DC SQUID

Diagram of a DC SQUID. The current ${\displaystyle I}$ enters and splits into the two paths, each with currents ${\displaystyle I_{a}}$ and ${\displaystyle I_{b}}$. The thin barriers on each path are Josephson junctions, which together separate the two superconducting regions. ${\displaystyle \Phi }$ represents the magnetic flux threading the DC SQUID loop.

Electrical schematic of a SQUID where ${\displaystyle I_{b}}$ is the bias current, ${\displaystyle I_{0}}$ is the critical current of the SQUID, ${\displaystyle \Phi }$ is the flux threading the SQUID and ${\displaystyle V}$ is the voltage response to that flux. The X-symbols represent Josephson junctions.

Left: Plot of current vs. voltage for a SQUID. Upper and lower curves correspond to ${\displaystyle n\cdot \Phi _{0}}$ and ${\displaystyle n+{\frac {1}{2}}\cdot \Phi _{0}}$ respectively. Right: Periodic voltage response due to flux through a SQUID. The periodicity is equal to one flux quantum, ${\displaystyle \Phi _{0}}$.

The DC SQUID was invented in 1964 by Robert Jaklevic, John J. Lambe, James Mercereau, and Arnold Silver of Ford Research Labs^[3] after Brian Josephson postulated the Josephson effect in 1962, and the first Josephson junction was made by John Rowell and Philip Anderson at Bell Labs in 1963.^[4] 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 ${\displaystyle I}$ splits into the two branches equally. If a small external magnetic field is applied to the superconducting loop, a screening current, ${\displaystyle I_{s}}$, 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.^[5] The induced current is in the same direction as ${\displaystyle I}$ in one of the branches of the superconducting loop, and is opposite to ${\displaystyle I}$ in the other branch; the total current becomes ${\displaystyle I/2+I_{s}}$ in one branch and ${\displaystyle I/2-I_{s}}$ in the other. As soon as the current in either branch exceeds the critical current, ${\displaystyle I_{c}}$, of the Josephson junction, a voltage appears across the junction.

Now suppose the external flux is further increased until it exceeds ${\displaystyle \Phi _{0}/2}$, 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 ${\displaystyle \Phi _{0}}$. The current now flows in the opposite direction, opposing the difference between the admitted flux ${\displaystyle \Phi _{0}}$ and the external field of just over ${\displaystyle \Phi _{0}/2}$. The current decreases as the external field is increased, is zero when the flux is exactly ${\displaystyle \Phi _{0}}$, 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 ${\displaystyle \Phi _{0}}$, with a change at maximum amperage every half-plus-integer multiple of ${\displaystyle \Phi _{0}}$ and at zero amps every integer multiple.

If the input current is more than ${\displaystyle I_{c}}$, 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 ${\displaystyle \Phi _{0}}$. Since the current-voltage characteristic of the DC SQUID is hysteretic, a shunt resistance, ${\displaystyle R}$ 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 ${\displaystyle \Delta \Phi }$ can be estimated as the function of ${\displaystyle \Delta V}$ (flux to voltage converter)^[6][7] as follows:

${\displaystyle \Delta V=R\cdot \Delta I}$

${\displaystyle 2\cdot \Delta I=2\cdot {\frac {\Delta \Phi }{L}}}$, where ${\displaystyle L}$ is the self inductance of the superconducting ring

${\displaystyle \Delta V={\frac {R}{L}}\cdot \Delta \Phi }$

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 ${\displaystyle L}$ of the loop is not so large. The general case can be evaluated by introducing a parameter

${\displaystyle \lambda ={\frac {i_{c}L}{\Phi _{0}}}}$

where ${\displaystyle i_{c}}$ is the critical current of the SQUID. Usually ${\displaystyle \lambda }$ is of order one.^[8]

RF SQUID

A prototype SQUID

The RF SQUID was invented in 1965 by Robert Jaklevic, John J. Lambe, Arnold Silver, and James Edward Zimmerman at Ford.^[7] It is based on the AC Josephson effect and uses only one Josephson junction. It is less sensitive compared to DC SQUID but is cheaper and easier to manufacture in smaller quantities. Most fundamental measurements in biomagnetism, even of extremely small signals, have been made using RF SQUIDS.^[9][10] The RF SQUID is inductively coupled to a resonant tank circuit.^[11] Depending on the external magnetic field, as the SQUID operates in the resistive mode, the effective inductance of the tank circuit changes, thus changing the resonant frequency of the tank circuit. These frequency measurements can be easily taken, and thus the losses which appear as the voltage across the load resistor in the circuit are a periodic function of the applied magnetic flux with a period of ${\displaystyle \Phi _{0}}$. For a precise mathematical description refer to the original paper by Erné et al.^[6][12]

Materials used

The traditional superconducting materials for SQUIDs are pure niobium or a lead alloy with 10% gold or indium, as pure lead is unstable when its temperature is repeatedly changed. To maintain superconductivity, the entire device needs to operate within a few degrees of absolute zero, cooled with liquid helium.^[13]

High-temperature SQUID sensors were developed in the late 1980s.^[14] They are made of high-temperature superconductors, particularly YBCO, and are cooled by liquid nitrogen which is cheaper and more easily handled than liquid helium. They are less sensitive than conventional low temperature SQUIDs but good enough for many applications.^[15]

In 2006, A proof of concept was shown for CNT-SQUID sensors built with an aluminium loop and a single walled carbon nanotube Josephson junction.^[16] The sensors are a few 100 nm in size and operate at 1K or below. Such sensors allow to count spins.^[17]

In 2022 a SQUID was constructed on magic angle twisted bilayer graphene (MATBG)^[18][19]

Transition-edge sensors

One of the largest uses of SQUIDs is to read out superconducting Transition-edge sensors. Hundreds of thousands of multiplexed SQUIDs coupled to transition-edge sensors are presently being deployed to study the Cosmic microwave background, for X-ray astronomy, to search for dark matter made up of Weakly interacting massive particles, and for spectroscopy at Synchrotron light sources.

Cold dark matter

Advanced SQUIDS called near quantum-limited SQUID amplifiers form the basis of the Axion Dark Matter Experiment (ADMX) at the University of Washington. Axions are a prime candidate for cold dark matter.^[28]

Proposed uses

A potential military application exists for use in anti-submarine warfare as a magnetic anomaly detector (MAD) fitted to maritime patrol aircraft.^[29]

SQUIDs are used in superparamagnetic relaxometry (SPMR), a technology that utilizes the high magnetic field sensitivity of SQUID sensors and the superparamagnetic properties of magnetite nanoparticles.^[30][31] These nanoparticles are paramagnetic; they have no magnetic moment until exposed to an external field where they become ferromagnetic. After removal of the magnetizing field, the nanoparticles decay from a ferromagnetic state to a paramagnetic state, with a time constant that depends upon the particle size and whether they are bound to an external surface. Measurement of the decaying magnetic field by SQUID sensors is used to detect and localize the nanoparticles. Applications for SPMR may include cancer detection.^[32]