Quantum Tunnelling Explained: How Particles Cross Energy Barriers

Roll a ball at a hill too high for it, and the ball rolls back every time. Send an electron at an energy barrier too high for it, and some of the time the electron turns up on the other side. It never had the energy to climb over, and it did not borrow any. This is quantum tunnelling. It powers the Sun, sets how fast many radioactive nuclei decay and stores the data in your phone. In October 2025 it won a Nobel Prize, for showing that a whole electrical circuit can tunnel. Here is how tunnelling works, why its odds swing so wildly, and what the newest experiments have found.

What quantum tunnelling is: crossing a barrier without the energy to climb it

In everyday physics a barrier is absolute. A ball without enough energy to reach the top of a hill cannot get past it. The ball slows, stops and rolls back, and nothing about that is uncertain.

Quantum mechanics describes a particle with a wave, and waves do not stop dead at a barrier. The wave pushes a short way into the forbidden region, fading as it goes. If the barrier is thin enough, some of the wave is still alive at the far side and carries on. The size of that surviving wave sets the odds of finding the particle there.

Two points make tunnelling less mysterious than it sounds. The particle gains no energy on the way: it arrives on the far side with exactly the energy it started with. And no single particle splits in two. Each one either turns up beyond the barrier or bounces back, at random, with odds the wave fixes precisely.

Why a quantum wave leaks through a barrier

The Schrödinger equation says how a particle’s wave behaves in each region. Where the particle’s energy E is above the potential energy V, the solution oscillates like any ordinary wave. Inside the barrier, where E is below V, it cannot oscillate. It must grow or shrink exponentially instead:

ψ(x) ∝ e^−κx, with κ = √(2m(V − E)) / ħ

Here m is the particle’s mass and ħ is Planck’s constant divided by 2π. The decay rate κ grows with the mass, and with how far the particle falls short of the barrier top. For a barrier of width d, the chance of getting through is roughly:

T ≈ e^−2κd

The approximation holds once the barrier is thick enough for the wave to fade a lot inside it. The exact formula for a flat-topped barrier adds a prefactor but keeps the same exponential. Almost everything interesting about tunnelling lives in that exponent.

Double the barrier, and far less gets through

How mass and barrier width control the odds of tunnelling

Because the width and the square root of the mass both sit inside an exponent, small changes have enormous effects. Take an electron with 1 electronvolt of energy, meeting a barrier 2 electronvolts high and 1 nanometre wide. That is a few atoms thick. The electron gets through about once in every 7,000 attempts.

Double the width to 2 nanometres, and the odds fall to about 5 in a billion, which is 28,000 times lower. Now send a proton, 1,836 times heavier, at the original barrier. Its chance is about 1 in 10¹⁹⁰. We calculated all three from the exact formula for this article.

This is why tunnelling rules the world of electrons and barely touches anything heavier than a light nucleus. It needs no exotic conditions. Electrons in every chip and every metal contact tunnel constantly, simply because they are light and the barriers are thin.

One popular story needs correcting. Tunnelling is often explained as the particle briefly borrowing energy under the uncertainty principle. Energy is conserved at every step of the calculation above. The wave simply does not vanish inside the barrier.

Who discovered quantum tunnelling, 1927 to 1928

Tunnelling turned up almost as soon as the Schrödinger equation existed. In 1927 Friedrich Hund used it to show that a molecule could flip between two mirror-image shapes, passing through the energy barrier between them. The same year, Lothar Nordheim showed that electrons meeting the barrier at a metal’s surface can be reflected or pass through.

In 1928 the idea spread fast. J. Robert Oppenheimer showed that a strong electric field could pull the electron out of a hydrogen atom by tunnelling. Ralph Fowler and Nordheim explained why cold metals emit electrons in intense fields. Then George Gamow, and independently Ronald Gurney and Edward Condon, used tunnelling to crack one of the great puzzles of the day: alpha decay.

The name came slightly later. Walter Schottky was using the German Tunneleffekt, the tunnel effect, by 1931.

