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John M. Martinis, Michel Devoret, John Clarke | Physical Review Letters | (1985)
Primary Link Pubmed DOI Openalex Full text (OA)

Abstract

We report the first observation of quantized energy levels for a macroscopic variable, namely the phase difference across a current-biased Josephson junction in its zero-voltage state. The position of these energy levels is in quantitative agreement with a quantum mechanical calculation based on parameters of the junction that are measured in the classical regime.

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Sample Definition And Size

The study investigated Nb–NbOₓ–PbIn Josephson tunnel junctions fabricated on silicon chips, with junctions in cross-strip geometries of either 10×10 µm² or 80×10 µm². The exact number of junctions tested is not specified in the available abstract. ([studylib.net](https://studylib.net/doc/28065259/physrevlett.55.1543?utm_source=openai))

Study Type

Experimental observational study reporting the first observation of quantized energy levels in a macroscopic variable (phase difference) of a current-biased Josephson junction in its zero-voltage state. ([journals.aps.org](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.55.1543?utm_source=openai))

Conflicts Of Interest

No conflicts of interest are declared in the accessible abstract or metadata. ([journals.aps.org](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.55.1543?utm_source=openai))

Results Summary

The authors observed quantized energy levels of the phase difference across the junction in the zero-voltage state. The positions of these energy levels quantitatively agreed with quantum mechanical calculations based on junction parameters measured in the classical (thermal) regime. ([journals.aps.org](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.55.1543?utm_source=openai))

Referenced In

StarTalk

Season 17, Episode 1: Understanding Macroscopic Quantum Tunnelling

Hey StarTalkers! The first episode of Season 17 saw Neil, Chuck and guest Professor John Martinis sit down to discuss superconductivity, quantum mechanics and quantum computing.

An Interview with the Winner of the 2025 Nobel Prize in Physics, John Martinis

For the initiated, the phrase “macroscopic quantum tunnelling” invokes a strange mixture of awe and fear. It’s the weirdness of the quantum world encroaching into our reality, like a virus reaching up from the deepest recesses of existence.

If you’re not sure why this was impactful enough to win Professor Martinis the 2025 Nobel Prize in physics, this post is for you. 

Quantum Tunnelling Explained

Quantum tunnelling basically means “very small objects getting to places they shouldn’t be able to reach.”

Imagine a ball rolling towards a hill. The hill is a potential energy barrier. It basically says “you need this many joules to cross.” If the ball has enough kinetic energy, it clears the hill. If not, it rolls back down.

But for analogous barriers in the quantum world, there is a probability that the particle appears on the other side even if it doesn’t seem to have enough energy.

Superconducting Circuits as Macroscopic Quantum Systems

So how could this happen at the macroscopic level? Professor Martinis’ team published a paper showing the key insight in 1985.

Using a Josephson junction – like a tiny, electric potential-based “hill” – they were able to show “quantization” in macroscopic superconducting systems (see image below).

How? Well, electrons in superconductors form “Cooper pairs,” which have a composite wavefunction. They behave as one quantum object. Professor Martinis describes this at 9:55 in the podcast. The team were able to create this behaviour in a many-particle system.

The Macroscopic Quantum Tunnelling Proof

The team’s follow-up paper proved that the voltage across the Josephson junction (the effect of the electron going over the “hill”) was not caused by heat energy.

The math shows that temperature isn’t relevant for quantum tunnelling. And sure enough, when they reduced the temperature below 25 mK (milli-Kelvin), the escape rate didn’t vary with temperature. This proved without a doubt that the effect was quantum tunnelling.

It’s like that slow-rolling ball just appeared on the other side of the hill. 

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