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In quantum physics, a virtual state is a very short-lived, unobservable quantum state.^[1]

In many quantum processes a virtual state is an intermediate state, sometimes described as "imaginary"^[2] in a multi-step process that mediates otherwise forbidden transitions. Since virtual states are not eigenfunctions of any operator,^[3] normal parameters such as occupation, energy and lifetime need to be qualified. No measurement of a system will show one to be occupied,^[4] but they still have lifetimes derived from uncertainty relations.^[5]^[6] While each virtual state has an associated energy, no direct measurement of its energy is possible^[7] but various approaches have been used to make some measurements (for example see^[8] and related work^[9]^[10] on virtual state spectroscopy) or extract other parameters using measurement techniques that depend upon the virtual state's lifetime.^[11] The concept is quite general and can be used to predict and describe experimental results in many areas including Raman spectroscopy,^[12] non-linear optics generally,^[5] various types of photochemistry,^[13] and/or nuclear processes.^[14]

References

^ "A glossary of terms in nuclear science and technology". Conference on Glossary of Terms in Nuclear Science and Technology. A series of nine sections. American Society of Mechanical Engineers. 1953. p. 61. {{cite book}}: |work= ignored (help)
^ Robinson AL (February 1985). "Tunable Far IR Molecular Lasers Developed: Stimulated Raman scattering associated with a series of closely spaced rotational states is the key to wavelength tunability". Science. 227 (4688). New York, N.Y.: 736–7. doi:10.1126/science.227.4688.736. PMID 17796721.
^ Masters BR (2008). "Historical Development of Non-linear Optical Microscopy and Spectroscopy". In Masters BR, So P (eds.). Handbook of Biomedical Nonlinear Optical Microscopy. US: Oxford University Press. p. 10. ISBN 978-0-19-516260-8.
^ Wardle DA (January 1999). Raman Scattering in Optical Fibres (PDF) (Doctor of Philosophy in Physics thesis). The University of Auckland. p. 22.
^ ^a ^b Abbi SC, Ahmad SA, eds. (2001). Nonlinear Optics and Laser Spectroscopy. Alpha Science International, Limited. p. 139. ISBN 978-81-7319-354-5.
^ Norman P, Ruud K (2006). "Microscopic theory of nonlinear optics.". In Papadopoulos MG, Sadlej AJ, Leszczynski J (eds.). Non-Linear Optical Properties of Matter. Dordrecht: Springer. p. 3. ISBN 978-1-4020-4849-4.
^ Belkic D (2004). "The Dyson Perturbation Expansion of the Evolution Operator". Principles of quantum scattering theory. CRC Press. p. 70. ISBN 978-0-7503-0496-2.
^ Saleh BE, Jost BM, Fei HB, Teich MC (April 1998). "Entangled-Photon Virtual-State Spectroscopy" (PDF). Physical Review Letters. 80 (16): 3483–3486. doi:10.1103/PhysRevLett.80.3483. ISSN 0031-9007.
^ Kojima J, Nguyen QV (1 October 2004). "Entangled biphoton virtual-state spectroscopy of the A2Σ+–X2Π system of OH". Chemical Physics Letters. 396 (4): 323–328. doi:10.1016/j.cplett.2004.08.051.
^ Lee DI, Goodson III T (2007). "Quantum spectroscopy of an organic material utilizing entangled and correlated photon pairs". Linear and Nonlinear Optics of Organic Materials VII. 6653. International Society for Optics and Photonics: 66530V. doi:10.1117/12.745492.
^ Boitier F, Godard A, Rosencher E, Fabre C (13 April 2009). "Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors". Nature Physics. 5 (4): 267–270. doi:10.1038/nphys1218 – via www.nature.com.
^ Peter R. Griffiths, James A. De Haseth Fourier Transform Infrared Spectrometry, Volume 83 second ed, Wiley-Interscience, 2007 ISBN 0-470-10629-8 ISBN 978-0-470-10629-7 page 16
^ Douglas C. Neckers, William S. Jenks, Thomas Wolff Advances in Photochemistry, Volume 29 John Wiley and Sons, 2006 ISBN 0-471-68240-3 ISBN 978-0-471-68240-0 page 116
^ Breit G (April 1967). "Virtual coulomb excitation in nucleon transfer". Proceedings of the National Academy of Sciences of the United States of America. 57 (4): 849–55. doi:10.1073/pnas.57.4.849. PMC 224623. PMID 16591541.

