Quantum Tunneling

Quantum tunneling is a phenomenon in which a particle can pass through a potential barrier that it classically could not overcome, due to its wave-like properties. In classical mechanics, a particle with energy less than the barrier height will be reflected. In quantum mechanics, the particle's wavefunction decays exponentially inside the barrier, but there is a non-zero probability that it emerges on the other side.¹

The probability of tunneling depends exponentially on the barrier width and the square root of the product of the particle mass and the barrier height. This means that tunneling is significant only for very small masses (like electrons) and very thin barriers (on the order of nanometers).²

The concept of tunneling was first proposed by Friedrich Hund in 1927 while studying molecular spectra, and later developed by George Gamow and others to explain alpha decay.³ Gamow applied quantum mechanics to show that alpha particles can escape from the nucleus despite the Coulomb barrier, a process that classical physics could not explain.

In 1928, Gamow, and independently Ronald Gurney and Edward Condon, used tunneling to explain alpha decay, marking the first major application of quantum mechanics to nuclear physics.⁴

Quantum tunneling is exploited in many electronic devices. The tunnel diode, invented by Leo Esaki in 1957, uses tunneling to produce negative resistance, enabling high-speed switching.⁵ Flash memory relies on Fowler-Nordheim tunneling to move electrons through a thin oxide layer to store data.⁶

Scanning tunneling microscopes (STM) use the exponential sensitivity of tunneling current to distance to image surfaces at the atomic scale, earning Gerd Binnig and Heinrich Rohrer the Nobel Prize in 1986.⁷

Quantum tunneling is essential for nuclear fusion in stars. The proton-proton chain, which powers the Sun, relies on protons tunneling through the Coulomb barrier to fuse, despite their thermal energies being insufficient to overcome it classically.⁸ This process was first explained by Robert Atkinson and Fritz Houtermans in 1929.

In biology, enzymes such as those in photosynthesis and DNA repair use tunneling to transfer electrons and protons efficiently, a field known as quantum biology.⁹

Beyond the well-known applications, quantum tunneling has several surprising and less-publicized facets. For instance, tunneling is responsible for the operation of the Josephson junction, which is used in superconducting quantum interference devices (SQUIDs) for extremely sensitive magnetometry.¹⁰

In chemistry, tunneling plays a role in reactions at low temperatures, where classical over-the-barrier transitions are negligible. For example, the reaction of hydrogen atoms with solid molecular hydrogen proceeds via tunneling even at temperatures near absolute zero.¹¹

Another edge case is the phenomenon of 'tunneling time' — the time a particle spends inside the barrier. This has been a subject of debate, with experiments suggesting that tunneling can be instantaneous or even superluminal, though this does not violate causality.¹²

Additionally, quantum tunneling is used in the design of non-volatile memory like EEPROM and in the emerging field of quantum computing, where qubits can be manipulated via tunneling in superconducting circuits.¹³

One of the most counterintuitive predictions of quantum mechanics is that a particle can tunnel through a barrier even if its energy is negative relative to the barrier height, leading to the concept of 'virtual particles' in quantum field theory.¹⁴

In astrophysics, tunneling is invoked to explain the synthesis of elements in stars, particularly the triple-alpha process that forms carbon, which requires two alpha particles to tunnel through the Coulomb barrier.¹⁵

There is also a phenomenon called 'tunneling ionization' in intense laser fields, where atoms are ionized by electrons tunneling through the potential barrier created by the laser field, a process used in attosecond physics.¹⁶

Potential barrier

A region of space where the potential energy is higher than the particle's total energy, classically preventing 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 tunneling

A form of quantum tunneling in which electrons pass through a triangular potential barrier in the presence of a strong electric field.

Josephson junction

A device made of two superconductors separated by a thin insulating layer, through which Cooper pairs tunnel, leading to a supercurrent.