In this paper, we calculate the quantum time delays for a neutral particle scattering off the Earth gravitational linear potential. The quantum time delays are obtained by subtracting the classical returning time (CRT) from the Wigner time, the dwell time and the Larmor time respectively. Different from the conventional definition, our Larmor time is defined by aligning the magnetic field along particle’s direction of motion, and this definition does give reasonable results for motions through a free region and a square barrier. It is worth noting that in the zero magnetic field limit, the Larmor time coincides well with the CRT, which is due to the special shape of linear barrier, and may have some relevance to the weak equivalence principle. It is also found that the classical forbidden region plays an essential role for the dwell time to match with the CRT, and the difference between the dwell and the phase times, i.e. the self-interference time delay, is barrier shape sensitive and clearly shows the peculiarity of the linear barrier. All the time delays are on the order of sub-millisecond and exhibit oscillating behaviors, signaling the self-interference of the scattering particle, and the oscillations become evident only when the de Broglie wavelength λ _k = 2π/k is comparable to the characteristic length . If the time delay measurement is experimentally realizable, it can probe the quantum nature for particle scattering off the gravitational potential in the temporal domain.

在本文中，我们计算了从地球引力线性势散射的中性粒子的量子时间延迟。量子时间延迟是通过分别从 Wigner 时间、停留时间和 Larmor 时间中减去经典返回时间 (CRT) 获得的。与传统定义不同，我们的拉莫尔时间是通过沿粒子运动方向对齐磁场来定义的，并且该定义确实为通过自由区域和正方形势垒的运动提供了合理的结果。值得注意的是，在零磁场极限下，Larmor时间与CRT吻合较好，这是由于线性势垒的特殊形状，可能与弱等效原理有一定的相关性。还发现经典禁区对停留时间起着至关重要的作用与 CRT 相匹配，并且驻留时间和相位时间之间的差异，即自干扰时间延迟，对势垒形状敏感，并清楚地显示了线性势垒的特性。所有的时间延迟都在亚毫秒级，并表现出振荡行为，表明散射粒子的自干扰，只有当德布罗意波长λ _k = 2 π / k与特性相当时，振荡才变得明显长度。如果时间延迟测量可以通过实验实现，它可以探测粒子在时域中从引力势散射的量子性质。