[1] "A glossary of terms in nuclear science and technology". Conference on Glossary of Terms in Nuclear Science and Technology. A series of nine sections. American Society of Mechanical Engineers. 1953. p. 61. {{cite book}}: |work= ignored (help)

[pmid17796721-2] Robinson AL (February 1985). "Tunable Far IR Molecular Lasers Developed: Stimulated Raman scattering associated with a series of closely spaced rotational states is the key to wavelength tunability". Science. 227 (4688). New York, N.Y.: 736–7. doi:10.1126/science.227.4688.736. PMID 17796721.

[3] Masters BR (2008). "Historical Development of Non-linear Optical Microscopy and Spectroscopy". In Masters BR, So P (eds.). Handbook of Biomedical Nonlinear Optical Microscopy. US: Oxford University Press. p. 10. ISBN 978-0-19-516260-8.

[4] Wardle DA (January 1999). Raman Scattering in Optical Fibres (PDF) (Doctor of Philosophy in Physics thesis). The University of Auckland. p. 22.

[Abbi_2001-5] Abbi SC, Ahmad SA, eds. (2001). Nonlinear Optics and Laser Spectroscopy. Alpha Science International, Limited. p. 139. ISBN 978-81-7319-354-5.

[6] Norman P, Ruud K (2006). "Microscopic theory of nonlinear optics.". In Papadopoulos MG, Sadlej AJ, Leszczynski J (eds.). Non-Linear Optical Properties of Matter. Dordrecht: Springer. p. 3. ISBN 978-1-4020-4849-4.

[7] Belkic D (2004). "The Dyson Perturbation Expansion of the Evolution Operator". Principles of quantum scattering theory. CRC Press. p. 70. ISBN 978-0-7503-0496-2.

[8] Saleh BE, Jost BM, Fei HB, Teich MC (April 1998). "Entangled-Photon Virtual-State Spectroscopy" (PDF). Physical Review Letters. 80 (16): 3483–3486. doi:10.1103/PhysRevLett.80.3483. ISSN 0031-9007.

[9] Kojima J, Nguyen QV (1 October 2004). "Entangled biphoton virtual-state spectroscopy of the A2Σ+–X2Π system of OH". Chemical Physics Letters. 396 (4): 323–328. doi:10.1016/j.cplett.2004.08.051.

[10] Lee DI, Goodson III T (2007). "Quantum spectroscopy of an organic material utilizing entangled and correlated photon pairs". Linear and Nonlinear Optics of Organic Materials VII. 6653. International Society for Optics and Photonics: 66530V. doi:10.1117/12.745492.

[11] Boitier F, Godard A, Rosencher E, Fabre C (13 April 2009). "Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors". Nature Physics. 5 (4): 267–270. doi:10.1038/nphys1218 – via www.nature.com.

[12] Peter R. Griffiths, James A. De Haseth Fourier Transform Infrared Spectrometry, Volume 83 second ed, Wiley-Interscience, 2007 ISBN 0-470-10629-8 ISBN 978-0-470-10629-7 page 16

[13] Douglas C. Neckers, William S. Jenks, Thomas Wolff Advances in Photochemistry, Volume 29 John Wiley and Sons, 2006 ISBN 0-471-68240-3 ISBN 978-0-471-68240-0 page 116

[14] Breit G (April 1967). "Virtual coulomb excitation in nucleon transfer". Proceedings of the National Academy of Sciences of the United States of America. 57 (4): 849–55. doi:10.1073/pnas.57.4.849. PMC 224623. PMID 16591541.

