# Josephson Effect

## Introduction to Josephson Effect Application

The effect is widely used in devices that are very susceptible to minute voltage changes. This can be seen in the functioning of SQUIDs; in other words, superconducting quantum interference devices. These devices are very sensitive and can have fluctuations with minute voltage. The magnetometers of the same device specifically operate through the usage of the Josephson effect. These devices are majorly used in the realm of science and engineering for an array of purposes.

In the area of precision metrology, the Josephson effect helps greatly in providing an accurately reproducible conversion rate in relation to frequency and voltage. It aids in getting an accurate reading of the conversion rate between frequency and voltage. In this case, the frequency is already present and is defined accurately through the medium of cesium standard. The phenomenon of the fractional Josephson effect is used, physically, to mainly provide an accepted and standard representation of a volt in the form of the Josephson voltage standard.

The Single-electron based transistors are mostly made up of superconducting materials. This allows them to use the Josephson effect, which aids them in achieving the desired and optimum effects. An example of the same can be seen in the device called a "superconducting single-electron transistor. The Josephson effect is further utilized for gaining the most precise and accurate measurements of the elementary charge. This measurement is taken based on the Josephson constant and von Klitzing, both of which are linked to the quantum Hall effect.

RSFQ digital electronic devices are also based upon the shunted Josephson junctions. In this case of RSFQ, the Josephson junction’s switching or altering event is attributed to the emission of a singular magnetic flux quantum. This aids in carrying the provided digital information in the said absence of any switching, which is equivalent to 0, while switching event in a variable of one carries a 1.

Josephson junctions are also an integral functioning mechanism in computing based upon the superconducting quantum. This can be seen in qubits, specifically in a flux qubit or other related mechanism where the said phase and charge function in the form of conjugate variables.

Superconducting tunnel junction detectors, also known as STJs, might become a dependable replacement for CCDs (charge-coupled devices) mainly because of astronomy and the respective study of astrophysics shortly. These devices have shown great promise and are greatly effective across a plethora of areas concerning the construction of a spectrum of ultraviolet to infrared. Moreover, this can also be used in X-ray technology in the coming years.

## Main Josephson Effects

### The DC Josephson Effect

As the name suggests, the DC Josephson effect is related to the direct current crossing, which goes over the insulator when there is no external electromagnetic field present. This crossing over the absence of the electromagnetic field takes place owing to Josephson tunneling. The DC Josephson current is directly proportional to the sine present in the Josephson phase. The Josephson phase is a phase difference revolving across the insulator itself, which always stays the same and constant over time.

### The AC Josephson Effect

When there is a fixed cross around the junction, the phase and values for the same will alter linearly in accordance with time. Owing to this, the current will be a sinusoidal AC (Alternating Current) with a certain amplitude and frequency. This effect is mainly used for proving that the Josephson junction can Also act as an accurate voltage-to-frequency converter.

### What is the Josephson Effect?

Josephson effect is perhaps the occurrence which happens when two superconductors are located in proximity and have some hindrance between them. Moreover this is an example of a microscopic quantum phenomenon. Here the effects of quantum mechanics can be observed at ordinary instead of the atomic scale. Likewise this effect also has practical application as it shows an accurate relationship between the different quantities of physics like frequency, voltage and high accurate measurements.

Moreover the josephson effect builds a current which is called supercurrent. This supercurrent flows continuously without any voltage across a device that is called josephson junction. Furthermore the josephson junction has two or more superconductors along with a weak link. Moreover the josephson junctions are applied in quantum mechanical circuits like RSFQ digital electronics, superconducting qubits, SQUIDS.

### Where is the Josephson Effect Applied

There are different types of josephson junction namely,  josephson junction, superconducting tunnel junction, long josephson junction. However the Dayem bridge is actually a thin film form of the josephson junction where the weak link is superconducting wire that on the scale has dimensions like some micrometers or less than that. Moreover the josephson junction count of a drive can be used as a criteria for its complex nature. The josephson effect can be used in many different areas. SQUIDS (superconducting quantum interference device) is a very sensitive magnetometer  which works through the josephson effect. Likewise in meteorology this effect will give precise conversion that takes place between the voltage and frequency.  However as the frequency is interpreted to be exact and practical by the caesium standard hence this effect can be used for practical purposes.

