Editing SQUID

{{Short description|Type of magnetometer}}
{{Other uses|Squid (disambiguation)}}
{{Use dmy dates|date=May 2024}}
[[File:SQUID by Zureks.jpg|thumb|Sensing element of a SQUID, 2008]]

A '''SQUID''' ('''superconducting quantum interference device''') is a very sensitive [[magnetometer]] used to measure extremely weak [[magnetic field]]s, based on [[Superconductivity|superconducting]] loops containing [[Josephson junction]]s.

SQUIDs are sensitive enough to measure [[magnetic flux units|fields]] as low as 5×10<sup>−18</sup> [[Tesla (unit)|T]] with a few days of averaged measurements.<ref name=Ran04>{{cite book |url=http://einstein.stanford.edu/content/education/GP-B_T-Guide4-2008.pdf |archive-url=https://web.archive.org/web/20080516072031/http://einstein.stanford.edu/content/education/GP-B_T-Guide4-2008.pdf |archive-date=2008-05-16 |url-status=live |last=Ran |first=Shannon K’doah |title=Gravity Probe B: Exploring Einstein's Universe with Gyroscopes |page=26 |year=2004 |publisher=[[NASA]]}}</ref> Their noise levels are as low as 3 [[femto-|f]]T·[[Hertz|Hz]]<sup>−{{frac|1|2}}</sup>.<ref>{{cite journal|url=http://ib.ptb.de/de/org/7/75/751/SQUID_Stromsensoren/Drung_ASC06_Preprint.pdf|archive-url=https://web.archive.org/web/20110719073509/http://ib.ptb.de/de/org/7/75/751/SQUID_Stromsensoren/Drung_ASC06_Preprint.pdf|url-status=dead|archive-date=2011-07-19|title=Highly sensitive and easy-to-use SQUID sensors|author1=D. Drung |author2=C. Assmann |author3=J. Beyer |author4=A. Kirste |author5=M. Peters |author6=F. Ruede |author7=Th. Schurig  |name-list-style=amp |journal=IEEE Transactions on Applied Superconductivity|year=2007|volume=17|issue=2|pages= 699–704|doi=10.1109/TASC.2007.897403|bibcode = 2007ITAS...17..699D |s2cid=19682964}}</ref> For comparison, a typical [[refrigerator magnet]] produces 0.01 tesla (10<sup>−2</sup> T), and some processes in animals produce very small magnetic fields between 10<sup>−9</sup> T and 10<sup>−6</sup> T. [[SERF]] atomic magnetometers, invented in the early 2000s are potentially more sensitive and do not require [[cryogenic]] [[refrigeration]] but are orders of magnitude larger in size (~1&nbsp;cm<sup>3</sup>) and must be operated in a near-zero magnetic field.

== History and design ==

There are two main types of SQUID: [[direct current]] (DC) and [[radio frequency]] (RF). RF SQUIDs can work with only one [[Josephson junction]] ([[superconducting tunnel junction]]), which might make them cheaper to produce, but are less sensitive.

=== 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>

=== RF SQUID ===
[[File:Squid prototype2.jpg|thumb|A prototype SQUID]]

The RF SQUID was invented in 1967 by Robert Jaklevic, John J. Lambe, Arnold Silver, and [[James Edward Zimmerman]] at Ford.<ref name=clarke/> 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.<ref>{{Cite journal | last1 = Romani | first1 = G. L. | last2 = Williamson | first2 = S. J. | last3 = Kaufman | first3 = L. | doi = 10.1063/1.1136907 | title = Biomagnetic instrumentation | journal = Review of Scientific Instruments | volume = 53 | issue = 12 | pages = 1815–1845 | year = 1982 | pmid =  6760371|bibcode = 1982RScI...53.1815R }}</ref><ref>{{Cite journal | last1 = Sternickel | first1 = K. | last2 = Braginski | first2 = A. I. | doi = 10.1088/0953-2048/19/3/024 | title = Biomagnetism using SQUIDs: Status and perspectives | journal = Superconductor Science and Technology | volume = 19 | issue = 3 | pages = S160 | year = 2006 |bibcode = 2006SuScT..19S.160S | s2cid = 122140082 }}</ref>
The RF SQUID is inductively coupled to a resonant tank circuit.<ref>{{Cite journal|last1=Nisenoff|first1=M.|last2=Wolf|first2=S.|date=1975-09-01|title=Observation of a $cos\ensuremath{\varphi}$ term in the current-phase relation for "Dayem"-type weak link contained in an rf-biased superconducting quantum interference device|journal=Physical Review B|volume=12|issue=5|pages=1712–1714|doi=10.1103/PhysRevB.12.1712}}</ref> 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 <math>\Phi_0</math>. For a precise mathematical description refer to the original paper by Erné et al.<ref name=du/><ref>{{cite journal|author1=S.N. Erné |author2=H.-D. Hahlbohm |author3=H. Lübbig |title=Theory of the RF biased Superconducting Quantum Interference Device for the non-hysteretic regime|journal=J. Appl. Phys.|volume=47|pages=5440–5442|year=1976|doi=10.1063/1.322574|bibcode = 1976JAP....47.5440E|issue=12 |doi-access=free}}</ref>

