Physics:Quantum carpet - Revision history

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	== See also ==		== See also ==
	* Talbot effect		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	~~== References ==<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags, these references will then appear here automatically-->~~

	~~== See also ==~~
	~~{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}~~
	== References ==		== References ==

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	{{Short description\|Quantum Collection topic on Quantum carpet}}		{{Short description\|Quantum Collection topic on Quantum carpet}}

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	\| archive-url = https://web.archive.org/web/20160304130621/http://striky.ece.jhu.edu/~sasha/AEK.pubs/108.pdf		\| archive-url = https://web.archive.org/web/20160304130621/http://striky.ece.jhu.edu/~sasha/AEK.pubs/108.pdf
	}}</ref>		}}</ref>
	is a regular art-like pattern drawn by the wave function evolution or the probability density in the space of the Cartesian product of the quantum particle position coordinate and time or in spacetime resembling carpet art. It is the result of self-interference of the wave function during its interaction with reflecting boundaries. For example, in the infinite potential well, after the spread of the initially localized ~~[[Physics:Wave packet#Gaussian wavepackets in quantum mechanics\|~~Gaussian wave packet]] in the center of the well, various pieces of the wave function start to overlap and interfere with each other after reflection from the boundaries. The geometry of a quantum carpet is mainly determined by the [[Physics:Quantum revival\|quantum fractional revivals]].		is a regular art-like pattern drawn by the wave function evolution or the probability density in the space of the Cartesian product of the quantum particle position coordinate and time or in spacetime resembling carpet art. It is the result of self-interference of the wave function during its interaction with reflecting boundaries. For example, in the infinite potential well, after the spread of the initially localized Gaussian wave packet in the center of the well, various pieces of the wave function start to overlap and interfere with each other after reflection from the boundaries. The geometry of a quantum carpet is mainly determined by the [[Physics:Quantum revival\|quantum fractional revivals]].

	Quantum carpets demonstrate many principles of quantum mechanics, including wave-particle duality, [[Physics:Quantum revival\|quantum revivals]], and [[Physics:Quantum decoherence\|decoherence]]. Thus, they illustrate certain aspects of theoretical physics.		Quantum carpets demonstrate many principles of quantum mechanics, including wave-particle duality, [[Physics:Quantum revival\|quantum revivals]], and [[Physics:Quantum decoherence\|decoherence]]. Thus, they illustrate certain aspects of theoretical physics.

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	}}</ref>		}}</ref>
	is a regular ~~[[Art\|~~art]]-like pattern drawn by the ~~[[Wave function\|~~wave function]] evolution or the probability density in the space of the [[Cartesian product]] of the quantum particle position coordinate and time or in ~~[[Physics:Spacetime\|~~spacetime]] resembling carpet art. It is the result of self-interference of the wave function during its interaction with reflecting boundaries. For example, in the infinite potential well, after the spread of the initially localized [[Physics:Wave packet#Gaussian wavepackets in quantum mechanics\|Gaussian wave packet]] in the center of the well, various pieces of the wave function start to overlap and interfere with each other after reflection from the boundaries. The geometry of a quantum carpet is mainly determined by the [[Physics:Quantum revival\|quantum fractional revivals]].		is a regular art-like pattern drawn by the wave function evolution or the probability density in the space of the Cartesian product of the quantum particle position coordinate and time or in spacetime resembling carpet art. It is the result of self-interference of the wave function during its interaction with reflecting boundaries. For example, in the infinite potential well, after the spread of the initially localized [[Physics:Wave packet#Gaussian wavepackets in quantum mechanics\|Gaussian wave packet]] in the center of the well, various pieces of the wave function start to overlap and interfere with each other after reflection from the boundaries. The geometry of a quantum carpet is mainly determined by the [[Physics:Quantum revival\|quantum fractional revivals]].

	Quantum carpets demonstrate many principles of quantum mechanics, including ~~[[Physics:Wave–particle duality\|~~wave-particle duality]], [[Physics:Quantum revival\|quantum revivals]], and [[Physics:Quantum decoherence\|decoherence]]. Thus, they illustrate certain aspects of ~~[[Physics:Theoretical physics\|~~theoretical physics]].		Quantum carpets demonstrate many principles of quantum mechanics, including wave-particle duality, [[Physics:Quantum revival\|quantum revivals]], and [[Physics:Quantum decoherence\|decoherence]]. Thus, they illustrate certain aspects of theoretical physics.

