Quantum tunnelling (or tunneling) is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. It can be generalized to other types of classically-forbidden transitions as well.

Consider rolling a ball up a hill. If the ball is not given enough velocity, then it will not roll over the hill. This scenario makes sense from the standpoint of classical mechanics, but is an inapplicable restriction in quantum mechanics simply because quantum mechanical objects do not behave like classical objects such as balls. On a quantum scale, objects exhibit wavelike behavior. For a quantum particle moving against a potential energy "hill", the wave function describing the particle can extend to the other side of the hill. This wave represents the probability of finding the particle in a certain location, meaning that the particle has the possibility of being detected on the other side of the hill. This behavior is called tunneling; it is as if the particle has 'dug' through the potential hill.

As this is a quantum and non-classical effect, it can generally only be seen in nanoscopic phenomena — where the wave behavior of particles is more pronounced.

History and consequences

In the early 1900s, radioactive materials were known to have characteristic exponential decay rates or half lives. At the same time, radiation emissions were known to have certain characteristic energies. By 1928, George Gamow had solved the theory of the alpha decay of a nucleus via tunneling. Classically, the particle is confined to the nucleus because of the high energy requirement to escape the very strong potential. Under this system, it takes an enormous amount of energy to pull apart the nucleus. In quantum mechanics, however, there is a probability the particle can tunnel through the potential and escape. Gamow solved a model potential for the nucleus and derived a relationship between the half-life of the particle and the energy of the emission.

Alpha decay via tunneling was also solved concurrently by Ronald Gurney and Edward Condon. Shortly thereafter, both groups considered whether particles could also tunnel into the nucleus.

After attending a seminar by Gamow, Max Born recognized the generality of quantum-mechanical tunneling. He realized that the tunneling phenomenon was not restricted to nuclear physics, but was a general result of quantum mechanics that applies to many different systems. Today the theory of tunneling is even applied to the early cosmology of the universe.

Quantum tunneling was later applied to other situations, such as the cold emission of electrons, and perhaps most importantly semiconductor and superconductor physics. Phenomena such as field emission, important to flash memory, are explained by quantum tunneling. Tunneling is a source of major current leakage in Very-large-scale integration (VLSI) electronics, and results in the substantial power drain and heating effects that plague high-speed and mobile technology.

Another major application is in electron-tunneling microscopes (see scanning tunneling microscope) which can resolve objects that are too small to see using conventional microscopes. Electron tunneling microscopes overcome the limiting effects of conventional microscopes (optical aberrations, wavelength limitations) by scanning the surface of an object with tunneling electrons.

Very recently it has been found that quantum tunneling may be the mechanism used by enzymes to speed up reactions in lifeforms to millions of times their normal speed.

One of the striking aspects of the tunneling is the speed of propagation through the barrier:

P.C. W. Davies, Australian Center for Astrobiology  

A simple heuristic argument to estimate the tunneling time
goes as follows. To surmount a square barrier of height V, a
particle with energy E must ‘‘borrow’’ an amount of energy
V-E. According to the uncertainty principle, this energy
must be ‘‘repaid’’ after a time T=1/(V-E) in units with
ħ=1. This time provides a crude upper bound for the tunneling
time. If the width of the barrier is a, then the effective
speed of the particle during the tunneling process must exceed
a(V-E). Because 'a' can be made as large as we please,
there is no upper bound on this effective velocity. In particular,
it may exceed the speed of light, in apparent violation of
relativistic causality. Moreover, this expression has the feature
that as the height of the potential hill is increased, the
tunneling time decreases, that is, the more repulsive the potential,
the faster the particle moves in the forward direction!

Source: Quantum Tunneling, American Association of Physics Teachers, 2004    

Source: Quantum Tunneling, American Association of Physics Teachers, 2004