A12_Josephson Junctions and SQuIDs_JZepeda

Josephson junctions and squids no no not those squids talking about superconducting quantum interference devices squids in this video we're going to work through some basic theory electrodynamics quantum mechanics and superconductivity before diving into the how and why Josephson junctions work then we'll turn our focus to the squids and how they work to detect even the smallest magnetic fields as you all know there are four equations that live in infamy the Maxwell equations the governing bodies of all things electromagnetic brought to you by the great Gauss Faraday ampere or the contribution from Maximo himself will be our first step into discovering how squids work we're gonna look at amperage law in particular and as much that both the changing electric field or a surface current can cause a magnetic field this is demonstrated in the following simple experiment take a straight wire and pass a current through it the current generates a magnetic field around the wire according to amperes law which tells us the direction and strength of the magnetic field given our input current this magnetic field is constant and that's going to give us some complications so now it's evident that a current could cause a magnetic field but the opposite is a bit trickier if you have the pleasure of putting two inductors near by each other and passing current through one you'll notice that the other inductor only produces a current when the magnetic flux changes generating what's called an electromotive force EMF like Faraday's law prescribes the EMF is given by the native time derivative of the magnetic flux over some surface sigma as you can see in these equations this is disappointing that means we cannot speed up or slow down charges with the static magnetic field this is very important to note as we're referring to it in our discussion on squids let us shift your discussion briefly to quantum mechanics the only part of this huge field that we'll need is the concept of quantum tunneling looking at only one dimension we can imagine a potential like so here we've introduced a rather tall but thin barrier at Z equals zero let's also introduce a particle with energy lower than the potential needed to get over the barrier classically this particle has no chance of getting through think of a ball trying to roll up a hill it cannot pass over the hill if it doesn't have more kinetic energy at the bottom to potential energy at the top typically the perceived phenomenon is the ball making it to a point and then rolling back down in our thought experiment we've made a few assumptions firstly the ground is frictionless and secondly the ground prevents the ball from sticking into it in our experience if we have a very very heavy ball it can push things in front of it to the side as it goes towards his destiny the kinetic energy is so large that it doesn't seem to lose any when it collides with other objects in front of it so what happens if we roll this ball against our hill our super heavy ball can break one of the assumptions that we've held originally it has enough inertia to displace the dirt of the hill allowing it to tunnel through and get to the other side I'll be with a little bit less energy we said this energy is actually lost due to absorption from the hill this essentially is what quantity rolling is all about any particle has a chance to tunnel through a non infinite potential barrier while suffering an exponential decay in its kinetic energy lastly we're going to a quick rundown on one of the most important features of superconductivity zero electrical DC resistance once a metal reaches its superconducting phase all DC resistances that it offers suddenly stop any current that was running in the wire or are induced later persist for what appears to be an eternity as long as the wire stays superconducting the reason these metals are able to offer no resistance is due to the formation of things called Cooper pairs they arise when two electrons are weakly bound together thanks to a phonon exchange Cooper pairs actually have an energy gap that needs to be overcome in order to break this bond normally the thermal energy in the lattice is enough to break it but when the temperature is so ridiculously low the Cooper pairs can't be broken and can move along their merry way without ever getting scattered we call that connectivity Sigma is defined on basis of the electron scattering time tau if the electrons never collide with anything then tau is infinite and so Sigma meaning that a resistivity Rho drops to zero and our macroscale resistance R also drops to zero we have super conductivity now to the fun part the justice in effect is what happens when you have super current flowing from one superconductor to another through a weak link this link could be an insulator a section of non superconducting metal or just the kink of the superconductor that causes the superconductivity to weaken a little bit these three types of Josephson junctions mostly differ under how thick the barrier is but let's focus on the insulator version to get an intuition through a lot of math we can find on each side of the insulator the wave function is just an amplitude times a phase this justice--and phase is defined to be the difference in phase between the two superconductors and seems to govern most of the behaviors of the Josephson junction while the voltage depends on the time derivative of the Josephson phase the current depends instead sinusoidal e upon it the just as soon Junction is known to cause three particular effects the DC effect which is due to the tunneling of electrons and varies between negative I see and I see the AC effect where using a fixed voltage causes the phase to vary linearly and the current to oscillate with a known amplitude and frequency as such you're able to convert voltage to frequency the IV characteristics of a justice injunction are rather interesting there is a line at V equals zero presenting the DC justice in effect while as you go further away there are large values that the current takes on is due to the finiteness of the superconductor band gap we're finally ready to talk about squids a squid is composed of a single wire that's spun to two and then rejoined to form a loop each side of the loop is fitted with the Josephson notion and the current is passed along the system normally the current would split across both branches equally but if we introduce an external magnetic field that threads the hole it will form a screening current based on the magnetic field this means that one side will have more current flowing than the other and once one side is a current greater than I see that just the situation will acquire a voltage hold on we've already established that we needed change in magnetic field to cause an electric field and that's correct however squids have an interesting phenomenon occur and the magnetic flux is over half a fox quanta Phi naught then the squid wanting an integer number of Phi's will push current such that the total flux is integer number similarly when the fluxes less'n have a quanta it will push currents as the total flux is zero providing a measurable current shift as such the magnetic field isn't causing this current the squid is assigning more current to one branch to cancel or enhance the flux to achieve an integer flux quanta as such the measured current flip between directions as the Fox increases I can actually measure the applied flux through the screening current thanks to Ohm's law the resultant voltage is actually given by in this case R as a shunt resistance applied across the junction to eliminate hysteresis and ellas the self inductance of the superconducting ring so with this and several days of waiting it's possible to measure magnetic fields as small as 10 to the 8th Tesla with noise levels near 10 to the minus 30 to Tesla per square root Hertz this absurd level of detail can easily measure the magnetic fields animals produce and the squid serves as one of the best Magneto meters out there

Channel: Rice Prof ELEC 571

Views: 6,149

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Id: sNOpmTWlMwk

Length: 7min 17sec (437 seconds)

Published: Sun Aug 25 2019