	In 1995, physicist Michael Berry created the first quantum carpet, which described the momentum of an excited atom. Today, physicists use quantum carpets to demonstrate complex theoretical principles.<ref name=":1">{{Cite web\|date=2001-06-05\|title=Quantum carpets, carpets of light\|url=https://physicsworld.com/a/quantum-carpets-carpets-of-light/\|access-date=2020-10-26\|website=Physics World\|language=en-GB}}</ref><ref name=":3">{{Cite journal\|last1=Hall\|first1=Michael J W\|last2=Reineker\|first2=Martina S\|last3=Schleich\|first3=Wolfgang P\|date=1999-11-26\|title=Unravelling quantum carpets: a travelling-wave approach\|url=https://iopscience.iop.org/article/10.1088/0305-4470/32/47/307\|journal=Journal of Physics A: Mathematical and General\|volume=32\|issue=47\|pages=8275–8291\|doi=10.1088/0305-4470/32/47/307\|issn=0305-4470\|arxiv=quant-ph/9906107\|bibcode=1999JPhA...32.8275H\|s2cid=16863219}}</ref>		In 1995, physicist Michael Berry created the first quantum carpet, which described the momentum of an excited atom. Today, physicists use quantum carpets to demonstrate complex theoretical principles.<ref name=":1">{{Cite web\|date=2001-06-05\|title=Quantum carpets, carpets of light\|url=https://physicsworld.com/a/quantum-carpets-carpets-of-light/\|access-date=2020-10-26\|website=Physics World\|language=en-GB}}</ref><ref name=":3">{{Cite journal\|last1=Hall\|first1=Michael J W\|last2=Reineker\|first2=Martina S\|last3=Schleich\|first3=Wolfgang P\|date=1999-11-26\|title=Unravelling quantum carpets: a travelling-wave approach\|url=https://iopscience.iop.org/article/10.1088/0305-4470/32/47/307\|journal=Journal of Physics A: Mathematical and General\|volume=32\|issue=47\|pages=8275–8291\|doi=10.1088/0305-4470/32/47/307\|issn=0305-4470\|arxiv=quant-ph/9906107\|bibcode=1999JPhA...32.8275H\|s2cid=16863219}}</ref>
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	=== Wave-particle duality ===		=== Wave-particle duality ===
	Quantum carpets demonstrate ~~[[Physics:Wave–particle duality\|~~wave-particle duality]] by showing interference within wave packets.		Quantum carpets demonstrate wave-particle duality by showing interference within wave packets.

	Wave particle duality is difficult to comprehend. However, quantum carpets provide an opportunity to visualize this property. Consider the graph of the ~~[[Probability distribution\|~~probability distribution]] of an excited electron in a confined space (particle in a box), where brightness of color corresponds to momentum. Lines of dull color (ghost terms or canals) appear across the quantum carpet. In these canals, the momentum of the electron is very small. ~~[[Physics:~~Destructive interference~~\|Destructive interference]]~~, when the trough of a wave overlaps with the crest of another wave, causes these ghost terms. In contrast, some areas of the graph display bright color. ~~[[Physics:Constructive interference\|~~Constructive interference]], when the crests of two waves overlap to form a larger wave, causes these bright colors. Thus, quantum carpets provide visual evidence of interference within electrons and other wave packets. Interference is a property of waves, not particles, so interference within these wave packets prove that they have properties of waves in addition to properties of particles. Therefore, quantum carpets display wave particle duality.<ref>{{Cite journal\|last1=Friesch\|first1=O M\|last2=Marzoli\|first2=I\|last3=Schleich\|first3=W P\|date=2000-03-06\|title=Quantum carpets woven by Wigner functions\|journal=New Journal of Physics\|volume=2\|issue=1\|page=4\|doi=10.1088/1367-2630/2/1/004\|bibcode=2000NJPh....2....4F\|issn=1367-2630\|doi-access=free}}</ref>		Wave particle duality is difficult to comprehend. However, quantum carpets provide an opportunity to visualize this property. Consider the graph of the probability distribution of an excited electron in a confined space (particle in a box), where brightness of color corresponds to momentum. Lines of dull color (ghost terms or canals) appear across the quantum carpet. In these canals, the momentum of the electron is very small. Destructive interference, when the trough of a wave overlaps with the crest of another wave, causes these ghost terms. In contrast, some areas of the graph display bright color. Constructive interference, when the crests of two waves overlap to form a larger wave, causes these bright colors. Thus, quantum carpets provide visual evidence of interference within electrons and other wave packets. Interference is a property of waves, not particles, so interference within these wave packets prove that they have properties of waves in addition to properties of particles. Therefore, quantum carpets display wave particle duality.<ref>{{Cite journal\|last1=Friesch\|first1=O M\|last2=Marzoli\|first2=I\|last3=Schleich\|first3=W P\|date=2000-03-06\|title=Quantum carpets woven by Wigner functions\|journal=New Journal of Physics\|volume=2\|issue=1\|page=4\|doi=10.1088/1367-2630/2/1/004\|bibcode=2000NJPh....2....4F\|issn=1367-2630\|doi-access=free}}</ref>

