Tunnelling of molecules and quantum decay

在我们的日常经验中，被困在能量井中的粒子只有当它们拥有比能量屏障更多的能量时才能逃脱；被困在碗里的大理石一直呆在里面，除非它有足够的能量升到碗的顶部并出来。对于微观粒子，即使其能量低于势垒，粒子也有可能逃逸。这种现象被称为“隧道效应”。隧道效应几乎只针对单个粒子进行了研究。对分子隧穿的研究是最近才开始的。最简单的分子有两个原子，因此具有拉长的结构。分子隧穿的研究很有趣，也很有挑战性，因为为了逃脱能垒内的限制，两个原子都需要隧穿出去。 在这项拟议的研究中，我们将研究如何将分子捕获到井内，并将其从隧道中挖出的可能性降至最低。我们将包括分子保持束缚状态或分裂成两个原子的情况。我们的结果将与实验研究进行比较。我们将考虑分子沿直线运动或三维运动的情况。在后者中，我们将扩展我们的工作，以包括具有许多非束缚态的分子的隧穿和反射；也就是说，我们有两个相互作用的原子而不是处于束缚分子态的许多方式。确定非束缚态在三维中影响隧穿和反射几率的方式将是很有意义的。我们的研究还将包括让分子入射到随时间变化的势垒上，这将使我们的工作更接近真实系统。此外，我们将研究具有许多束缚态的分子，这也是更现实的。我们的最终目标是生成一幅与真实实验系统互补的理论图景。还将对竖立在重力井中的圆柱体的寿命进行调查；我们将计算这样一个圆柱体在倾倒和坠落之前保持直立的时间，这是微观圆柱体的量子力学特征。我们的工作对重要的技术进步有影响，例如“量子有限静电计”和“量子逻辑门”。

In our everyday experience, particles trapped inside energy wells can escape only if they have more energy than the energy barrier; a marble trapped in a bowl stays inside unless it has enough energy to rise to the top of the bowl and get out. For microscopic particles it is possible for the particle to escape even if its energy is less than the barrier. This phenomenon is called "tunnelling." Tunnelling has been investigated almost solely for single particles. Investigation into the tunnelling of molecules began relatively recently. The simplest molecule has two atoms and thus has an elongated structure. The study of tunnelling of molecules is interesting and challenging because, in order to escape confinement inside an energy barrier, both atoms need to tunnel out. In the proposed research we will investigate ways to trap a molecule inside a well and to minimize the probability that it can tunnel out of the trap. We will include cases where the molecule remains in a bound state or breaks up into two atoms. Our results will be compared to experimental studies. We will consider cases where the molecule moves in a straight line or the motion is in three dimensions. In the latter, we will extend our work to include tunnelling and reflection of a molecule with many unbound states; that is, many ways in which we have two interacting atoms which are not in a bound molecular state. It will be of interest to determine the manner in which the unbound states affect the probabilities of tunnelling and of reflection in three dimensions. Our study will also include having a molecule incident upon a potential barrier that changes with time, which brings our work even closer to real systems. Further, we will look into molecules having many bound states, which is also more realistic. Our ultimate goal is to generate a theoretical picture that is complementary to real experimental systems. There will also be an investigation into the lifetime of a cylinder standing in a gravity well; we will calculate the time that such a cylinder can remain upright before it tips and falls, a quantum mechanical feature of microscopic cylinders. Our work has implications for important technological advances, such as the "quantum limited electrometer" and "quantum logic gates."