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Chinese Physics Letters

Phase-Dependent Effects in Stern-Gerlach Experiments

许顼, 周小计

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

在量力学的框架，我们认为 spin-1/2 的一个整体是通过一台 Stern-Gerlach 仪器的中立粒子并且探索他们的运动怎么取决于二个内部旋转状态之间的起始的阶段差别。假定沿着 Y 轴移动的粒子，由于纺纱之间的起始的阶段差别说，他们不仅沿着纵的方向(Z 轴) 切开而且分开侧面的方向(X 轴) 。起始的阶段差别上的侧面的排水量的依赖提醒一量干扰的图画。这概括干扰提供一条其他的途径给测量起始的阶段差别。有 ultracold 原子或 Bose 爱因斯坦冷凝物的试验性的实现也被讨论。[从作者抽象]

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在量力学的框架，我们认为 spin-1/2 的一个整体是通过一台 Stern-Gerlach 仪器的中立粒子并且探索他们的运动怎么取决于二个内部旋转状态之间的起始的阶段差别。假定沿着 Y 轴移动的粒子，由于纺纱之间的起始的阶段差别说，他们不仅沿着纵的方向(Z 轴) 切开而且分开侧面的方向(X 轴) 。起始的阶段差别上的侧面的排水量的依赖提醒一量干扰的图画。这概括干扰提供一条其他的途径给测量起始的阶段差别。有 ultracold 原子或 Bose 爱因斯坦冷凝物的试验性的实现也被讨论。[从作者抽象]
In the frame of quantum mechanics, we consider an ensemble of spin-½ neutral particles passing through a Stern–Gerlach apparatus and explore how their motions depend on the initial phase difference between two internal spin states. Assuming the particles moving along y-axis, due to the initial phase difference between spin states, they not only split along the longitudinal direction (z-axis) but also separate along the lateral direction (x-axis). The dependence of the lateral displacement on the initial phase difference reminds one of the picture of a quantum interference. This generalized interference provides an alternative approach to measuring the initial phase difference. The experimental realization with ultracold atoms or Bose–Einstein condensates is also discussed.
Abstract The Stern–Gerlach (SG) experiment is a fundamental experiment for revealing the existence of “spin”. In this experiment, beams of silver atoms are sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac’s equation with a potential barrier, revealing an extraordinary spin effect. Beams of Dirac particles can be regarded as matter waves. Based on Dirac’s equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can exhibit notable spatial shifts, which depend on the spin direction and the incident angle of the wave. The electric-type SG effect has potential applications for separating Dirac particles with different spin directions and for estimating the spin direction of Dirac particles. Some discussions related to the interaction between spin and the electric field are also presented.
A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH 0 ) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.