	=== Quantum revivals ===		=== Quantum revivals ===
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	== History ==		== History ==
	While performing an experiment on optics, English physicist ~~[[Biography:~~Henry Fox Talbot~~\|Henry Fox Talbot]]~~ inadvertently discovered the key to quantum carpets. In this experiment, a wave struck a ~~[[Physics:Diffraction grating\|~~diffraction grating]], and Talbot noticed that the patterns of grating repeated themselves with periodic regularity. This phenomenon became known as the ~~[[Physics:Talbot effect\|~~Talbot effect]]. The bands of light that Talbot discovered were never graphed on an axis, and thus, he never created a true quantum carpet.<ref>{{Cite journal\|last1=Wen\|first1=Jianming\|last2=Zhang\|first2=Yong\|last3=Xiao\|first3=Min\|date=2013-03-31\|title=The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics\|url=https://www.osapublishing.org/aop/abstract.cfm?uri=aop-5-1-83\|journal=Advances in Optics and Photonics\|language=en\|volume=5\|issue=1\|page=83\|doi=10.1364/AOP.5.000083\|bibcode=2013AdOP....5...83W\|issn=1943-8206\|url-access=subscription}}</ref> However, the bands of light were similar to the images on a quantum carpet. Centuries later, physicists graphed the Talbot effect, creating the first quantum carpet. Since then, scientists have turned to quantum carpets as visual evidence for quantum theory.<ref name=":1" />		While performing an experiment on optics, English physicist Henry Fox Talbot inadvertently discovered the key to quantum carpets. In this experiment, a wave struck a diffraction grating, and Talbot noticed that the patterns of grating repeated themselves with periodic regularity. This phenomenon became known as the Talbot effect. The bands of light that Talbot discovered were never graphed on an axis, and thus, he never created a true quantum carpet.<ref>{{Cite journal\|last1=Wen\|first1=Jianming\|last2=Zhang\|first2=Yong\|last3=Xiao\|first3=Min\|date=2013-03-31\|title=The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics\|url=https://www.osapublishing.org/aop/abstract.cfm?uri=aop-5-1-83\|journal=Advances in Optics and Photonics\|language=en\|volume=5\|issue=1\|page=83\|doi=10.1364/AOP.5.000083\|bibcode=2013AdOP....5...83W\|issn=1943-8206\|url-access=subscription}}</ref> However, the bands of light were similar to the images on a quantum carpet. Centuries later, physicists graphed the Talbot effect, creating the first quantum carpet. Since then, scientists have turned to quantum carpets as visual evidence for quantum theory.<ref name=":1" />

	== See also ==		== See also ==
	* ~~[[Physics:~~Talbot effect~~\|Talbot effect]]~~		* Talbot effect

	== References ==<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags, these references will then appear here automatically-->		== References ==<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags, these references will then appear here automatically-->

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	== References ==<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags, these references will then appear here automatically-->		== References ==<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags, these references will then appear here automatically-->

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
			== References ==

	<references responsive="1"></references>		<references responsive="1"></references>
	[[Category:Quantum mechanics]]		[[Category:Quantum mechanics]]

			{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum carpet\|1}}
	{{Sourceattribution\|Quantum carpet}}

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	{{Quantum article nav\|previous=Physics:Quantum Density of states\|previous label=Density of states\|next=Physics:Quantum Time evolution\|next label=Time evolution}}		{{Quantum article nav\|previous=Physics:Quantum Density of states\|previous label=Density of states\|next=Physics:Quantum Time evolution\|next label=Time evolution}}