CND-25

Josephson frequency

f = 2 e V / h = V / Φ₀. Voltage-to-frequency of a superconducting junction.

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SuperconductivityJosephson

Governing equation

f=2eV/h

$V \in \left[0.1, 500\right]$

where

V: Voltage (µV)
f: Josephson frequency (GHz)

The figure, part by part

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①

Governing law — red

f=2eV/h

$V \in \left[0.1, 500\right]$

$V = 0.1$ $f = 0.048$

Along the curve

②

Domain of the variable — blue

V_{\min} = 0.1,\quad V_{\max} = 500

$V \in \left[0.1, 500\right]$

$V = 0.1$ $V = 0.1$

Along the curve

③

Response curve — green

f=2eV/h

$V \in \left[0.1, 500\right]$

$V = 0.1$ $f = 0.048$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}f}{\mathrm{d}V}

$V \in \left[0.1, 500\right]$

$V = 3.244$ $f^{\prime} = 0.484$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-25 — Josephson frequency) is the form associated with Josephson. Working symbols: $V$ $\rightarrow$ $f$ . Φ₀ = h/2e = 2.068×10⁻¹⁵ Wb. The volt is realised with this relation.

Purpose

Purpose: compute

f

from

V

in Condensed matter via

f=2eV/h

f = 2 e V / h = V / Φ₀. Voltage-to-frequency of a superconducting junction. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 20.000\,\mathrm{\mu V}

, the governing relation

f=2eV/h

yields

f = 9.672\,\mathrm{GHz}

. A junction, a voltage, a microwave tone. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Voltage V20 µV

Outputs

Josephson frequency f9.672 GHz

Reading speed

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Narration of this film

A junction, a voltage, a microwave tone.

Φ₀ = h/2e = 2.068×10⁻¹⁵ Wb. The volt is realised with this relation.

Reading speed

Watch on YouTube