However the single electron transistors are usually made out of superconducting materials which allows the use of the josephson effect to get its best effect. Moreover the device is known as a superconducting single electron transistor.

Moreover the josephson junction performs the main function in superconducting quantum computing as Qubits just like in flux qubit or in any other scheme. The josephson effect has been observed in superfluid helium quantum interference devices (called as SHeQUIDS) that is the superfluid helium analog of a dc-SQUID.

### Let's Discuss About the DC Josephson Effect

However the DC josephson effect is actually a direct current that crosses the insulator when any kind of external electromagnetic field is not present due to tunneling. However this DC josephson current is equivalent to sine of the josephson phase which is a phase difference across the insulator that is constant over time.

### The AC Josephson Effect

However as the voltage is fixed across the junction this phase will differ linearly along with time and the current will be sinusoidal AC and will have amplitude and frequency. Hence this  indicates that the josephson junction can also act as the ideal voltage to frequency converter.

## FAQs on Josephson Effect

1. What do You understand about the RCSJ model?

The RCSJ stands for Resistively Capacitance Shunted Junction model, or in other words, shunted junction model. This is inclusive of the effect of an AC impedance of an ideal Josephson junction, which is made up of two basic Josephson relations. As per Thévenin's theorem, the ac and dc Josephson effect impedance in regards to the junction can be adequately represented by a singular capacitor paired along with a shunt resistor. Both of these shall be parallel to the present Josephson Junction. The complete expression for the current becomes –

$I_{ext}$ = $C_{J}\frac{dV}{dt} + I_{c} sin\phi + \frac{V}{R’}$

2. What do you mean by josephson penetration depth?

The Josephson penetration depth is used for determining the usual length upon which an external magnetic field may penetrate in the ideal long Josephson junction. In mathematical terms, it is usually denoted by-

$\lambda_{j} = \sqrt{\frac{\phi_{0}}{2\pi\mu_{0}d’jc’}}$

3. How is the josephson effect applied?

The josephson junctions have some important applications especially in the quantum mechanical circus for eg; SQUIDS which is known as superconducting qubits and RSFQ digital electronics. However the Suids are sensitive  magnetometers that work through the josephson effect.  These are used in engineering and science. However RSFQ digital electronics is actually based on josephson junctions. Likewise in this case the switching event of the junction is linked with emission of one magnetic flux quantum that further carries on the digital information.

4. Why is the josephson effect important?

However the josephson effect is the centre of operation of the SUID (superconducting quantum interference device). Moreover this is a very sensitive detector of the magnetic fields which can be used to measure small differences in the magnetic field of earth and also of the human body.

5. What is josephson junction made of?

The josephson junction is perhaps a quantum mechanical device which consists of two superconducting electrodes. This is further segregated by a thin barrier which is ferromagnet, thin insulating tunnel barrier, semiconductor, normal metal and many others. However the josephson  junctions have some unusual properties  for instance if one connects the superconducting electrodes with inductance then we can expect a voluntary supercurrent.

6.  How are josephson junctions useful in quantum computing?

Josephson junctions are good for the candidates to make quantum bits (qubits) for quantum computing. This system is good because of its low dissipation that is in the superconductors  for long coherence times. Also as it has complex superconducting circuits can be microfabricated with the help of integrated circuit processing methods which can go up to a large number of qubits will be straightforward.

7. What role does josephson junction in squid plays?

The SQUID is made up of a loop that consists of two josephson junctions which breaks up the loop. A SQUID is very sensitive to the whole amount of magnetic field that sticks to the area of the loop which is the voltage which you can measure across the device and is related to the total magnetic field around the loop.

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