Ciro Santilli @cirosantilli 34

 Incoming links: Josephson junction

AC Josephson effect  Updated 2024-12-15  +Created 1970-01-01

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

φ

just increases linearly without bound.

Therefore, from the first equation:

I (t) = I_{c} sin (φ (t))

(1)

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 G H z / m V

, 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: Figure "Electron microscope image of a Josephson junction its I-V curve".

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 $\pm I_{c}$ , 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 1.

Superconducting Transition of Josephson junction by Christina Wicker (2016)

Source. Amazing video that presumably shows the screen of a digital oscilloscope doing a voltage sweep as temperature is reduced and superconductivity is reached.

Figure 2.
I-V curve of a superconducting tunnel junction
. So it appears that there is a zero current between $V = 0$ and $V = 2 Δ / e$ . Why doesn't it show up on the oscilloscope sweeps, e.g. Video 1. "Superconducting Transition of Josephson junction by Christina Wicker (2016)"?

 Read the full article

Ampere in the 2019 redefinition of the SI base units  Updated 2024-12-15  +Created 1970-01-01

 View more

Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.

This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!

Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:

quantum Hall effect, which has discrete resistances of type:
$R_{x y} = \frac{V _{Hall}}{I _{channel}} = \frac{h}{e ^{2} ν}$
(1)
for integer values of $ν$ .
Josephson effect, used in the Josephson voltage standard. With the Inverse AC Josephson effect we are able to produce:
$K_{J} = \frac{2 e}{h} V \cdot s$
(2)
per Josephson junction. This is about 2 microvolt / GHz, where GHz is a practical input frequency. Video "The evolution of voltage metrology to the latest generation of JVSs by Alain Rüfenacht" mentions that a typical operating frequency is 20 GHz.
Therefore to attain a good 10 V, we need something in the order of a million Josephson junctions.
But this is possible to implement in a single chip with existing micro fabrication techniques, and is exactly what the Josephson voltage standard does!

Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.

 Read the full article

Ciro's ASCII art circuit diagram notation  Updated 2024-12-15  +Created 1970-01-01

 View more

This notation is designed to be relatively easy to write. This is achieved by not drawing ultra complex ASCII art boxes of every component. It would be slightly more readable if we did that, but prioritizing the writer here.

Two wires are only joined if + is given. E.g. the following two wires are not joined:

  |
--|--
  |

but the following are:

  |
--+--
  |

Simple symmetric components:

-, + and |: wire
AC: AC source. Parameters:
- Hz: frequency
- V: peak voltage
e.g.:
```
AC_1Hz_2V
```
If only one side is given, the other is assumed to be at a ground G.
C: capacitor
G: ground. Often used together with DC, e.g.:
```
DC_10---R_10---G
```
means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 A
L: inductor
MICROPHONE. As a multi-letter symmetric component, you can connect the two wires anywhere, e.g.
```
---MICROPHONE---
```
or:
```
|
MICROPHONE
    |
```
SPEAKER
R: resistor
SQUID: SQUID device
X: Josephson junction

Asymmetric components have multiple letters indicating different ports. The capital letter indicates the device, and lower case letters the ports. The wires then go into the ports:

D: diode
- a: anode (where electrons can come in from)
- c: cathode
Sample usage in a circuit:
```
--aDc--
```
Can also be used vertically like aany other circuit:
```
|
a
D
c
|
```
We can also change the port order, the device is still the same due to capital D:
```
--cDa--

 |
Dac--

 |
Dca--

   |
--caD
```
DC DC source. Ports:
- p: positive
- n: negative
E.g. a 10 V source with a 10 Ohm resistor would be:
```
+---pDC_10_n---+
|              |
+----R_10------+
```
If only one side is given, the other is assumed to be at a the ground G. We can also omit p and m in that case and assume that p is the one used, e.g. the above would be equivalent to:
```
DC_10---R_10---G
```
If the voltage is not given, it is assumed to be a potentiometer.
T: transistor. The ports are sgTd:
- s: source
- g: gate
- d: gate
Sample usage in a circuit:
```
---+
   |
--sgTd--
```
All the following are also equivalent:
```
   |
   g
--sTd--

    |
--Tsgd--
   |
```
I: electric current source. Ports:
- s: electron source
- d: electron destination
V: Voltmeter. Ports:
- p: positive
- n: negative
If we don't need to specify explicit positive and negative sides, we can just use:
```
---V---
```
without any ports. This is notably often the case for AC circuits.
Optionaly, we can also add the sides as in:

Numbers characterizing components are put just next to each component with an underscore. When there is only one parameter, standard units are assumed, e.g.:

+-----+
|     |
C_1p  R_2k
|     |
+-----+

means:

a capacitor with 1 pico Faraday
a resistor with 2 k Ohms

Micro is denoted as u.

Wires can just freely come in and out of specs of a component, they are then just connected to the component, e.g.:

DC_10---R_10---G

means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 A

If a component has more than two parameters, units are used to distinguish them when possible, e.g.:

AC_1kV_2MHz

means an AC source with:

1 kV voltage
1 MHz frequency

 Read the full article

DC SQUID  Updated 2024-12-15  +Created 1970-01-01

 View more

Two parallel Josephson junctions.

