= Josephson effect
{c}
{title2=$I_s=I_c\sin\phi,\quad\dot\phi=2eV/\hbar$}
{wiki}
In the ideal sinusoidal <Josephson junction>, the pair <electric current> and <quantum phase> obey
$$
I_s=I_c\sin\phi,\qquad \frac{d\phi}{dt}=\frac{2e}{\hbar}V.
$$
Here $e>0$ is the magnitude of the <Electron> <electric charge>, $\hbar=h/(2\pi)$ uses the <Planck constant>, and $I_c$ is the junction's <superconducting critical current> under the specified conditions. Define the signs as follows: positive conventional <electric current> flows from terminal 2 to terminal 1, and $V$ is the voltage of terminal 2 relative to terminal 1. The <Gauge-invariant Josephson phase> below fixes the matching orientation of $\phi$. The <DC Josephson effect> and <AC Josephson effect> follow from these relations. <Possible new effects in superconductive tunnelling by Brian D. Josephson>[Josephson (1962), p. 252, predictions (i) and (ii): zero-voltage supercurrent and frequency 2eV/h]{ref}
\Image[/josephson-phase-dc-ac-signatures.png]
{title=Phase, zero-voltage current branch and voltage-driven oscillations of an ideal Josephson junction}
{description=Original stipulated sinusoidal model, not measured data. The middle panel shows possible static states with adjustable <quantum phase>, not a uniquely selected <electric current> under ideal zero-voltage bias. The last panel shows only the pair <electric current>, with initial phase zero and constant $V=10\,\mathrm{\mu V}$; a quasiparticle contribution is excluded from that panel.}
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