What is quantum tunnelling?

Roll a ball at a hill without enough speed and it rolls back. Every time.

In the quantum world a barrier is anything a particle would need more energy to cross than it has. It might be a thin layer of insulator between two wires, or the grip that holds a nucleus together.

A particle comes with a wave (chapter 1, Part C), and the wave sets the odds of finding it in each place (chapter 4). At a barrier the wave doesn't stop dead. Inside, it fades away fast.

If the barrier is thick, the wave fades to nothing. If it's thin, a little of the wave is left on the far side, and that gives a small chance of finding the particle there. The particle doesn't climb over or dig through. It simply turns up on the other side, with the energy it started with.

The chance falls very steeply as the barrier gets thicker or higher. Tunnelling matters across gaps a few atoms wide, which is why you'll never walk through a wall.

In radioactive decay. Some nuclei throw out an alpha particle even though it doesn't have the energy to escape the nucleus's grip. In 1928 George Gamow, and separately Ronald Gurney and Edward Condon, explained this as tunnelling. It also explained why some nuclei decay in a fraction of a second and others last billions of years: small differences in the barrier make huge differences to the odds.

• Electronics. In 1957 Leo Esaki made a diode that worked by electrons tunnelling. In 1962 Brian Josephson predicted that pairs of electrons in a superconductor could tunnel through a thin insulating gap. Both shared the 1973 Nobel Prize in Physics.
• Memory. Most flash memory, in phones and USB sticks, stores each bit by pushing electrons through a very thin insulating layer onto a trapped island, and the same tunnelling empties it again.
• Seeing atoms. In 1981 Gerd Binnig and Heinrich Rohrer at IBM in Zurich built the scanning tunnelling microscope. A sharp tip hovers just above a surface, and the tunnelling current changes so sharply with distance that it maps single atoms. They shared the 1986 Nobel Prize.
• Quantum computers. Superconducting qubits are built around Josephson's junction (chapter 9). The 2025 Nobel Prize in Physics went to John Clarke, Michel Devoret and John Martinis for showing that a whole circuit can tunnel as one quantum object (page 9c). Annealers may also use tunnelling to escape the wrong valley (chapter 10).