How tunnelling explains alpha decay

Some heavy nuclei throw out alpha particles, tight clusters of two protons and two neutrons. The puzzle was energy. Ernest Rutherford had fired fast alpha particles at uranium and found the electric barrier around the nucleus was at least twice as high as the energy of the alphas uranium itself emits. So how did those alphas get out?

Gamow’s answer was that they never climb out. An alpha particle rattles around inside the nucleus, and each time it hits the barrier it has a tiny chance of tunnelling through. For uranium-238 the barrier peaks at about 28 megaelectronvolts, the alpha carries 4.3, and the forbidden region is 51 femtometres wide. Our calculation gives a chance of about 1 in 10³⁸ per hit, with close to 10²¹ hits every second.

Uranium-238: an alpha particle tunnels through 51 femtometres

Put together, those numbers mean a typical nucleus waits billions of years. Our simple estimate gives a half-life of 4.6 billion years, against the measured 4.5 billion. That near-perfect match is partly luck. Shrink the assumed nuclear radius by 10 percent, and the estimate becomes 240 billion years. But even the crude version gets the scale right, which no classical picture can. Gurney and Condon captured the change of view: the alpha particle “slips away almost unnoticed.”

Why tiny energy differences change alpha half-lives enormously

The same exponent explains an old rule of thumb. In 1911 Hans Geiger and John Nuttall noticed that nuclei whose alphas fly farther decay faster, following a steep and regular pattern. Tunnelling explains the steepness. A more energetic alpha faces a lower and thinner stretch of barrier, and both effects enter the exponent.

The effect is extreme. Give uranium-238’s alpha an extra 0.1 megaelectronvolts, about 2 percent, and our estimated half-life drops roughly sevenfold. Real nuclei span a far wider range. Polonium-212 emits 8.8 megaelectronvolt alphas and has a half-life of 0.3 microseconds.

Bismuth-209 emits alphas of about 3.1 megaelectronvolts, and its half-life is about 2 × 10¹⁹ years, over a billion times the age of the universe. The alpha energies differ by less than a factor of three. The half-lives differ by a factor of about 10³³.

How tunnelling lets the Sun shine

By the 1920s Arthur Eddington suspected that stars shine by fusing hydrogen into helium. The numbers seemed to forbid it. Two protons repel each other, and to get close enough to fuse they must climb a barrier of roughly 1 megaelectronvolt. The Sun’s core is about 15.7 million kelvin, where a typical proton carries only about 1.35 kiloelectronvolts. That is less than a thousandth of the barrier.

Classically, the core would need to be about 740 times hotter. Some protons move faster than average, but not nearly fast enough. At the core’s temperature, the share of protons with 1 megaelectronvolt is about 1 in 10³²¹. The Sun holds about 10⁵⁷ protons, so without tunnelling not one pair would ever fuse.

Tunnelling changes the arithmetic. Robert Atkinson and Fritz Houtermans applied Gamow’s result to stars in 1929. The protons that matter are the few moving several times faster than average, at around 6 kiloelectronvolts. For them, our estimate of the chance of tunnelling on a close approach is about 1 in 10,000. Across the Sun’s enormous number of collisions, that is enough.

Tunnelling is not the only brake. The first fusion step also needs the weak nuclear force to turn a proton into a neutron during the encounter, which rarely happens. That second bottleneck is why a typical proton in the core waits billions of years to fuse, and why the Sun burns steadily instead of exploding.

The three Nobel Prizes awarded for tunnelling

Tunnelling sits at the centre of three Nobel Prizes in Physics.

1973: Leo Esaki, Ivar Giaever and Brian Josephson. In 1957 Esaki, at the company that became Sony, built a diode whose current fell as the voltage rose, because electrons tunnelled through an extremely thin junction. In 1960 Giaever, at General Electric, tunnelled electrons into a superconductor and used them to measure its energy gap. In 1962 Josephson, a 22-year-old Cambridge student, predicted that pairs of electrons in a superconductor could tunnel through a thin insulator with no voltage at all. That Josephson effect is at the heart of the 2025 prize.

