# Josephson effect regime

## AC Josephson effect

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 a positive constant, then just increases linearly without bound.
Therefore, from the first equation:
we see that the current will just vary sinusoidally between .
This meas that we can use a Josephson junction as a perfect voltage to frequency converter.
Wikipedia mentions that this frequency is , 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. Figure 1. I-V curve of the AC Josephson effect. Source. 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 ±Ic​, 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? Figure 2. I-V curve of a superconducting tunnel junction. So it appears that there is a zero current between V=0 and V=2Δ/e. Why doesn't it show up on the oscilloscope sweeps, e.g. Video 1. "Superconducting Transition of Josephson junction by Christina Wicker (2016)"?

## Inverse AC Josephson effect

If you shine microwave radiation on a Josephson junction, it produces a fixed average voltage that depends only on the frequency of the microwave. TODO how is that done more preciesely? How to you produce and inject microwaves into the thing?
It acts therefore as a perfect frequency to voltage converter.
The Wiki page gives the formula: en.wikipedia.org/wiki/Josephson_effect#The_inverse_AC_Josephson_effect You get several sinusoidal harmonics, so the output is not a perfect sine. But the infinite sum of the harmonics has a fixed average voltage value.
And en.wikipedia.org/wiki/Josephson_voltage_standard#Josephson_effect mentions that the effect is independent of the junction material, physical dimension or temperature.
All of the above, compounded with the fact that we are able to generate microwaves with extremely precise frequency with an atomic clock, makes this phenomenon perfect as a Volt standard, the Josephson voltage standard.
TODO understand how/why it works better.