Editing SQUID (section)

=== DC SQUID ===
[[File:DC SQUID.svg|thumb|200px|Diagram of a DC SQUID. The current <math>I</math> enters and splits into the two paths, each with currents <math>I_a</math> and <math>I_b</math>. The thin barriers on each path are Josephson junctions, which together separate the two superconducting regions. <math>\Phi</math> represents the magnetic flux threading the DC SQUID loop.]]

[[File:SQUID IV.svg|thumb|Electrical schematic of a SQUID where <math>I_b</math> is the bias current, <math>I_0</math> is the critical current of the SQUID, <math>\Phi</math> is the flux threading the SQUID and <math>V</math> is the voltage response to that flux. The X-symbols represent [[Josephson junction]]s.]]
[[File:IV curve.svg|thumb|Left: Plot of current vs. voltage for a SQUID. Upper and lower curves correspond to <math>n \cdot \Phi_0</math> and <math>n+\frac{1}{2} \cdot \Phi_0</math> respectively. Right: Periodic voltage response due to flux through a SQUID. The periodicity is equal to one flux quantum, <math>\Phi_0</math>.]]

The DC SQUID was invented in 1964 by Robert Jaklevic, John J. Lambe, James Mercereau, and Arnold Silver of Ford Research Labs<ref name=Jaklevic64>{{cite journal|author1=R. C. Jaklevic |author2=J. Lambe |author3=A. H. Silver |author4=J. E. Mercereau  |name-list-style=amp |title=Quantum Interference Effects in Josephson Tunneling|journal=Physical Review Letters|volume=12|pages=159–160|year=1964|doi=10.1103/PhysRevLett.12.159|bibcode=1964PhRvL..12..159J|issue=7}}</ref> after [[Brian Josephson]] postulated the [[Josephson effect]] in 1962, and the first Josephson junction was made by John Rowell and [[Philip Warren Anderson|Philip Anderson]] at [[Bell Labs]] in 1963.<ref>{{Cite journal | last1 = Anderson | first1 = P. | last2 = Rowell | first2 = J. | doi = 10.1103/PhysRevLett.10.230 | title = Probable Observation of the Josephson Superconducting Tunneling Effect | journal = Physical Review Letters | volume = 10 | issue = 6 | pages = 230–232 | year = 1963 |bibcode = 1963PhRvL..10..230A }}</ref> It has two Josephson junctions in parallel in a superconducting loop. It is based on the DC Josephson effect. In the absence of any external magnetic field, the input current <math>I</math> splits into the two branches equally. If a small external magnetic field is applied to the superconducting loop, a screening current, <math>I_s</math>, begins to circulate the loop that generates the magnetic field canceling the applied external flux, and creates an additional Josephson phase which is proportional to this external magnetic flux.<ref>{{Cite web|url=https://feynmanlectures.caltech.edu/III_21.html|title=The Feynman Lectures on Physics Vol. III Ch. 21: The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity, Section 21–9: The Josephson junction|website=feynmanlectures.caltech.edu|access-date=2020-01-08}}</ref> The induced current is in the same direction as <math>I</math> in one of the branches of the superconducting loop, and is opposite to <math>I</math> in the other branch; the total current becomes <math>I/2 + I_s</math> in one branch and <math>I/2 - I_s</math> in the other. As soon as the current in either branch exceeds the critical current, <math>I_c</math>, of the [[Josephson junction]], a voltage appears across the junction.

Now suppose the external flux is further increased until it exceeds <math>\Phi_0/2</math>, half the [[magnetic flux quantum]]. Since the flux enclosed by the superconducting loop must be an integer number of flux quanta, instead of screening the flux the SQUID now energetically prefers to increase it to <math>\Phi_0</math>. The current now flows in the opposite direction, opposing the difference between the admitted flux <math>\Phi_0</math> and the external field of just over <math>\Phi_0/2</math>. The current decreases as the external field is increased, is zero when the flux is exactly <math>\Phi_0</math>, and again reverses direction as the external field is further increased. Thus, the current changes direction periodically, every time the flux increases by additional half-integer multiple of <math>\Phi_0</math>, with a change at maximum amperage every half-plus-integer multiple of <math>\Phi_0</math> and at zero amps every integer multiple.

If the input current is more than <math>I_c</math>, then the SQUID always operates in the resistive mode. The voltage, in this case, is thus a function of the applied magnetic field and the period equal to <math>\Phi_0</math>. Since the current-voltage characteristic of the DC SQUID is hysteretic, a shunt resistance, <math>R</math> is connected across the junction to eliminate the hysteresis (in the case of copper oxide based [[high-temperature superconductors]] the junction's own intrinsic resistance is usually sufficient). The screening current is the applied flux divided by the self-inductance of the ring. Thus <math>\Delta \Phi</math> can be estimated as the function of <math>\Delta V</math> (flux to voltage converter)<ref name=du>{{cite book|author=E. du Trémolet de Lacheisserie, D. Gignoux, and M. Schlenker (editors)|title=Magnetism: Materials and Applications|volume=2|publisher=Springer|year=2005}}</ref><ref name=clarke>{{cite book|author=J. Clarke and A. I. Braginski (Eds.)|title=The SQUID handbook|volume=1|publisher=Wiley-Vch|year=2004}}</ref> as follows:

:<math>\Delta V = R \cdot \Delta I</math>

:<math>2 \cdot \Delta I = 2 \cdot \frac{\Delta \Phi}{L}</math>, where <math>L</math> is the self inductance of the superconducting ring

:<math>\Delta V = \frac{R}{L} \cdot \Delta \Phi</math>

The discussion in this section assumed perfect flux quantization in the loop. However, this is only true for big loops with a large self-inductance. According to the relations, given above, this implies also small current and voltage variations. In practice the self-inductance <math>L</math> of the loop is not so large. The general case can be evaluated by introducing a parameter

:<math>\lambda = \frac{i_cL}{\Phi_0}</math>

where <math>i_c</math> is the critical current of the SQUID. Usually <math>\lambda</math> is of order one.<ref>{{cite journal|author1=A.TH.A.M. de Waele  |author2=R. de Bruyn Ouboter |name-list-style=amp |title=Quantum-interference phenomena in point contacts between two superconductors|journal=Physica|volume= 41|year=1969|pages=225–254|doi=10.1016/0031-8914(69)90116-5|issue=2|bibcode = 1969Phy....41..225D }}</ref>