1986: Gerd Binnig and Heinrich Rohrer, for the scanning tunnelling microscope they built at IBM in Zurich. A sharp tip hovers about two atoms’ width above a surface. The tunnelling current between them changes about ninefold for every 0.1 nanometre of distance, so holding it steady while scanning traces individual atoms. They shared the prize with Ernst Ruska, who designed the first electron microscope.

2025: John Clarke, Michel Devoret and John Martinis, for showing that tunnelling is not only for single particles.

What the 2025 Nobel Prize in Physics was awarded for

On 7 October 2025 the Royal Swedish Academy of Sciences named the three laureates: Clarke of the University of California, Berkeley, Devoret of Yale and UC Santa Barbara, and Martinis of UC Santa Barbara. The citation reads: “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit.” They shared 11 million Swedish kronor equally. Clarke called the news “the surprise of my life.”

The key word is macroscopic. Quantum mechanics had been tested on electrons, atoms and nuclei. Nobody knew whether a system made of billions of particles could act as one quantum object and tunnel as a whole. From the late 1970s the theorist Anthony Leggett argued that a superconducting circuit was the place to look.

In a superconductor, billions of paired electrons, called Cooper pairs, move in lockstep. Across a Josephson junction, their collective state is described by a single number, the phase difference. If that phase could tunnel, then a property of a whole circuit would be obeying quantum mechanics directly. The Nobel committee described the circuit as big enough to be held in the hand.

How Clarke, Devoret and Martinis made a circuit tunnel

The experiments ran at Berkeley in 1984 and 1985, in Clarke’s group, with Martinis as a graduate student and Devoret as a postdoctoral researcher. The heart of the circuit was a Josephson junction: two superconductors separated by an insulating layer thin enough for Cooper pairs to tunnel across.

They fed a steady current through the junction. While the phase stayed trapped, the junction carried that current with zero voltage. The trap is a dip in a tilted, washboard-shaped energy landscape, and the phase behaves like a particle sitting in it. If the phase escapes the dip, it runs downhill and a voltage suddenly appears. So the team switched the circuit on again and again, recorded when the voltage appeared, and turned those records into an escape rate.

The Nobel experiment: a circuit escapes its trap

The test was temperature. Escape by a thermal jolt over the top of the barrier gets rarer as the circuit cools, and should all but stop near absolute zero. Escape by tunnelling does not care about temperature. Below a few hundredths of a kelvin, the escape rate stopped falling and levelled off. The phase of the whole circuit was tunnelling.

The hard part was ruling out fakes. Stray electrical noise can kick the phase out and mimic a temperature-independent escape rate, which had clouded earlier claims. The team filtered and shielded their wiring heavily. They also measured the junction’s properties at higher temperatures, where it behaves classically, so the quantum prediction had no adjustable parameters. It matched.

How microwaves showed the circuit had energy levels

The second half of the citation, energy quantisation, came from a companion paper published in October 1985. A quantum particle trapped in a well cannot have just any energy. It sits on one of a ladder of allowed levels, like an electron in an atom.

Martinis, Devoret and Clarke shone microwaves on the circuit. At most frequencies nothing changed. At particular frequencies the escape rate jumped, because the microwaves lifted the phase to a higher rung, from which it tunnelled out far more easily. The resonant frequencies matched the level spacing predicted for the well, and the rungs sat closer together higher up, as theory said they should. The circuit had a spectrum. Circuits like it are now often called artificial atoms.

How the prize-winning circuit led to superconducting quantum computers

A circuit with discrete energy levels can store quantum information. Use its two lowest rungs as 0 and 1, and it becomes a qubit. Because the rungs are unevenly spaced, a microwave pulse can drive the step from 0 to 1 without also driving the next step up. That uneven spacing is exactly what the 1985 experiment observed.

The laureates built on it. Martinis demonstrated a phase qubit in 2002 and later led Google’s quantum hardware team, including the 2019 Sycamore experiment. Devoret’s groups at Saclay and Yale developed several of the superconducting circuits that followed, including the fluxonium qubit, and he now also works with Google Quantum AI. The superconducting chips behind the latest quantum computers descend from the 1985 circuit.

