{-19}$ N $\cdot$ μ m的量级。我们提出了一个实验来观察这种扭矩时，钡钛板浸泡在乙醇中，另一个双折射盘放在它的顶部。在这种情况下，延迟范德华力（或Casimir Lifshitz）之间的两个双折射板是排斥。圆盘将平行于平板浮动一段距离，在该距离处，其净重被延迟的范德华斥力抵消，自由旋转以响应非常小的驱动扭矩。
英文摘要：
We present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in plane optical anisotropy, separated by either vacuum or a liquid (ethanol). The torque is found to vary as $\sin(2θ)$, where $θ$ represents the angle between the two optical axes, and its magnitude rapidly increases with decreasing plate separation $d$. For a 40 $μ$m diameter disk, made out of either quartz or calcite, kept parallel to a Barium Titanate plate at $d\simeq 100$ nm, the maximum torque (at $θ={π\over 4}$) is of the order of $\simeq 10^{-19}$ N$\cdot$m. We propose an experiment to observe this torque when the Barium Titanate plate is immersed in ethanol and the other birefringent disk is placed on top of it. In this case the retarded van der Waals (or Casimir-Lifshitz) force between the two birefringent slabs is repulsive. The disk would float parallel to the plate at a distance where its net weight is counterbalanced by the retarded van der Waals repulsion, free to rotate in response to very small driving torques.
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