标题： 自由下落中的量子到达时间 显示英文标题

标题： Quantum arrival times in free fall

摘要： 时间测量$T_x$在位置$x$的概率分布可以根据在时间$t$处的位置测量$X_t$的概率分布推断得出，如 Born 规则所述 [连续量子系统的到达时间分布及其在量子回流中的应用，Phys. Rev. A 110, 052217 (2024)]。在自由下落的应用中，这一发现被用来预测在长时间飞行范围内，相对于经典到达时间，掉落的量子粒子存在质量相关的正相对位移 [M. Beau 和 L. Martellini, 自由下落原子的到达时间量子延迟，Phys. Rev. A 109, 012216 (2024)]。本文在两个重要方向上扩展了这些结果。我们首先表明，对于质量为$m$的高斯量子粒子，在均匀重力场$g$中下落时，时间测量和位置测量的不确定性由关系$ \Delta T_x \Delta X_t \geq \frac{\hbar}{2mg} . $相关联。这种新的不确定性关系形式表明，选择初始状态以获得较低的测量位置不确定性会导致测量到达时间的不确定性增加。其次，我们研究了从非高斯初始叠加态开始自由下落的粒子情况，我们预测在探测器位置作为平均到达时间的函数中会出现由重力引起的干涉和振荡，这可以解释为类似 Zitterbewegung 效应的特征。 显示英文摘要

摘要： The probability distribution of a time measurement $T_x$ at position $x$ can be inferred from the probability distribution of a position measurement $X_t$ at time $t$ as given by the Born rule [Time-of-arrival distributions for continuous quantum systems and application to quantum backflow, Phys. Rev. A 110, 052217 (2024)]. In an application to free-fall, this finding has been used to predict the existence of a mass-dependent positive relative shift with respect to the classical time-of-arrival in the long time-of-flight regime for dropped quantum particles [M. Beau and L. Martellini, Quantum delay in the time of arrival of free-falling atoms, Phys. Rev. A 109, 012216 (2024).]. The present paper extends these results in two important directions. We first show that for a Gaussian quantum particle of mass $m$ dropped in a uniform gravitational field $g$, the uncertainties about time and position measurements are related by the relation $ \Delta T_x \Delta X_t \geq \frac{\hbar}{2mg} . $ This novel form of uncertainty relation suggests that choosing the initial state so as to obtain a lower uncertainty in the measured position leads to a higher uncertainty in the measured arrival time. Secondly, we examine the case of a free-falling particle starting from a non-Gaussian initial superposed state, for which we predict the presence of gravitationally induced interferences and oscillations in the mean time-of-arrival as a function of the detector's position that can be interpreted as the signature of a Zitterbewegung-like effect.