• Pixel-art sticker of Junctra, personifying AC Josephson Effect, with the caption "Voltage Makes Me Oscillate."

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Junctra

AC Josephson Effect Physics

\[f = \frac{2eV}{h}\]
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Meet Junctra, a thin barrier between two superconductors: hold a DC voltage across her and her paired-electron current oscillates at f = 2eV/h, about 483.6 MHz per microvolt. That exact link between voltage and frequency underpins the volt standard. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Junctra, a Josephson junction: two superconductors with a whisper-thin barrier between them. Give her a voltage and she oscillates.

In a superconductor, electrons pair up into Cooper pairs that share a single quantum phase. Pairs can tunnel through a thin insulating barrier between two superconductors. Brian Josephson predicted in 1962 that if a steady DC voltage V is held across the junction, the phase difference grows steadily in time, and the supercurrent alternates at a frequency f = 2eV/h. The 2e is there because the carriers are pairs of electrons.

The ratio 2e/h is about 483.6 megahertz per microvolt. So a junction biased at just ten microvolts oscillates at about 4.8 gigahertz.

Run the relation backwards and a frequency, which can be measured extremely precisely, defines a voltage. Arrays of many junctions are used as voltage standards in metrology labs, and since 2019 the SI fixes e and h exactly, which gives the Josephson constant an exact value.

Junctra only behaves this way when she is cold enough to be superconducting, typically a few kelvin for the niobium junctions used in standards.

Equations

\[f = \frac{2eV}{h}\]
Symbols
SymbolMeaningUnit
\(f\) frequency of the alternating supercurrent \(\mathrm{Hz}\)
\(e\) elementary charge \(\mathrm{C}\)
\(V\) DC voltage across the junction \(\mathrm{V}\)
\(h\) Planck constant \(\mathrm{J·s}\)