=== 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]].<ref>{{cite journal |last1=Clarke |first1=John |title=SQUIDs |journal=Scientific American |date=August 1994 |volume=271 |issue=2 |pages=46–53 |doi=10.1038/scientificamerican0894-46 |jstor=24942801 |bibcode=1994SciAm.271b..46C |url=https://www.jstor.org/stable/24942801 |access-date=18 August 2022|url-access=subscription }}</ref>

High-temperature SQUID sensors were developed in the late 1980s.<ref>M.S. Colclough, C.E. Gough et al, Radiofrequency SQUID operation usinga ceramic high temperature superconductor,  Nature 328, 47 (1987)</ref> They are made of [[High-temperature superconductivity|high-temperature superconductors]], particularly [[yttrium barium copper oxide|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.<ref>LP Lee et al., Monolithic 77K DC SQUID magnetometer, Applied Physics Letters 59, 3051 (1991)</ref>

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.<ref>{{Cite journal | last1 = Cleuziou | first1 = J.-P. | last2 = Wernsdorfer | first2 = W. | doi = 10.1038/nnano.2006.54 | title = Carbon nanotube superconducting quantum interference device | journal = Nature Nanotechnology | volume = 1 | issue = October | pages = 53–59| year = 2006 | pmid =  18654142|bibcode =  2006NatNa...1...53C| s2cid = 1942814 }}</ref> The sensors are a few 100&nbsp;nm in size and operate at 1K or below. Such sensors allow to count spins.<ref>{{Cite journal | last1 = Aprili | first1 = Marco | doi = 10.1038/nnano.2006.78 | title = The nanoSQUID makes its debut | journal = Nature Nanotechnology | volume = 1 | issue = October | pages = 15–16| year = 2006 | pmid =  18654132|bibcode =2006NatNa...1...15A | s2cid = 205441987 }}</ref>

In 2022 a SQUID was constructed on [[Twistronics|magic angle twisted bilayer graphene (MATBG)]]<ref>{{Cite journal |last1=Portolés |first1=Elías |last2=Iwakiri |first2=Shuichi |last3=Zheng |first3=Giulia |last4=Rickhaus |first4=Peter |last5=Taniguchi |first5=Takashi |last6=Watanabe |first6=Kenji |last7=Ihn |first7=Thomas |last8=Ensslin |first8=Klaus |last9=de Vries |first9=Folkert K. |date=24 October 2022 |title=A tunable monolithic SQUID in twisted bilayer graphene |url=https://www.nature.com/articles/s41565-022-01222-0 |journal=Nature Nanotechnology |language=en |volume=17 |issue=11 |pages=1159–1164 |doi=10.1038/s41565-022-01222-0 |pmid=36280761 |arxiv=2201.13276 |bibcode=2022NatNa..17.1159P |s2cid=246430218 |issn=1748-3395}}</ref><ref>{{Cite web |title=A new quantum component made from graphene |url=https://ethz.ch/en/news-and-events/eth-news/news/2022/11/a-new-quantum-component-made-from-graphene.html |access-date=2022-11-15 |website=ethz.ch |date=3 November 2022 |language=en}}</ref>

== Uses ==
[[File:Squid prototype.jpg|thumb|The inner workings of an early SQUID, circa 1990<!-- seems to have been built after the [[National Bureau of Standards]] was renamed [[NIST]] in 1988.  Much more primitive SQUIDS were built at NBS in the first half of the 1970s. -->]]

The extreme sensitivity of SQUIDs makes them ideal for studies in biology. [[Magnetoencephalography]] (MEG), for example, uses measurements from an array of SQUIDs to make inferences about [[neuron|neural]] activity inside brains. Because SQUIDs can operate at acquisition rates much higher than the highest temporal frequency of interest in the signals emitted by the brain (kHz), MEG achieves good temporal resolution. Another area where SQUIDs are used is [[magnetogastrography]], which is concerned with recording the weak magnetic fields of the stomach. A novel application of SQUIDs is the [[magnetic marker monitoring]] method, which is used to trace the path of orally applied drugs. In the clinical environment SQUIDs are used in [[cardiology]] for [[magnetic field imaging]] (MFI), which detects the magnetic field of the heart for diagnosis and risk stratification.