In Ciro's ASCII art circuit diagram notation:

  |
+-+-+
|   |
X   X
|   |
+-+-+
  |

 Read the full article

Flux qubit  Updated 2024-12-15  +Created 1970-01-01

 View more

In Ciro's ASCII art circuit diagram notation, it is a loop with three Josephson junctions:

+----X-----+
|          |
|          |
|          |
+--X----X--+

https://upload.wikimedia.org/wikipedia/en/0/04/Flux_Qubit_-_Holloway.jpg

Video 1.

Superconducting Qubit by NTT SCL (2015)

Source.

Offers an interesting interpretation of superposition in that type of device (TODO precise name, seems to be a flux qubit): current going clockwise or current going counter clockwise at the same time. youtu.be/xjlGL4Mvq7A?t=1348 clarifies that this is just one of the types of qubits, and that it was developed by Hans Mooij et. al., with a proposal in 1999 and experiments in 2000. The other type is dual to this one, and the superposition of the other type is between N and N + 1 copper pairs stored in a box.

Their circuit is a loop with three Josephson junctions, in Ciro's ASCII art circuit diagram notation:

+----X-----+
|          |
|          |
|          |
+--X----X--+

They name the clockwise and counter clockwise states

∣ L ⟩

and

∣ R ⟩

(named for Left and Right).

When half the magnetic flux quantum is applied as microwaves, this produces the ground state:

∣ 0 ⟩ = ∣ L ⟩ + ∣ R ⟩

(1)

where

L

and

R

cancel each other out. And the first excited state

∣ 1 ⟩

is:

∣ 0 ⟩ = ∣ L ⟩ - ∣ R ⟩

(2)

Then he mentions that:

to go from 0 to 1, they apply the difference in energy
if the duration is reduced by half, it creates a superposition of $∣ 0 ⟩ + ∣ 1 ⟩$ .

 Read the full article

Josephson current  Updated 2024-12-15  +Created 1970-01-01

 View more

Maximum current that can flow across a Josephson junction, as can be directly seen from the Josephson equations.

Is a fixed characteristic value of the physical construction of the junction.

 Read the full article

Josephson effect  Updated 2024-12-15  +Created 1970-01-01

 View more

Discrete quantum effect observed in superconductors with a small insulating layer, a device known as a Josephson junction.

To understand the behaviour effect, it is important to look at the Josephson equations consider the following Josephson effect regimes separately:

A good summary from Wikipedia by physicist Andrew Whitaker:

at a junction of two superconductors, a current will flow even if there is no drop in voltage; that when there is a voltage drop, the current should oscillate at a frequency related to the drop in voltage; and that there is a dependence on any magnetic field

Bibliography:

www.youtube.com/watch?v=cnZ6exn2CkE "Superconductivity: Professor Brian Josephson". Several random excerpts from Cambridge people talking about the Josephson effect

 Read the full article

Josephson junction  Updated 2024-12-15  +Created 1970-01-01

 View more

A device that exhibits the Josephson effect.

Figure 1.
Electron microscope image of a Josephson junction its I-V curve
. Source.

 Read the full article

Superconducting tunnel junction  Updated 2024-12-15  +Created 1970-01-01

 View more

Specific type of Josephson junction. Probably can be made tiny and in huge numbers through photolithography.

Video 1.

Quantum Transport, Lecture 14: Josephson effects by Sergey Frolov (2013)

Source. youtu.be/-HUVGWTfaSI?t=878 mentions maskless electron beam lithography being used to produce STJs.

 Read the full article

System of units  Updated 2024-12-15  +Created 1970-01-01

 View more

The key thing in a good system of units is to define units in a way that depends only on physical properties of nature.

Ideally (or basically necessarily?) the starting point generally has to be discrete phenomena, e.g.

number of times some light oscillates per second
number of steps in a quantum Hall effect or Josephson junction

What we don't want is to have macroscopic measurement artifacts, (or even worse, the size of body parts! Inset dick joke) as you can always make a bar slightly more or less wide. And even metals evaporate over time! Though the mad people of the Avogadro project still attempted otherwise well into the 2010s!

Standards of measure that don't depend on artifacts are known as intrinsic standards.

 Read the full article

Transmon  Updated 2024-12-15  +Created 1970-01-01

 View more

Used e.g. in the Sycamore processor.

The most basic type of transmon is in Ciro's ASCII art circuit diagram notation, an LC circuit e.g. as mentioned at youtu.be/cb_f9KpYipk?t=180 from Video "The transmon qubit by Leo Di Carlo (2018)":

+----------+
| Island 1 |
+----------+
   |   |
   X   C
   |   |
+----------+
| Island 2 |
+----------+

youtu.be/eZJjQGu85Ps?t=2443 from Video "Superconducting Qubits I Part 1 by Zlatko Minev (2020)" describes a (possibly simplified) physical model of it, as two superconducting metal islands linked up by a Josephson junction marked as X in the diagram as per-Ciro's ASCII art circuit diagram notation:

+-------+       +-------+
|       |       |       |
| Q_1() |---X---| Q_2() |
|       |       |       |
+-------+       +-------+

The circuit is then analogous to a LC circuit, with the islands being the capacitor. The Josephson junction functions as a non-linear inductor.

Others define it with a SQUID device instead: youtu.be/cb_f9KpYipk?t=328 from Video "The transmon qubit by Leo Di Carlo (2018)". He mentions that this allows tuning the inductive element without creating a new device.

Video 1.

The superconducting transmon qubit as a microwave resonator by Daniel Sank (2021)

Source.

Video 2.

Calibration of Transmon Superconducting Qubits by Stefan Titus (2021)

Source. Possibly this Keysight which would make sense.

 Read the full article