Super Conducting Qubit-I

In the previous tutorial, we discussed briefly about all different kind of qubits.

In this tutorial we will talk about superconducting qubits in detail  

But before start on superconducting let us recall some basic concepts about conductors

Current

Current is flow of electrons towards positive charge inside some conductor (any good conductor like copper wire), more about this you can read in below blog 

Source: https://www.askiitians.com/iit-jee-electric-current/current-density/

Voltage

 Voltage is the electrical potential difference between two points e.g. Difference between two nodes of a battery (+ and -), + end has lack of electron, while – end has surplus of electrons and because electron are attracted towards protons ,they move towards + sides and causes the flow of current . But this will happen, only if we will close this circuit, means connect these two nodes of battery through some wire. If we will place anything in between these two wires like bulb, electron will pass through the bulb and it will lighten up. 

Resistance

Now the wire which we use to connect two ends of a battery are usually conductors like iron, copper etc. Because conductors have a free electron in its outer shell, so it allows the movement of electrons freely through them.

Assume you are sitting in some open field without holding to anything, suddenly a running crowd appears and pushes you forwards, what will happen?

You will find yourself moving with crowd as nothing to hold on to .Similar thing happened with  electrons  of conductors ,as they are not bonded well enough with conductor atom ,so they move along with crowd of electrons ,which is coming from the negative source of battery and going towards positive source of battery . Now Assume, while you are running towards positive source of battery, some hurdles come in your way, like stones, trees etc, what will happen? . You will collide with them and get bruised ,why you don’t have any control on your speed ,you are pushed forward by the wave of electron with great pressure ,so you can’t do much right?

Now electrons of conductor also find themselves in similar situation, they are pushed forward by wave of electrons, so they get collided by other atoms of copper wires, dissipate, and generate heat, this is called resistance. Because of the resistance, battery drained after some time, and current stopped flowing, as all the electrons converted into heat.

There is one more piece in above story ,This collision between electrons and atoms happened because of two things random and uncontrolled motion of electron and vibrations of atoms because of heat. In a copper wire atoms also vibrate because of heat ,now these vibration of atoms creates a hurdle in electrons path ,electron don’t have control on themselves as they are moving very fast and these atoms comes in their path because of the vibration , electrons collided with them and their kinetic energy changes into thermal energy and causes resistance.

Refer this blog to know more about resistance https://www.fluke.com/en-in/learn/best-practices/measurement-basics/electricity/what-is-resistance

To know more about all the above concepts, refer this you tube playlist

Magnetic Field

Magnetic Field is a vector field emanated by a magnet in its surrounding region. Why did I call it vector field? because it has direction. So magnetic field induces by south pole of magnet is in opposite direction of field induces by north pole of magnet.

Now Because we know opposites attract each other, south pole of two magnets repel each other while north and south pole of two magnets attract each other.

Magnetic Flux

Magnetic Flux denotes the intensity of Magnetic Field

Magnetic Field produces by Current

Before 1820, it was assumed that magnetic field is a natural occurring phenomenon and can be exhibited by magnets only. But in 1820, Hans Christian Oersted accidentally discovered that magnetic field can be produced using the current as well. Till 1820 current was used to produce light and heat, but it was realized in 1820 that when current passes through a conductor, it also induces a magnetic field around this conductor. This field can be visualized as circular lines around this wire, which carries the current.

Source: https://courses.lumenlearning.com/boundless-physics/chapter/magnetism-and-magnetic-fields/

As mentioned earlier current can flow in a wire by attaching it to a battery source which has surplus of electrons at one end and deficit of electrons at other end and once these two ends of this battery source closed by a wire, electrons start moving from surplus end to deficit end and current flow starts and this current flow in turn creates magnetic field around it .

Now we can move towards superconducting and we will see how above landscape changes completely when a conductor or any other substance becomes a superconductor.

 What is Superconductivity

Cooling down a substance to a temperature when its resistance becomes 0 is called superconductivity. This temperature is different for different metals

Refer Below YouTube Playlist for more information

Superconductivity – A Level Physics

When substance is in superconducting state and we pass the current through this substance, substance atoms do not interact with electrons so this current never dies down.

So, means at this critical temperature no resistance has been exhibited by these substances. http://www.supraconductivite.fr/en/index.php?p=supra-resistance-supra

So, in nutshell in superconductors because of no resistance current never dies down

But why? Atomic configuration of Metal Wire is still the same still surge of extra electrons are running towards positive end of battery, so they should still bump with metal atoms, right? And that bumping should cause the loss of electrons into heat which in turn is resistance.