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 In [[quantum physics]], a '''virtual state''' is a very short-lived, unobservable quantum state.<ref>{{cite book | chapter-url = https://books.google.com/books?id=LDkrAAAAYAAJ&pg=PA61&dq=%22virtual+state%22+fictitious+quantum&lr=&ei=BM-dSvinKZOMzgT_qoDhDg#v=onepage&q=%22virtual%20state%22%20fictitious%20quantum&f=false | chapter = A glossary of terms in nuclear science and technology | series = A series of nine sections | work = National Research Council (U.S.). | title = Conference on Glossary of Terms in Nuclear Science and Technology | publisher = American Society of Mechanical Engineers | date = 1953 | page = 61 }}</ref>
-In many quantum processes  a virtual state is an intermediate state, sometimes described as "imaginary"<ref name="pmid17796721">{{cite journal | vauthors = Robinson AL | title = Tunable Far IR Molecular Lasers Developed: Stimulated Raman scattering associated with a series of closely spaced rotational states is the key to wavelength tunability | journal = Science | location = New York, N.Y. | volume = 227 | issue = 4688 | pages = 736–7 | date = February 1985 | pmid = 17796721 | doi = 10.1126/science.227.4688.736 }}</ref> in a multi-step process that mediates otherwise forbidden transitions. Since virtual states are not [[eigenfunction]]s of any operator,<ref>{{cite book | vauthors = Masters BR | chapter = Historical Development of Non-linear Optical Microscopy and Spectroscopy | veditors = Masters BR, So P | title = Handbook of Biomedical Nonlinear Optical Microscopy | publisher = Oxford University Press| location = US | date = 2008 | isbn = 978-0-19-516260-8 | pages = 10 | chapter-url = https://books.google.com/books?id=4mki1ThMgGYC&pg=PA10 }}</ref> normal parameters such as occupation, energy and lifetime need to be qualified. No measurement of a system will show one to be occupied,<ref>{{cite thesis | url = http://researchspace.auckland.ac.nz/bitstream/2292/433/2/02whole.pdf | vauthors = Wardle DA | title = Raman Scattering in Optical Fibres | degree = Doctor of Philosophy in Physics | publisher = The University of Auckland | date = January 1999 | page = 22 }}</ref> but they still have lifetimes derived from [[Uncertainty principle|uncertainty]] relations.<ref name = "Abbi_2001">{{cite book | url = https://books.google.com/books?id=bnuGcAZR14IC&pg=PA139 | title = Nonlinear Optics and Laser Spectroscopy | veditors = Abbi SC, Ahmad SA | publisher = Alpha Science International, Limited | date = 2001 | page = 139 | isbn = 978-81-7319-354-5 }}</ref><ref>[https://books.google.com/books?id=eeE8OrohX3sC&pg=PA3&dq=%22the+virtual+state%22+photon&lr=&ei=bWKRSv6MOYvgyQTt1sitBw#v=onepage&q=%22the%20virtual%20state%22%20photon&f=false  Non-linear optical properties of matter: from molecules to condensed phases  By Manthos G. Papadopoulos, Andrzej Jerzy Sadlej, Jerzy Leszczynski ] page 3 Springer, 2006
+In many quantum processes  a virtual state is an intermediate state, sometimes described as "imaginary"<ref name="pmid17796721">{{cite journal | vauthors = Robinson AL | title = Tunable Far IR Molecular Lasers Developed: Stimulated Raman scattering associated with a series of closely spaced rotational states is the key to wavelength tunability | journal = Science | location = New York, N.Y. | volume = 227 | issue = 4688 | pages = 736–7 | date = February 1985 | pmid = 17796721 | doi = 10.1126/science.227.4688.736 }}</ref> in a multi-step process that mediates otherwise forbidden transitions. Since virtual states are not [[eigenfunction]]s of any operator,<ref>{{cite book | vauthors = Masters BR | chapter = Historical Development of Non-linear Optical Microscopy and Spectroscopy | veditors = Masters BR, So P | title = Handbook of Biomedical Nonlinear Optical Microscopy | publisher = Oxford University Press| location = US | date = 2008 | isbn = 978-0-19-516260-8 | pages = 10 | chapter-url = https://books.google.com/books?id=4mki1ThMgGYC&pg=PA10 }}</ref> normal parameters such as occupation, energy and lifetime need to be qualified. No measurement of a system will show one to be occupied,<ref>{{cite thesis | url = http://researchspace.auckland.ac.nz/bitstream/2292/433/2/02whole.pdf | vauthors = Wardle DA | title = Raman Scattering in Optical Fibres | degree = Doctor of Philosophy in Physics | publisher = The University of Auckland | date = January 1999 | page = 22 }}</ref> but they still have lifetimes derived from [[Uncertainty principle|uncertainty]] relations.<ref name = "Abbi_2001">{{cite book | url = https://books.google.com/books?id=bnuGcAZR14IC&pg=PA139 | title = Nonlinear Optics and Laser Spectroscopy | veditors = Abbi SC, Ahmad SA | publisher = Alpha Science International, Limited | date = 2001 | page = 139 | isbn = 978-81-7319-354-5 }}</ref><ref>{{cite book | vauthors = Norman P, Ruud K | chapter = Microscopic theory of nonlinear optics. | veditors = Papadopoulos MG, Sadlej AJ, Leszczynski J | title = Non-Linear Optical Properties of Matter | date = 2006 | pages = 3 | publisher = Springer | location = Dordrecht | chapter-url =https://books.google.com/books?id=eeE8OrohX3sC&pg=PA3 | isbn = 978-1-4020-4849-4}}</ref> While each virtual state has an associated energy, no direct measurement of its energy is possible<ref>{{cite book | vauthors = Belkic D | chapter = The Dyson Perturbation Expansion of the Evolution Operator | title = Principles of quantum scattering theory | chapter-url = https://books.google.com/books?id=V9YY6Bmg6ngC&pg=PA70&lpg=PA70 | page = 70 | publisher = CRC Press | date = 2004 | isbn = 978-0-7503-0496-2 }}</ref> but various approaches have been used to make some measurements (for example see<ref>{{Cite journal| vauthors = Saleh BE, Jost BM, Fei HB, Teich MC |date = April 1998 |title=Entangled-Photon Virtual-State Spectroscopy|url=http://people.bu.edu/teich/pdfs/PRL-80-3483-1998.pdf|journal=Physical Review Letters|language=en|volume=80|issue=16|pages=3483–3486|doi=10.1103/PhysRevLett.80.3483|issn=0031-9007|via=}}</ref> and related work<ref>{{cite journal|title=Entangled biphoton virtual-state spectroscopy of the A2Σ+–X2Π system of OH| vauthors = Kojima J, Nguyen QV |date=1 October 2004|journal=Chemical Physics Letters|volume=396|issue=4|pages=323–328 |doi=10.1016/j.cplett.2004.08.051}}</ref><ref>{{Cite journal| vauthors = Lee DI, Goodson III T |date=2007|title=Quantum spectroscopy of an organic material utilizing entangled and correlated photon pairs|url=|journal=Linear and Nonlinear Optics of Organic Materials VII|publisher=International Society for Optics and Photonics|volume=6653|pages=66530V|doi=10.1117/12.745492 }}</ref> on virtual state spectroscopy) or extract other parameters using measurement techniques that depend upon the virtual state's lifetime.<ref>{{Cite journal|url=https://www.nature.com/articles/nphys1218|title=Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors| vauthors = Boitier F, Godard A, Rosencher E, Fabre C |date=13 April 2009|journal=Nature Physics|volume=5|issue=4|pages=267–270|via=www.nature.com|doi=10.1038/nphys1218}}</ref> The concept is quite general and can be used to predict and describe experimental results in many areas including [[Raman spectroscopy]],<ref>[https://books.google.com/books?id=ZecrNiUkHToC&pg=PA16&dq=%22virtual+state%22+raman&ei=RqWWSsLsA5-UygSKgZXPBw#v=onepage&q=%22virtual%20state%22%20raman&f=false Peter R. Griffiths, James A. De Haseth Fourier Transform Infrared Spectrometry, Volume 83 second ed, Wiley-Interscience, 2007] {{ISBN|0-470-10629-8}} {{ISBN|978-0-470-10629-7}} page 16</ref> [[non-linear optics]] generally,<ref name = "Abbi_2001" /> various types of [[photochemistry]],<ref>[https://books.google.com/books?id=Ik0bDuWzEHYC&pg=PA118&lpg=PA118&dq=%22virtual+state%22++maria&source=bl&ots=KdFiH2pslc&sig=Hd__eQsXuQVnNLppiHK7-4_clX8&hl=en&ei=hKiWSsnBFNXktgeV5-2-Dg&sa=X&oi=book_result&ct=result&resnum=8#v=onepage&q=%22virtual%20state%22%20%20maria&f=false Douglas C. Neckers, William S. Jenks, Thomas Wolff Advances in Photochemistry, Volume 29 John Wiley and Sons, 2006] {{ISBN|0-471-68240-3}} {{ISBN|978-0-471-68240-0}} page 116</ref> and/or [[Nuclear physics|nuclear]] processes.