连续测量下耦合量子系统向经典混沌的转变
The transition to classical chaos in a coupled quantum system through continuous measurement
摘要：
对量子系统的连续观测产生了一个测量记录，它忠实地再现了经典预测的轨迹，前提是测量足够强以将状态定位在相空间中，但足够弱以使量子反作用噪声可以忽略不计。我们调查的条件下，经典动力学出现，通过连续的位置测量，为一个粒子运动在一个谐波井与其位置耦合到内部自旋。作为这种耦合的结果，我们发现，经典动力学出现时，只有位置和自旋的行动都是大相比，$\hbar$。这些条件被量化的协方差矩阵的大小上放置的界限，它描述了在相空间的扩展区域的离域量子相干性。从这个结果可以得出，对于连续观测到的自旋为1/2的粒子，不存在混合量子-经典区域（其中一个子系统可以被经典地处理，而另一个子系统不能）。当满足经典性的条件时（在大自旋极限下），量子轨道既再现经典的周期轨道，也再现经典的混沌相空间区域。作为这种收敛性的定量测试，我们计算的最大李雅普诺夫指数直接从测量的量子轨迹，并表明它符合经典值。
英文摘要：
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling we find that classical dynamics emerges only when the position and spin actions are both large compared to $\hbar$. These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin 1/2 particle. When the conditions for classicallity are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.
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