Physics:Quantum Superconductivity - Revision history

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	{{Short description\|Quantum Collection topic on Quantum Superconductivity}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Superconductivity}}

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	~~~~{{Short description\|Quantum Collection topic on Quantum Superconductivity}}		{{Short description\|Quantum Collection topic on Quantum Superconductivity}}Book I

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	'''~~Quantum superconductivity~~''' is the study of superconductivity as a macroscopic quantum phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.		'''Superconductivity''' quantum superconductivity is the study of superconductivity as a macroscopic quantum phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid. Superconductivity is one of the best-known examples of a macroscopic quantum phenomenon, together with superfluidity, the Josephson effect, the quantum Hall effect, and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances. Magnetic flux lines penetrating a type-II superconductor. The field enters in quantized vortex lines while superconductivity remains between the lower and upper critical fields. A superconducting state is described by a macroscopic wave function,

	Superconductivity is one of the best-known examples of a ~~'''~~macroscopic quantum phenomenon~~'''~~, together with superfluidity, the Josephson effect, the quantum Hall effect, and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>
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	Magnetic flux lines penetrating a type-II superconductor. The field enters in quantized vortex lines while superconductivity remains between the lower and upper critical fields.
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			{{Short description\|Quantum Collection topic on Quantum Superconductivity}}

	{{Quantum book backlink\|Condensed matter and solid-state physics}}		{{Quantum book backlink\|Condensed matter and solid-state physics}}

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	'''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum mechanics\|quantum]] phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the [[Meissner effect]]. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.		'''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum mechanics\|quantum]] phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the [[Meissner effect]]. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.

	Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the [[Josephson effect]], the [[quantum Hall effect]], and [[Bose–Einstein condensate]]s. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>		Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the [[Josephson effect]], the [[quantum Hall effect]], and [[Bose–Einstein condensate]]s. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>
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	~~[[File:Flux lines in a superconductor01.jpg\|400px]]~~
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	Magnetic flux lines penetrating a type-II superconductor. The field enters in quantized vortex lines while superconductivity remains between the lower and upper critical fields.		Magnetic flux lines penetrating a type-II superconductor. The field enters in quantized vortex lines while superconductivity remains between the lower and upper critical fields.
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			[[File:Flux lines in a superconductor01.jpg\|thumb\|280px\|Quantum Superconductivity.]]
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	== Macroscopic quantum state ==		== Macroscopic quantum state ==

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	'''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum ~~mechanics\|quantum]]~~ phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.		'''Quantum superconductivity''' is the study of superconductivity as a macroscopic quantum phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.

	Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the Josephson effect, the [[quantum Hall effect]], and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>		Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with superfluidity, the Josephson effect, the quantum Hall effect, and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>
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	== Relation to superfluidity ==		== Relation to superfluidity ==

	Superconductivity is closely related to [[superfluidity]], but it is not the same phenomenon. Superfluidity is frictionless mass flow, while superconductivity is resistance-free charge flow.		Superconductivity is closely related to superfluidity, but it is not the same phenomenon. Superfluidity is frictionless mass flow, while superconductivity is resistance-free charge flow.

	In [[superfluid helium]], the particles are neutral, so <math>q=0</math>. The velocity of the superfluid is then determined only by the phase gradient:		In superfluid helium, the particles are neutral, so <math>q=0</math>. The velocity of the superfluid is then determined only by the phase gradient:

	:<math>\vec{v}_s = \frac{1}{m}\frac{h}{2\pi}\vec{\nabla}\varphi.</math>		:<math>\vec{v}_s = \frac{1}{m}\frac{h}{2\pi}\vec{\nabla}\varphi.</math>
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	== Cooper pairs ==		== Cooper pairs ==

	In conventional superconductors, the particles forming the macroscopic quantum state are Cooper pairss. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or ~~[[phonon]]s~~.		In conventional superconductors, the particles forming the macroscopic quantum state are Cooper pairss. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or phonons.

	Although electrons are ~~[[fermion]]s~~, a Cooper pair behaves as a composite [[boson]]. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect.		Although electrons are fermions, a Cooper pair behaves as a composite boson. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect.

	For a Cooper pair,		For a Cooper pair,

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	'''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum mechanics\|quantum]] phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the [[Meissner effect]]. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.		'''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum mechanics\|quantum]] phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.

	Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the [[Josephson effect]], the [[quantum Hall effect]], and [[Bose–Einstein ~~condensate]]s~~. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>		Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the Josephson effect, the [[quantum Hall effect]], and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal\|last1=Jaeger\|first1=Gregg\|title=What in the (quantum) world is macroscopic?\|journal=American Journal of Physics\|date=September 2014\|volume=82\|issue=9\|pages=896–905\|doi=10.1119/1.4878358\|bibcode=2014AmJPh..82..896J}}</ref>
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	== Cooper pairs ==		== Cooper pairs ==

	In conventional superconductors, the particles forming the macroscopic quantum state are [[Cooper ~~pair]]s~~. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or [[phonon]]s.		In conventional superconductors, the particles forming the macroscopic quantum state are Cooper pairss. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or [[phonon]]s.

