Quantum Tunneling – Quantum Games Course

When met with an obstacle our general understanding is that in order to continue on our way we must go over the obstacle. In the microscopic scale of atoms, the so-called subatomic particles do not necessarily care about potential barriers on their way and can penetrate and in most cases tunnel through barriers that would seem like obstacles to larger constructs. Tunneling is essential in both the nuclear fusion of the sun and future of transistors, falling under the domain of the nanoscale world of quantum mechanics.

Imagine a mountain with a bowl shaped small dent on top of it holding a ball inside it. If the ball has enough energy to overcome the potential energy of the resisting bowl lip it will be able to travel on top of the lip and roll down the mountain side. We could say that the kinetic energy of the ball has won over the energy of the containing bowl, one energy has been enough to overcome another resisting one. This is a classical idea controlled by the simple Law of Conservation of Energy approach.

Pic 1. Kinetic energy of the moving particle vs. potential energy of an obstacle.

If the ball does not have enough kinetic energy to overcome the bowl lip and stops before reaching the maximum height of the bowl side, it will be reflected back and roll to the valley where it came from. When we apply quantum effects into the physics the ball can move through the hill or “tunnel” through the potential energy barrier to the other valley even if its kinetic energy is insufficient to overcome the potential energy of the obstacle. This seemingly paradoxical situation becomes clearer when we consider the way particles behave in the quantum size of things.

Microscopic particles such as protons or electrons behave as a consequence of the wave-particle duality and can be described by means of a probability wave. While the majority of the wave that collides with an obstacle may never penetrate the barrier, a small part of it does. This allows the possibility of the particle which is generating the wave to suddenly be located on the other side of the obstacle. Tunneling is often explained with the help of Heisenberg’s uncertainty principle that limits the amount of certainty we can have of a particle’s position and momentum. When certainty cannot be achieved we must describe things with probabilities.

Fig 1. The laws of Quantum Mechanics allow a particle to penetrate through a potential energy barrier that is higher in energy than the particle’s kinetic energy.

Because of tunneling particles such as electrons can pass through extremely thin walls. For electronics that depend upon controlling the flow of electrons to work this poses a problem to be solved. Enough small nanoscale transistors for example are no longer able to work as a reliable barrier for the electric current and the semiconductor barrier escaping electrons could result in data loss. Developing material technology and the wide area of applicability of quantum tunneling has had a great impact on the dynamics of electrons in materials, such as microscopy, semiconductors, and superconductors.

In regards to superconducting tunneling happens in certain temperature ranges where the current can flow indefinitely without resistive heating occurring. Superconducting pairs of electrons (Cooper pairs) can tunnel through a barrier to carry the superconducting current.

The history of quantum tunneling is intertwined with other remarkable discoveries of physics, such as understanding nuclear fusion and radioactive decay. Radioactive decay defines for example the half life of certain unstable atoms, such as uranium-232 (halflife 68,9 years). Particles stuck inside the nucleus of the atom can escape because of quantum tunneling.