Probably the most common commercial use of SQUIDs is in magnetic property measurement systems (MPMS). These are [[Turnkey|turn-key]] systems, made by several manufacturers, that measure the magnetic properties of a material sample which typically has a temperature between 300 mK and 400 K.<ref>{{Cite journal | last1 = Kleiner | first1 = R. | last2 = Koelle | first2 = D. | last3 = Ludwig | first3 = F. | last4 = Clarke | first4 = J. | title = Superconducting quantum interference devices: State of the art and applications | doi = 10.1109/JPROC.2004.833655 | journal = Proceedings of the IEEE | volume = 92 | issue = 10 | pages = 1534–1548 | year = 2004 | s2cid = 20573644 }}</ref> With the decreasing size of SQUID sensors since the last decade, such sensor can equip the tip of an [[Atomic force microscopy|AFM]] probe. Such device allows simultaneous measurement of roughness of the surface of a sample and the local magnetic flux.<ref>{{cite web|url=http://neel.cnrs.fr/spip.php?article914&lang=en|title=Microscopie à microsquid - Institut NÉEL|website=neel.cnrs.fr}}</ref>

For example, SQUIDs are being used as detectors to perform [[magnetic resonance imaging]] (MRI). While high-field MRI uses precession fields of one to several teslas, SQUID-detected MRI uses measurement fields that lie in the microtesla range. In a conventional MRI system, the signal scales as the square of the measurement frequency (and hence precession field): one power of frequency comes from the thermal polarization of the spins at ambient temperature, while the second power of field comes from the fact that the induced voltage in the pickup coil is proportional to the frequency of the precessing magnetization. In the case of untuned SQUID detection of prepolarized spins, however, the NMR signal strength is independent of precession field, allowing MRI signal detection in extremely weak fields, on the order of Earth's magnetic field. SQUID-detected MRI has advantages over high-field MRI systems, such as the low cost required to build such a system, and its compactness. The principle has been demonstrated by imaging human extremities, and its future application may include tumor screening.<ref>{{cite book|last1=Clarke|first1=J.|last2=Lee|first2=A.T.|last3=Mück|first3=M.|last4=Richards|first4=P.L.
|chapter=Chapter 8.3|title=Nuclear Magnetic and Quadrupole Resonance and Magnetic Resonance Imaging|pages=56–81}} in {{harvnb|Clarke|Braginski|2006}}</ref>

Another application is the [[scanning SQUID microscope]], which uses a SQUID immersed in liquid [[helium]] as the probe. The use of SQUIDs in [[Petroleum|oil]] [[prospecting]], [[mineral exploration]],<ref>{{cite journal|author1=P. Schmidt |author2=D. Clark |author3=K. Leslie |author4=M. Bick  |author5=D. Tilbrook|author6-link=Cathy Foley |author6=C. Foley |s2cid=14994533 |name-list-style=amp |title=GETMAG—A SQUID magnetic tensor gradiometer for mineral and oil exploration|journal=Exploration Geophysics|volume=35|pages=297–305|year=2004|doi=10.1071/eg04297|issue=4|bibcode=2004ExG....35..297S }}</ref> earthquake prediction and [[geothermal energy]] surveying is becoming more widespread as superconductor technology develops; they are also used as precision movement sensors in a variety of scientific applications, such as the detection of [[gravitational wave]]s.<ref>{{cite book
|last=Paik
|first=Ho J.
|chapter=Chapter 15.2 
|title = "Superconducting Transducer for Gravitational-Wave Detectors" in [volume 2 of] "The SQUID Handbook: Applications of SQUIDs and SQUID Systems"
|pages=548–554
}} in {{harvnb|Clarke|Braginski|2006}}</ref>
A SQUID is the sensor in each of the four gyroscopes employed on [[Gravity Probe B]] in order to test the limits of the theory of [[general relativity]].<ref name=Ran04/>

A modified RF SQUID was used to observe the [[Dynamical Casimir Effect|dynamical Casimir effect]] for the first time.<ref>{{cite magazine|url=http://www.technologyreview.com/blog/arxiv/26813/|title=First Observation of the Dynamical Casimir Effect|magazine=Technology Review}}</ref><ref>{{cite journal|last1=Wilson|first1=C. M.|title=Observation of the Dynamical Casimir Effect in a Superconducting Circuit|journal=Nature|volume=479|pages=376–379|year=2011|doi=10.1038/nature10561|arxiv = 1105.4714 |bibcode = 2011Natur.479..376W|pmid=22094697|issue=7373|s2cid=219735}}</ref>