	Although electrons are [[fermion]]s, a Cooper pair behaves as a composite [[boson]]. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect.		Although electrons are [[fermion]]s, a Cooper pair behaves as a composite [[boson]]. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect.
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	'''Type-II superconductors''' have two critical fields. Between the lower critical field <math>H_{c1}</math> and the upper critical field <math>H_{c2}</math>, magnetic flux penetrates the superconductor in quantized vortex tubes. The material remains superconducting around these vortices.		'''Type-II superconductors''' have two critical fields. Between the lower critical field <math>H_{c1}</math> and the upper critical field <math>H_{c2}</math>, magnetic flux penetrates the superconductor in quantized vortex tubes. The material remains superconducting around these vortices.

	This mixed state was explained by [[Alexei Abrikosov]] using [[Ginzburg–Landau theory]]. In a type-II superconductor, the vortices can form an ordered triangular lattice, now called the [[Abrikosov vortex]] lattice.<ref>{{Cite journal\|last1=Landau\|first1=Lev Davidovich\|last2=Ginzburg\|first2=Vitaly L\|date=1950\|title=On the theory of superconductivity\|url=https://cds.cern.ch/record/486430\|journal=Zh. Eksp. Teor. Fiz.\|volume=20}}</ref><ref>{{Cite journal \|last=Abrikosov \|first=Alexei A. \|date=2004-07-19 \|title=Type H Superconductors and the Vortex Lattice \|journal=ChemPhysChem \|volume=5 \|issue=7 \|pages=924–929 \|doi=10.1002/cphc.200400138 \|pmid=15298378 \|doi-access=free}}</ref>		This mixed state was explained by Alexei Abrikosov using Ginzburg–Landau theory. In a type-II superconductor, the vortices can form an ordered triangular lattice, now called the Abrikosov vortex lattice.<ref>{{Cite journal\|last1=Landau\|first1=Lev Davidovich\|last2=Ginzburg\|first2=Vitaly L\|date=1950\|title=On the theory of superconductivity\|url=https://cds.cern.ch/record/486430\|journal=Zh. Eksp. Teor. Fiz.\|volume=20}}</ref><ref>{{Cite journal \|last=Abrikosov \|first=Alexei A. \|date=2004-07-19 \|title=Type H Superconductors and the Vortex Lattice \|journal=ChemPhysChem \|volume=5 \|issue=7 \|pages=924–929 \|doi=10.1002/cphc.200400138 \|pmid=15298378 \|doi-access=free}}</ref>

	== Josephson effect ==		== Josephson effect ==

	The [[Josephson effect]] occurs when two superconductors are separated by a thin insulating barrier or weak link. Even without a voltage, a supercurrent can tunnel through the barrier.		The Josephson effect occurs when two superconductors are separated by a thin insulating barrier or weak link. Even without a voltage, a supercurrent can tunnel through the barrier.

	The DC Josephson relation is		The DC Josephson relation is
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	:<math>\nu = \frac{2eV}{h} = \frac{V}{\Phi_0}.</math>		:<math>\nu = \frac{2eV}{h} = \frac{V}{\Phi_0}.</math>

	Josephson junctions are essential in superconducting electronics, ~~[[SQUID]]s~~, voltage standards, and superconducting quantum circuits.		Josephson junctions are essential in superconducting electronics, SQUIDss, voltage standards, and superconducting quantum circuits.

	== SQUIDs ==		== SQUIDs ==

	A ~~[[SQUID]]~~ is a superconducting quantum interference device. It usually consists of a superconducting loop interrupted by one or more Josephson junctions. Because the total flux through the loop is quantized, the current through the SQUID depends sensitively on the applied magnetic field.		A SQUIDs is a superconducting quantum interference device. It usually consists of a superconducting loop interrupted by one or more Josephson junctions. Because the total flux through the loop is quantized, the current through the SQUID depends sensitively on the applied magnetic field.

	This makes SQUIDs among the most sensitive magnetometers known. They are used in physics, materials science, geophysics, and biomedical measurements.		This makes SQUIDs among the most sensitive magnetometers known. They are used in physics, materials science, geophysics, and biomedical measurements.
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	== Superconductivity and phonons ==		== Superconductivity and phonons ==

	In conventional superconductors, phonons provide the attractive interaction that binds electrons into Cooper pairs. This electron–phonon mechanism is central to [[BCS theory]]. The isotope effect, in which the superconducting critical temperature depends on ionic mass, provides evidence for the role of lattice vibrations in conventional superconductivity.		In conventional superconductors, phonons provide the attractive interaction that binds electrons into Cooper pairs. This electron–phonon mechanism is central to BCS theory. The isotope effect, in which the superconducting critical temperature depends on ionic mass, provides evidence for the role of lattice vibrations in conventional superconductivity.

