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Geometrical Interpretation of Quantum Weak Measurement

机译：量子弱测量的几何解释

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We revisit the quantum weak measurement (QWM) by sketching the polarisation state dynamics on the Poincare sphere and the associated geometric phase, which is considered the soul of QWM. Our experimental arrangement comprises a coherent laser beam as a source of pure state, two polarizers corresponding to pre- and post-selection and a tilted wave plate placed in-between them to introduce weak interaction. The pre-selected state is a linearly polarised beam that can be represented as a point on the Poincare sphere equator and the weak interaction with the wave plate results in a small spread in S_3 axis. Now, an orthogonal projection of this state leads two different geodesics on the surface of the sphere through its poles, starting from both sides of the spread to the orthogonal point. The post-selection is made by moving the projection point slightly away from the orthogonal position so that both geodesics shift to the equator which results in a rapid accumulation of geometric phase in the beam cross-section. A gradient in the linear momentum is developed as a consequence which gives amplified shift in the beam position.
机译：我们通过在庞加莱球上的极化态动力学及其相关的几何相位上绘制草图来重新审视量子弱测量（QWM），这被认为是QWM的灵魂。我们的实验装置包括一个作为纯态源的相干激光束，两个对应于预选择和后选择的偏振器，以及一个放置在它们之间的倾斜波片，以引入弱相互作用。预选状态是线偏振光束，可以表示为Poincare球赤道上的一个点，与波片的弱相互作用会导致S_3轴上的扩展很小。现在，这种状态的正交投影通过球体的极点在球体表面上引导两个不同的测地线，从散布的两侧开始到正交点。通过将投影点稍微远离正交位置进行移动来进行后选择，以便两个测地线都移动到赤道，这导致光束横截面中几何相位的快速累积。结果产生了线性动量的梯度，其导致了束位置的放大偏移。

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