论文标题
使用有限的热浴模型模拟旋转测量
Simulating spin measurement with a finite heat bath model for the environment
论文作者
论文摘要
旋转测量是作为旋转耦合到代表仪表和设备的环境的统一时间演变的。将环境建模为热水浴，仅包括有限数量的玻色子模式并以连贯状态表示，在Davydov Ansatz之后，它可以完全包含在总系统的量子时间演化中。我们对极化的投射测量进行数值模拟，最初以中性纯状态制备旋转。同样，环境的纯初始状态被构造为玻色子模式的相干状态的产物，其质心随机分布围绕相空间的起源。通过时间依赖性调制，自旋和耦合耦合到热浴的自我能力，我们根据自旋的长时间行为观察到测量结果的结果。与热浴相互作用，旋转与之纠缠并失去连贯性，从而重现了“波函数的崩溃”。最终状态中的预期量子随机性在我们的模拟中表现为旋转接近测量旋转算子的两个特征态之一的倾向，从而恢复了几乎纯净的状态。统一的时间演变使我们能够将这些随机最终状态与环境的各个初始状态相关联，并根据两个子系统之间的纯度和相互熵来监视两个子系统之间的信息交换。
Spin measurement is studied as a unitary time evolution of the spin coupled to an environment representing the meter and the apparatus. Modelling the environment as a heat bath comprising only a finite number of boson modes and represented in a basis of coherent states, following the Davydov ansatz, it can be fully included in the quantum time evolution of the total system. We perform numerical simulations of projective measurements of the polarization, with the spins prepared initially in a neutral pure state. The likewise pure initial state of the environment is constructed as a product of coherent states of the boson modes with a random distribution of their centroids around the origin of phase space. Switching the self-energy of the spin and the coupling to the heat bath on and off by a time-dependent modulation, we observe the outcome of the measurement in terms of the long-time behaviour of the spin. Interacting with the heat bath, the spins get entangled with it and lose coherence, thus reproduce the "collapse of the wavefunction". The expected quantum randomness in the final state is manifest in our simulations as a tendency of the spin to approach either one of the two eigenstates of the measured spin operator, recovering an almost pure state. The unitary time evolution allows us to reproducibly relate these random final states to the respective initial states of the environment and to monitor the exchange of information between the two subsystems in terms of their purity and mutual entropy.