SQUIDs constructed from super-cooled [[niobium]] wire loops are used as the basis for [[D-Wave Systems]] 2000Q [[quantum computer]].<ref>{{cite web|title=Not Magic Quantum|accessdate=2021-10-26|website=Lanl.gov|date=July 2016|url=http://www.lanl.gov/discover/publications/1663/2016-july/_assets/docs/1663_JULY-2016-Not-Magic-Quantum.pdf |archive-url=https://web.archive.org/web/20160729074720/http://www.lanl.gov/discover/publications/1663/2016-july/_assets/docs/1663_JULY-2016-Not-Magic-Quantum.pdf |archive-date=2016-07-29 |url-status=live}}</ref>

===Transition-edge sensors===
One of the largest uses of SQUIDs is to read out superconducting [[Transition-edge sensor]]s. 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]].<ref>A Squid-Based Microwave Cavity Search For Axions By ADMX; SJ Sztalos, G Carlos, C Hagman, D Kinion, K van Bibber, M Hotz, L Rosenberg, G Rybka, J Hoskins,  J Hwang, P Sikivie, DB Tanner, R Bradley, J Clarke; Phys.Rev.Lett. 104:041301; 2010</ref>

===Proposed uses===
A potential military application exists for use in [[anti-submarine warfare]] as a [[magnetic anomaly detector]] (MAD) fitted to [[maritime patrol aircraft]].<ref>{{cite web|url=http://www.aip.org/tip/INPHFA/vol-4/iss-2/p20.pdf |title=SQUID Sensors Penetrate New Markets |first=Jennifer |last=Ouellette |page=22 |publisher=The Industrial Physicist |url-status=dead |archive-url=https://web.archive.org/web/20080518032905/http://aip.org/tip/INPHFA/vol-4/iss-2/p20.pdf |archive-date=18 May 2008 }}</ref>

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 [[nanoparticle]]s.<ref>{{Cite journal|last1=Flynn|first1=E R|last2=Bryant|first2=H C|title=A biomagnetic system for in vivo cancer imaging|journal=Physics in Medicine and Biology|volume=50|issue=6|pages=1273–1293|doi=10.1088/0031-9155/50/6/016|pmc=2041897|pmid=15798322|bibcode=2005PMB....50.1273F|year=2005}}</ref><ref>{{Cite journal|last1=De Haro|first1=Leyma P.|last2=Karaulanov|first2=Todor|last3=Vreeland|first3=Erika C.|last4=Anderson|first4=Bill|last5=Hathaway|first5=Helen J.|last6=Huber|first6=Dale L.|last7=Matlashov|first7=Andrei N.|last8=Nettles|first8=Christopher P.|last9=Price|first9=Andrew D.|date=2015-10-01|title=Magnetic relaxometry as applied to sensitive cancer detection and localization|journal= Biomedical Engineering / Biomedizinische Technik|volume=60|issue=5|pages=445–455|doi=10.1515/bmt-2015-0053|pmid=26035107|osti=1227725|s2cid=13867059|issn=1862-278X|doi-access=free}}</ref> 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.<ref>{{Cite journal|last1=Hathaway|first1=Helen J.|last2=Butler|first2=Kimberly S.|last3=Adolphi|first3=Natalie L.|last4=Lovato|first4=Debbie M.|last5=Belfon|first5=Robert|last6=Fegan|first6=Danielle|last7=Monson|first7=Todd C.|last8=Trujillo|first8=Jason E.|last9=Tessier|first9=Trace E.|date=2011-01-01|title=Detection of breast cancer cells using targeted magnetic nanoparticles and ultra-sensitive magnetic field sensors|journal=Breast Cancer Research|volume=13|issue=5|pages=R108|doi=10.1186/bcr3050|issn=1465-542X|pmc=3262221|pmid=22035507 |doi-access=free }}</ref>

== See also ==
* [[Aharonov–Bohm effect]]
* [[Electromagnetism]]
* [[Geophysics]]
* [[Macroscopic quantum phenomena]]

== Notes ==

{{Reflist|30em}}

== References ==
* {{cite book
|volume=2
|title=The SQUID Handbook: Applications of SQUIDs and SQUID Systems
|editor1-first=John |editor1-last=Clarke
|editor2-first=Alex I. |editor2-last=Braginski
|isbn=978-3-527-40408-7
|publisher=Wiley-VCH
|year=2006 }}

{{Superconductivity}}
{{Authority control}}

{{DEFAULTSORT:Squid}}
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