论文标题
连续同时测量粒子的位置和动量
Continuous simultaneous measurement of position and momentum of a particle
论文作者
论文摘要
我们制定了一个量子粒子的模型，该量子粒子通过同时测量其位置和动量的检测器连续监测。我们通过假设在检测到粒子后发现粒子作为相干状态的离散子集的一个仪表之一，实现了波函数崩溃的假设。如米所观察到的那样，动力学是连贯状态之间跳跃的随机序列。我们使用Monte Carlo波函数法生成此类轨迹。对于稀疏分布的检测器，我们使用随机过程更新理论的方法来获得一些半分析结果。特别地，鉴定并进行定量讨论了自由粒子动力学的不同状态：在质疑频率较低的情况下，从频闪运动到延迟的动态，如果经常进行监测，请让人想起Zeno效应。对于米的半连续空间分布，显示了经典轨迹的出现。讨论了它们的统计特性，并将其与其他检测方案进行了比较，在该方案中，测量的效果对应于波功能的“空间滤波”。
We formulate a model of a quantum particle continuously monitored by detectors measuring simultaneously its position and momentum. We implement the postulate of wavefunction collapse by assuming that upon detection the particle is found in one of the meters' states chosen as a discrete subset of coherent states. The dynamics, as observed by the meters, is thus a random sequence of jumps between coherent states. We generate such trajectories using the Monte Carlo Wavefunction method. For sparsely distributed detectors, we use methods from renewal theory of stochastic processes to obtain some semi-analytic results. In particular, the different regimes of dynamics of the free particle are identified and quantitatively discussed: from stroboscopic motion in the case of low interrogation frequency, to delayed dynamics reminiscent of the Zeno effect if monitoring is frequent. For a semi-continuous spatial distribution of meters the emergence of classical trajectories is shown. Their statistical properties are discussed and compared to other detection schemes in which the effect of measurement corresponds to "spatial filtering" of the wavefunction.