The same physics sets their limits. Every stray interaction that blurs the circuit’s quantum state is decoherence, and fighting it is the job of quantum error correction.

How long tunnelling takes, and why physicists still disagree

A simple question has resisted a simple answer for nearly a century: how long does a particle spend inside the barrier? The difficulty is that the particle is never caught there. Different ways of defining the time give different answers, and each answers a slightly different question.

Experiments now measure some of them. In 2019 an attoclock experiment in Australia on hydrogen atoms found that electrons tunnelled out with no measurable delay, under 1.8 attoseconds. In 2020 Aephraim Steinberg’s group in Toronto sent ultracold rubidium atoms through a barrier of laser light 1.3 micrometres thick. Each atom’s spin served as a stopwatch that ticked only inside the barrier. It read 0.61 milliseconds.

Both results can be right. A 2026 theory paper in Communications Physics argues that the two clocks measure different things. The attoclock records a delay seen far from the atom, and the spin clock records time spent inside the barrier. That is one proposed reconciliation, not yet a consensus. Some measurements have also suggested tunnelling can look faster than light, but no experiment has used it to send a signal faster than light.

Latest research: seven atoms tunnelling as one object (2026)

The newest experiments ask how big a tunnelling object can get. In May 2026 Bing Yang’s group at the Southern University of Science and Technology in Shenzhen reported in Nature Physics that clusters of up to seven rubidium atoms tunnelled together between the two sides of a double well made of laser light. Each cluster, with a mass of 608 atomic mass units, moved as a single object.

That should be hard. Earlier in this article, extra mass crushed the odds of tunnelling. Something similar happens here: the cluster crosses through a chain of intermediate steps, and each extra atom weakens the process sharply. The team held the two sides of each well at precisely equal energy, which kept the tunnelling alive. Hundreds of clusters ran side by side.

Each cluster ended up in a superposition of sitting entirely on the left and entirely on the right, a small Schrödinger’s cat. The team confirmed the atoms were entangled. Superpositions of up to five atoms measured energy shifts more precisely than the same number of independent atoms could.

Context matters. Heavier superpositions already exist: molecules above 25,000 atomic mass units have shown interference. What is new is making cat states by tunnelling, in a way that could scale. The long-term aim is to put ever heavier objects in superposition, and to test whether quantum mechanics, or gravity, eventually sets a limit.

Where tunnelling is used in everyday technology

Tunnelling is also routine engineering. Flash memory, in phones, solid-state drives and USB sticks, stores each bit as trapped charge sealed in by insulating layers. Writing or erasing a bit pushes electrons through a thin insulator by tunnelling, the process Fowler and Nordheim described in 1928.

Inside processors, tunnelling is the enemy. As transistors shrank, their insulating layers grew so thin that electrons leaked straight through. From 2007 chipmakers switched to hafnium-based insulators, which can be thicker for the same performance, largely to cut that leakage. Hard drives read data with sensors based on tunnel magnetoresistance, where the tunnelling current depends on how two magnetic layers are aligned.

What is established, contested and still unproven

Established. Tunnelling itself, measured in countless systems. It explains alpha decay, field emission and fusion in the Sun, and it is built into flash memory, microscopes and superconducting qubits. Tunnelling of a whole circuit’s phase, recognised by the 2025 Nobel Prize, has been reproduced many times since 1985.

Contested. What tunnelling time means, and which clock answers which question. How much tunnelling matters in biology is also debated. Hydrogen tunnelling in some enzyme reactions is widely accepted from isotope experiments. A 2022 computational study argued that proton tunnelling helps cause DNA mutations, but nobody has tested that in living cells.

Unproven. Whether tunnelling and superposition hold for arbitrarily large objects. Some theories predict that quantum behaviour breaks down above a certain mass. No experiment has seen such a limit, and the 2026 seven-atom clusters are one step in the search.