Josephson Effect

Introduction to Josephson Effect

The Josephson effect refers to the flow of electric current that takes place between two singular objects which are made of superconducting material. These two objects are bifurcated by a minute and thin layered covering, making up of insulating material. Now, what are superconductors? Essentially, Superconductors are those objects that give out all of their inherent electrical resistance when they are cooled below a specific temperature which is in the proximity of absolute zero. This effect was first propounded by the English physicist named Brian D. Josephson. He pioneered this effect when he accurately predicted the usual flow of current, based on the BCS theory of superconductivity.

What is the Josephson Effect?

The Josephson effect is a scientific phenomenon based in the realm of supercurrent. In a nutshell, it refers to a singular current that can flow continuously without the aid of any voltage. In other words, no voltage is applied to the same flow of current. This phenomenon can be performed only across a device which is also named after the English physicist named Brian D. Josephson, called Josephson junction. 

This said junction is made up of two or more superconductors, and these two superconductors are meant to be connected by a weak link. The weak link for performing can be assembled through the usage of a thin insulating barrier. This thin insulating barrier is termed as a superconductor–insulator–superconductor junction or Josephson effect in superconductor, an abbreviated version of the same is referred to as S-I-S. For creating this weak link, a restricted or a short section consisting of non-superconducting metal can be used. Further, a physical constriction that can help in weakening the superconductivity right the appointment of contact can also be used for creating a weak link.

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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 being 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.

FAQs (Frequently Asked Questions)

Q.1 What do You Understand About the RCSJ Model?

Ans: 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 – 

Iext= CJ dV/dt + Ic sin  + V/R'

Q.2 What do You Mean by Josephson Penetration Depth?

Ans: 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- 

λj= √Φ0/2πμ0d'jc'