	Not all superconductors are fully explained by simple electron–phonon coupling. High-temperature superconductors, heavy-fermion superconductors, and unconventional superconductors involve more complex mechanisms.		Not all superconductors are fully explained by simple electron–phonon coupling. High-temperature superconductors, heavy-fermion superconductors, and unconventional superconductors involve more complex mechanisms.
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	== Quantum gases and mechanical systems ==		== Quantum gases and mechanical systems ==

	Macroscopic quantum behaviour is not limited to superconductors and superfluid helium. Dilute atomic gases cooled to nanokelvin temperatures can form [[Bose–Einstein ~~condensate]]s~~, in which many atoms occupy a single quantum state.<ref>{{cite journal\|author1=Anderson, M.H.\|author2=Ensher, J.R.\|author3=Matthews, M.R.\|author4=Wieman, C.E.\|author5=Cornell, E.A.\|title=Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor\|journal=Science\|volume=269\|pages=198–201\|year=1995\|doi=10.1126/science.269.5221.198\|pmid=17789847\|issue=5221\|bibcode=1995Sci...269..198A\|doi-access=free}}</ref>		Macroscopic quantum behaviour is not limited to superconductors and superfluid helium. Dilute atomic gases cooled to nanokelvin temperatures can form Bose–Einstein condensatess, in which many atoms occupy a single quantum state.<ref>{{cite journal\|author1=Anderson, M.H.\|author2=Ensher, J.R.\|author3=Matthews, M.R.\|author4=Wieman, C.E.\|author5=Cornell, E.A.\|title=Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor\|journal=Science\|volume=269\|pages=198–201\|year=1995\|doi=10.1126/science.269.5221.198\|pmid=17789847\|issue=5221\|bibcode=1995Sci...269..198A\|doi-access=free}}</ref>

	Macroscopic quantum states have also been demonstrated in engineered mechanical systems. In quantum optomechanics and circuit electromechanics, mechanical resonators can be cooled close to their quantum ground state and controlled at the level of individual phonons.<ref>{{Cite journal \|last1=Aspelmeyer \|first1=Markus \|last2=Kippenberg \|first2=Tobias J. \|last3=Marquardt \|first3=Florian \|title=Cavity optomechanics \|journal=Reviews of Modern Physics \|volume=86 \|issue=4 \|pages=1391–1452 \|year=2014 \|doi=10.1103/RevModPhys.86.1391 \|arxiv=1303.0733 \|bibcode=2014RvMP...86.1391A}}</ref><ref>{{Cite journal \|first1=A. D. \|last1=O’Connell \|first2=M. \|last2=Hofheinz \|first3=M. \|last3=Ansmann \|first4=R. C. \|last4=Bialczak \|first5=M. \|last5=Lenander \|first6=E. \|last6=Lucero \|first7=M. \|last7=Neeley \|first8=D. \|last8=Sank \|first9=H. \|last9=Wang \|first10=M. \|last10=Weides \|first11=J. \|last11=Wenner \|first12=John M.\|last12=Martinis \|first13=A. N. \|last13=Cleland \|title=Quantum ground state and single-phonon control of a mechanical resonator \|journal=Nature \|volume=464 \|issue=7289\|pages=697–703 \|year=2010 \|doi=10.1038/nature08967 \|bibcode=2010Natur.464..697O \|pmid=20237473}}</ref>		Macroscopic quantum states have also been demonstrated in engineered mechanical systems. In quantum optomechanics and circuit electromechanics, mechanical resonators can be cooled close to their quantum ground state and controlled at the level of individual phonons.<ref>{{Cite journal \|last1=Aspelmeyer \|first1=Markus \|last2=Kippenberg \|first2=Tobias J. \|last3=Marquardt \|first3=Florian \|title=Cavity optomechanics \|journal=Reviews of Modern Physics \|volume=86 \|issue=4 \|pages=1391–1452 \|year=2014 \|doi=10.1103/RevModPhys.86.1391 \|arxiv=1303.0733 \|bibcode=2014RvMP...86.1391A}}</ref><ref>{{Cite journal \|first1=A. D. \|last1=O’Connell \|first2=M. \|last2=Hofheinz \|first3=M. \|last3=Ansmann \|first4=R. C. \|last4=Bialczak \|first5=M. \|last5=Lenander \|first6=E. \|last6=Lucero \|first7=M. \|last7=Neeley \|first8=D. \|last8=Sank \|first9=H. \|last9=Wang \|first10=M. \|last10=Weides \|first11=J. \|last11=Wenner \|first12=John M.\|last12=Martinis \|first13=A. N. \|last13=Cleland \|title=Quantum ground state and single-phonon control of a mechanical resonator \|journal=Nature \|volume=464 \|issue=7289\|pages=697–703 \|year=2010 \|doi=10.1038/nature08967 \|bibcode=2010Natur.464..697O \|pmid=20237473}}</ref>