Quantum tunnelling: exploring the invisible atom by atom

Quantum tunnelling: a counter-intuitive but real phenomenon

A particle facing an insurmountable barrier

In classical mechanics, a particle confronted with a potential barrier higher than its energy is inevitably reflected. Yet, in the quantum world, the laws are different: a particle has a non-zero probability of crossing such a barrier. This is the famous tunnelling effect. This phenomenon follows directly from the wave nature of particles described by the Schrödinger equation.

The wave function in the forbidden region

Mathematically, the wave function $\psi(x)$ of a particle in a classically forbidden region (where $E < V(x)$) does not vanish, but decays exponentially: $$ \psi(x) \sim e^{-\kappa x}, \quad \text{with } \kappa = \sqrt{\frac{2m(V_0 - E)}{\hbar^2}}. $$ Thus, even if the probability density is very small, it is not zero, which allows the particle to "tunnel" through the barrier.

Concrete applications of quantum tunnelling

Scanning tunnelling microscopy (STM)

Quantum tunnelling is not a mere theoretical concept: it has major technological applications. The most emblematic example is the scanning tunnelling microscope (STM), which makes it possible to observe surfaces with atomic resolution. In this device, a tunnelling current is measured between a conducting tip and the surface of a sample, separated by only a few ångströms.

Transistors and Josephson junctions

Another example: the tunnel transistor and the Josephson junctions in superconducting circuits, where tunnelling allows the passage of Cooper pairs through an insulating barrier, a phenomenon crucial to the development of quantum computers.

Alpha decay

Even at the nuclear level, this effect explains alpha decay, where an alpha particle escapes from the atomic nucleus by crossing a nuclear potential barrier.

Quantum tunnelling: a window onto the probabilistic nature of the quantum world

The end of classical determinism

Quantum tunnelling calls into question our intuition based on classical causality. It reveals that, in the quantum world, there is no deterministic trajectory. Quantum mechanics provides only probabilities. The very existence of this phenomenon is experimental proof that particles are not localised objects, but entities governed by probability amplitudes.

A jewel of modern physics

In short, quantum tunnelling is one of the most surprising jewels of modern physics. It perfectly illustrates how the rules of quantum mechanics defy our intuitive understanding of the world, while having concrete repercussions in advanced technologies.

The scanning tunnelling microscope (STM)

The Scanning Tunnelling Microscope: A Window onto the Quantum World

Invention and Nobel Prize

The scanning tunnelling microscope, invented in 1981 by Gerd Binnig (1947-) and Heinrich Rohrer (1933-2013), Nobel Prize 1986, relies directly on the phenomenon of quantum tunnelling. In an STM, a very fine metal tip is brought to within about a nanometre of a conducting surface. When a voltage is applied between the tip and the sample, a tunnelling current appears, even though the two are not in physical contact. This current is extremely sensitive to the distance between the tip and the surface (decaying exponentially), which makes it possible to map the electronic topography with a lateral resolution below 0.1 nm.

Operating principle

Its operation relies on the local density of electronic states (LDOS) of the sample, accessible through the measured tunnelling current. By maintaining a constant current via a feedback system, the vertical position of the tip reveals the atomic topography of the surface. Thus, the STM makes it possible to "see" individual atoms, which makes it a fundamental tool in condensed matter physics, nanotechnology and surface chemistry.