Quantum tunnelling

In classical mechanics, a particle with energy E less than the height V of a potential barrier is reflected. In quantum mechanics, the particle is described by a wavefunction that extends into the barrier region and decays exponentially. If the barrier is thin enough, the wavefunction on the far side has a small but non-zero amplitude, meaning there is a probability that the particle emerges on the other side. This probability depends exponentially on the barrier width and the square root of the product of the particle mass and the barrier height above the particle's energy.¹

The phenomenon is a direct consequence of the Heisenberg uncertainty principle: the particle can momentarily 'borrow' energy to overcome the barrier, as long as the violation of energy conservation is brief enough. However, the more rigorous treatment via the time-independent Schrödinger equation shows that tunnelling is a steady-state phenomenon, not a transient one.²

The first successful explanation of tunnelling was given in 1928 by George Gamow, who applied it to explain alpha decay of atomic nuclei.³ Independently, Ronald Gurney and Edward Condon published a similar explanation in the same year.⁴ Earlier, in 1927, Friedrich Hund had considered tunnelling in molecular potentials, but his work was less influential. The concept was initially met with skepticism because it seemed to violate classical intuition, but it quickly became a cornerstone of quantum theory.

Tunnelling is exploited in many devices. The scanning tunnelling microscope (STM), invented by Gerd Binnig and Heinrich Rohrer in 1981, uses the exponential sensitivity of tunnelling current to distance to image surfaces at atomic resolution.⁵ Flash memory relies on Fowler–Nordheim tunnelling to move electrons through a thin oxide layer to store data. Tunnel diodes and resonant tunnelling diodes use quantum tunnelling to achieve negative resistance, enabling high-speed switching. In addition, tunnelling is essential for the operation of superconducting tunnel junctions (Josephson junctions), which are used in SQUIDs and quantum computing.

In stars, nuclear fusion occurs at temperatures where classical kinetic energies are far too low to overcome the Coulomb barrier. Tunnelling allows protons to fuse, powering the Sun and other stars. In chemistry, tunnelling of protons and electrons plays a role in many reactions, including enzyme catalysis and photosynthesis. In biology, it is invoked to explain mutations in DNA via proton transfer between base pairs, though the significance is debated.

Beyond the standard examples, tunnelling appears in surprising contexts. In cosmology, the universe's initial expansion may be described by tunnelling from 'nothing' in some models. In electronics, the tunnel diode was invented by Leo Esaki in 1957, who later shared the Nobel Prize for his work on tunnelling in semiconductors. A lesser-known fact is that the concept of tunnelling was anticipated by Friedrich Hund in 1927 when he studied the inversion of ammonia molecules. Also, tunnelling is not limited to particles; it can occur for macroscopic objects in principle, but the probability is astronomically small. In the field of attosecond physics, researchers have measured the time it takes for an electron to tunnel out of an atom, which is on the order of hundreds of attoseconds (10^-18 s).⁶

Potential barrier

A region of space where the potential energy is higher than the particle's total energy, classically forbidding passage.

Wavefunction

A mathematical function that describes the quantum state of a particle, from which probabilities of position and momentum are derived.

Alpha decay

A type of radioactive decay in which an atomic nucleus emits an alpha particle (two protons and two neutrons).

Fowler–Nordheim tunnelling

Field-induced electron tunnelling through a triangular potential barrier, often used in flash memory.

Josephson junction

A device made of two superconductors separated by a thin insulating barrier, through which Cooper pairs tunnel.