= AC Josephson effect
{c}
This is what happens when you apply a <DC voltage> across a <Josephson junction>.
It is called "AC effect" because when we apply a <DC voltage>, it produces an <alternating current> on the device.
By looking at the <Josephson equations>, we see that $V(t) = k$ a positive constant, then $\varphi$ just increases linearly without bound.
Therefore, from the first equation:
$$
I(t) = I_c \sin (\varphi (t))
$$
we see that the current will just vary sinusoidally between $\pm I_c$.
This meas that we can use a <Josephson junction> as a perfect voltage to frequency converter.
Wikipedia mentions that this frequency is $484 GHz/mV$, so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.
Also it is likely not going to be very useful for many practical applications in this mode.
An <I-V curve> can also be seen at: <image Electron microscope image of a Josephson junction its I-V curve>.
\Image[https://upload.wikimedia.org/wikipedia/commons/d/dd/I-V_characteristics_of_Josephson_Junction.JPG]
{title=<I-V curve> of the <AC Josephson effect>}
{description=
Voltage is horizontal, current vertical. The vertical bar in the middle is the effect of interest: the current is going up and down very quickly between $\pm I_c$, the <Josephson current> of the device. Because it is too quick for the <oscilloscope>, we just see a solid vertical bar.
The non vertical curves at right and left are just other effects we are not interested in.
TODO what does it mean that there is no line at all near the central vertical line? What happens at those voltages?
}
\Video[https://www.youtube.com/watch?v=FYnDcWFYyVA]
{title=Superconducting Transition of <Josephson junction> by Christina Wicker (2016)}
{description=Amazing video that presumably shows the screen of a digital <oscilloscope> doing a voltage sweep as temperature is reduced and superconductivity is reached.}
\Image[https://upload.wikimedia.org/wikipedia/en/6/6b/STJ_IV_Curve.jpg?20110816180152]
{title=<I-V curve> of a <superconducting tunnel junction>}
{description=So it appears that there is a zero current between $V=0$ and $V=2\Delta/e$. Why doesn't it show up on the <oscilloscope> sweeps, e.g. <video Superconducting Transition of Josephson Junction by Christina Wicker (2016)>?}