Quantum Tunnelling

Quantum tunnelling is a fundamental phenomenon in quantum mechanics in which a particle passes through a potential energy barrier that it classically should not be able to surmount. It arises from the wave-like nature of particles described by quantum theory and has profound implications across physics, chemistry, and modern technology. Quantum tunnelling underlies many natural processes and advanced technologies, such as nuclear fusion in stars, semiconductor operation, and scanning tunnelling microscopy.

Concept and Quantum Explanation

In classical physics, a particle must possess enough kinetic energy to overcome a potential barrier. For instance, a ball cannot roll over a hill if its energy is less than the height of the hill. However, quantum mechanics introduces the concept of wave–particle duality, where particles such as electrons, protons, or neutrons exhibit both particle and wave characteristics.
According to the Schrödinger equation, a particle’s position is described by a wavefunction, which gives the probability of finding the particle at different locations. When this wavefunction encounters a potential barrier, it does not abruptly stop at the barrier’s edge. Instead, it extends slightly into and beyond the barrier, decaying exponentially in amplitude but remaining non-zero. If the barrier is thin enough or not too high, part of the wavefunction can exist on the other side of the barrier. Consequently, there is a finite probability that the particle will appear beyond the barrier even though, classically, it lacks the energy to cross it.
This process, where a particle effectively “tunnels” through an energy barrier, is known as quantum tunnelling. It does not violate energy conservation laws; rather, it reflects the probabilistic nature of quantum systems and the fact that particles are not strictly localised points but quantum waves with finite spatial spread.

Historical Background

The concept of tunnelling emerged in the early twentieth century during attempts to understand radioactive decay. In 1928, George Gamow, along with Ronald Gurney and Edward Condon, independently applied quantum mechanics to explain alpha decay in atomic nuclei. They discovered that alpha particles could escape from a nucleus by tunnelling through the nuclear potential barrier, even though their energy was lower than the barrier’s height.
This explanation marked one of the first major successes of quantum mechanics in describing physical phenomena that were impossible to explain using classical physics. The tunnelling concept was later generalised to many other systems, including electrons in solid materials and chemical reactions at the atomic scale.

Mathematical Description (Without Formulae)

Mathematically, tunnelling is described by solving the Schrödinger equation for a particle encountering a potential barrier. The wavefunction of the particle decreases rapidly within the barrier but does not drop to zero. The probability of transmission, or the likelihood that a particle will tunnel through, depends on several factors:

• Barrier width: Narrower barriers increase tunnelling probability.
• Barrier height: Lower energy barriers are easier to tunnel through.
• Particle mass and energy: Lighter particles and higher energy levels make tunnelling more likely.

This means that quantum tunnelling is extremely significant at atomic and subatomic scales but negligible for macroscopic objects.

Examples and Natural Occurrences

Quantum tunnelling is not just a theoretical prediction; it manifests in many natural and artificial processes.

• Nuclear Fusion in Stars: In the Sun and other stars, nuclei must overcome repulsive electrostatic forces (the Coulomb barrier) to fuse. At stellar temperatures, nuclei do not possess sufficient classical energy to overcome this barrier. However, quantum tunnelling allows them to merge, releasing the immense energy that powers stars. Without tunnelling, stellar fusion and therefore life as we know it would not exist.
• Alpha Decay: Certain radioactive elements emit alpha particles through tunnelling. Inside the nucleus, these particles are trapped by a strong nuclear potential well. Tunnelling enables them to escape, leading to measurable decay rates that match observed data precisely.
• Electron Tunnelling in Semiconductors: In solid-state physics, electrons can tunnel between energy states or across insulating barriers in devices such as tunnel diodes and Josephson junctions. This property is exploited to create ultra-fast electronic components and quantum computing elements.
• Scanning Tunnelling Microscope (STM): This powerful imaging tool uses tunnelling current between a sharp metal tip and a conductive surface to map atomic-scale structures. When the tip is brought extremely close to the surface, electrons tunnel through the small gap, generating a current that depends sensitively on the distance. The STM revolutionised surface science by allowing direct imaging and manipulation of individual atoms.
• Chemical Reactions and Enzyme Activity: Tunnelling can influence reaction rates by allowing particles such as protons or electrons to pass through energy barriers rather than over them. In biological systems, quantum tunnelling plays a role in enzyme catalysis and photosynthesis, enhancing reaction efficiency at relatively low temperatures.

Applications in Modern Technology

Quantum tunnelling has become the foundation of several technological innovations:

• Tunnel Diodes: These devices utilise tunnelling effects to achieve very fast switching speeds. They were among the earliest quantum devices used in electronics.
• Flash Memory: In semiconductor memory devices, electrons tunnel through thin oxide layers to store data, making tunnelling essential for data retention in non-volatile memory.
• Quantum Computing: Tunnelling underpins certain types of quantum bits (qubits) and is used in quantum annealing, a method of solving optimisation problems using quantum systems.
• Superconducting Devices: Josephson junctions, composed of two superconductors separated by a thin insulator, rely on tunnelling of Cooper pairs (paired electrons) and are vital components in quantum sensors and superconducting qubits.

Physical Implications and Significance

Quantum tunnelling demonstrates that the microscopic world operates according to fundamentally different rules than those of classical physics. It illustrates the probabilistic and non-deterministic nature of quantum mechanics, where particles cannot be described by definite trajectories. Instead, their existence is governed by probability amplitudes that allow them to “leak” through forbidden regions.
The phenomenon also has deep implications in theoretical physics. For instance:

• Quantum Cosmology: Tunnelling is invoked to explain how the universe might have originated from a quantum vacuum fluctuation.
• Field Theory and Particle Physics: Virtual particles and transitions between quantum states often involve tunnelling effects across potential energy barriers.
• Nanotechnology: As devices shrink to atomic scales, tunnelling becomes increasingly important, influencing current flow and limiting miniaturisation in transistors.

Factors Affecting Tunnelling Probability

The likelihood of tunnelling depends on several interacting factors:

• Barrier thickness and height: Thicker or higher barriers drastically reduce the probability.
• Particle mass: Heavier particles tunnel less easily than lighter ones.
• Particle energy: Higher energy increases tunnelling likelihood.
• Temperature: In some systems, thermal energy assists tunnelling, particularly in solid-state and molecular processes.

Because of these dependencies, tunnelling becomes more prominent at very small scales and low energies precisely the conditions encountered in atomic and subatomic systems.

Limitations and Challenges

While quantum tunnelling is well understood theoretically, controlling it precisely in practical applications remains challenging. In semiconductor technology, for example, unwanted tunnelling can cause leakage currents, reducing efficiency in microprocessors and memory devices. Researchers continually seek to balance the benefits of tunnelling for speed and sensitivity against its drawbacks for stability and energy loss.
In experimental physics, measuring tunnelling processes requires advanced instrumentation and extremely stable conditions because tunnelling probabilities can be exceedingly small.

Broader Significance

Quantum tunnelling unites theory and observation in one of the most striking ways possible showing that what appears impossible in classical physics becomes routine in the quantum world. It serves as a cornerstone of quantum mechanics, demonstrating the limits of deterministic reasoning and the power of probabilistic description.
From nuclear reactions in the heart of stars to electron motion in nanoscale circuits, tunnelling explains processes that shape both the universe and modern technology. It exemplifies how quantum principles translate into real-world effects, enabling progress in physics, chemistry, electronics, and emerging fields such as quantum computing and nanoscience.