连续量子测量中薛定谔猫态的形成和动力学
Formation and Dynamics of a Schrödinger-Cat State in Continuous Quantum Measurement
摘要：
我们考虑的过程中，一个真正的连续测量量子力学的一个例子，使用磁共振力显微镜（MRFM）的单自旋测量。这种技术对于不同的应用也很重要，包括量子计算中量子比特状态的测量。测量发生在通过一个准经典悬臂梁的相互作用的一个单一的自旋，由一个量子振荡器在一个准经典的参数区域中的相干态。整个系统被严格处理的框架内的薛定谔方程，没有任何人为的假设。计算机模拟的自旋悬臂梁动力学，其中的自旋是连续旋转的循环绝热反转，表明悬臂梁演变成薛定谔猫状态：悬臂位置的概率分布开发两个不对称的峰值，准周期性出现和消失。对于一个多自旋系统，我们的方程减少到经典的运动方程，我们准确地描述了传统的MRFM实验涉及循环绝热反转的自旋系统。我们推测悬臂与环境的相互作用将导致波函数的坍缩;然而，我们表明，在这种情况下，自旋不会跳到自旋本征态。
英文摘要：
We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) as an example of a truly continuous measurement in quantum mechanics. This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a quasi-classical cantilever, modeled by a quantum oscillator in a coherent state in a quasi-classical region of parameters. The entire system is treated rigorously within the framework of the Schrödinger equation, without any artificial assumptions. Computer simulations of the spin-cantilever dynamics, where the spin is continuously rotated by means of cyclic adiabatic inversion, show that the cantilever evolves into a Schrödinger-cat state: the probability distribution for the cantilever position develops two asymmetric peaks that quasi-periodically appear and vanish. For a many-spin system our equations reduce to the classical equations of motion, and we accurately describe conventional MRFM experiments involving cyclic adiabatic inversion of the spin system. We surmise that the interaction of the cantilever with the environment would lead to a collapse of the wave function; however, we show that in such a case the spin does not jump into a spin eigenstate.
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