Reason

At high temperatures electrons of current are bumping with copper atoms in totally random manner, which cause the loss of electrical energy and produces heat. But at low temperature these random motion of electrons stopped and vibration of copper atoms also stopped .So these electrons follow a very controlled motion ,it’s like that you are sitting in an open ground and you see that straight line of people going somewhere ,as you are unhitched with the current ground ,so you also decided to follow the people ,but now because no one is pushing you ,so you have full control on your velocity ,so you will not collide anywhere ,so you won’t be bruised and you don’t feel tired much ,as it’s a pleasant walk now from negative towards positive . That is why resistance goes down to zero in superconductors and current never dies down

Very good explanation here –https://www.quora.com/Why-do-electrons-have-no-resistance-in-super-conductors

Other Properties of Superconductors

Persistent Current – As mentioned earlier that when current passes through a wire it induces a magnetic field and this current passes through a wire when it is connected to some battery right?

What if the current flows in wire without connecting it to battery source, it will induce a magnetic field right? Because that is the property of current

In superconductor this current flows and it’s called persistent current and this current opposes the external magnetic field this phenomenon is called Meissner effect .

https://en.wikipedia.org/wiki/Persistent_current#In_resistive_conductors

As these currents are not dependent on any battery source and they cannot die down because there is no resistance in superconductor that’s why they are called persistence currents.

These current flows in resistive conductors also but because of resistance they die down quickly, and they are not  able to induce magnetic field which can oppose the externally applied magnetic field

Meissner Effect

When a conductor placed inside a magnetic field ,magnetic field passes through the conductor . When a superconductor placed inside a magnetic field ,it opposes this magnetic field because of the persistent current .There is one more point to this ,if before reaching to critical temperature conductor placed inside a magnetic field then magnetic field can passed inside it and when temperature of this conductor reduces which makes it superconductor it doesn’t expel this magnetic field ,instead it considers it as internal magnetic field and if any changes made to this magnetic field from outside persistent current generates to maintain this magnetic field .

Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.

Source: https://en.wikipedia.org/wiki/Meissner_effect

Meissner effect incurs the magnet levitation .MegLev trains works on this concept

Very Interesting video on Magnetic levitation

Now what is the reason behind Meissner effect and Persistent current in superconductors

Cooper Pairs

This controlled movement of electron because of reduced temperature creates one more phenomenon ,this is called formation of copper pair

When new electrons of current shove free electron of copper atom ,atom becomes positively charged and new incoming electron attract towards this atom ,now when another electron of current follows this electron ,this also becomes attracted to this positive charge ,and because of the common attraction towards this positive charge ,these electron create a pair called cooper pair to a limited distance .

Source : https://courses.physics.illinois.edu/phys498art/sp2018/PHYS489ART_SC_KP.pdf

A very entertaining video to explain this concept

Why these copper pairs are not formed in normal conductors ? Because of heat atoms vibrations are high and electrons motions are random ,so before forming a copper pair ,electrons collides with atoms and destroy and not able to attract towards another electron.

Why this behaviour is so important ,

As we know that in an atom electrons revolves around the nucleus which consist of positive charge in different energy levels ,which represent a different orbital path around nucleus

Source: https://byjus.com/physics/energy-level/

But two electrons can’t orbit around nucleus in the same path

Source:https://www.online-sciences.com/the-matter/atomic-structure-of-matter-energy-levels-electronic-distribution-chemical-activity/

Because as per pauli’s exclusion principle ,this behaviour is exhibited by photon’s not electron ,so basically photon can occupy the same state ,but electron can’t

But in case of copper pairing, electron starts behaving like photons and they start orbiting the nucleus in same energy level

Now why this is important? It is important as per the Bose-Einstein Condensate theory

https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate

As per this theory if electron or photons will form a pair then quantum state of this can be measured macroscopically as well

If you remember from my first blog, the problem with wave function of electron is – It is collapsed as soon as we try to measure it

But once electrons form cooper pair, this wave function can be measured macroscopically How?

As mentioned earlier because of cooper pair formation persistent current flows in conductor and due to this it expels the external magnetic field. This phenomenon of expulsion of external magnetic field by cooper pairs can be used to identify the cooper pair wave function without destroying it .In next post ,we will read , how this phenomenon is helpful in measuring this wavefunction from outside. Apart from this we will study about other important concepts of of superconducting qubits e.g. Josephson junctions and squids.

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