Tunnelling of molecules and quantum decay

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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."