<ref>{{cite journal | vauthors = Breit G | title = Virtual coulomb excitation in nucleon transfer | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 57 | issue = 4 | pages = 849–55 | date = April 1967 | pmid = 16591541 | pmc = 224623 | doi = 10.1073/pnas.57.4.849 }}</ref>
-{{ISBN|1-4020-4849-1}}, {{ISBN|978-1-4020-4849-4}}</ref> While each virtual state has an associated energy, no direct measurement of its energy is possible<ref>[https://books.google.com/books?id=V9YY6Bmg6ngC&pg=PA70&lpg=PA70&dq=%22the+virtual+state%22+photon++lifetime++uncertainty&source=bl&ots=8RV3UHXecq&sig=wEHEECoLz-_RfZWwWSVvGW1stVw&hl=en&ei=3oqRSrnAEMintgeI5ZDPBA&sa=X&oi=book_result&ct=result&resnum=3#v=onepage&q=%22the%20virtual%20state%22%20photon%20%20lifetime%20%20uncertainty&f=false Dzevad Belkic Principles of quantum scattering theory] page 70 CRC Press, 2004 {{ISBN|0-7503-0496-0}}, {{ISBN|978-0-7503-0496-2}}</ref> but various approaches have been used to make some measurements (for example see<ref>{{Cite journal|last=Saleh|first=Bahaa E. A.|last2=Jost|first2=Bradley M.|last3=Fei|first3=Hong-Bing|last4=Teich|first4=Malvin C.|date=1998-04-20|title=Entangled-Photon Virtual-State Spectroscopy|url=http://people.bu.edu/teich/pdfs/PRL-80-3483-1998.pdf|journal=Physical Review Letters|language=en|volume=80|issue=16|pages=3483–3486|doi=10.1103/PhysRevLett.80.3483|issn=0031-9007|via=}}</ref> and related work<ref>{{Cite journal|title=Entangled biphoton virtual-state spectroscopy of the A2Σ+–X2Π system of OH|first1=Jun|last1=Kojima|first2=Quang-Viet|last2=Nguyen|date=1 October 2004|journal=Chemical Physics Letters|volume=396|issue=4|pages=323–328|via=ScienceDirect|doi=10.1016/j.cplett.2004.08.051}}</ref><ref>{{Cite journal|last=Lee|first=Dong-Ik|last2=Goodson III|first2=Theodore|date=2007|title=Quantum spectroscopy of an organic material utilizing entangled and correlated photon pairs|url=|journal=Linear and Nonlinear Optics of Organic Materials VII|publisher=International Society for Optics and Photonics|volume=6653|pages=66530V|doi=10.1117/12.745492|via=}}</ref> on virtual state spectroscopy) or extract other parameters using measurement techniques that depend upon the virtual state's lifetime.<ref>{{Cite journal|url=https://www.nature.com/articles/nphys1218|title=Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors|first1=F.|last1=Boitier|first2=A.|last2=Godard|first3=E.|last3=Rosencher|first4=C.|last4=Fabre|date=13 April 2009|journal=Nature Physics|volume=5|issue=4|pages=267–270|via=www.nature.com|doi=10.1038/nphys1218}}</ref> The concept is quite general and can be used to predict and describe experimental results in many areas including [[Raman spectroscopy]],<ref>[https://books.google.com/books?id=ZecrNiUkHToC&pg=PA16&dq=%22virtual+state%22+raman&ei=RqWWSsLsA5-UygSKgZXPBw#v=onepage&q=%22virtual%20state%22%20raman&f=false Peter R. Griffiths, James A. De Haseth Fourier Transform Infrared Spectrometry, Volume 83 second ed, Wiley-Interscience, 2007] {{ISBN|0-470-10629-8}} {{ISBN|978-0-470-10629-7}} page 16</ref> [[non-linear optics]] generally,<ref name = "Abbi_2001" /> various types of [[photochemistry]],<ref>[https://books.google.com/books?id=Ik0bDuWzEHYC&pg=PA118&lpg=PA118&dq=%22virtual+state%22++maria&source=bl&ots=KdFiH2pslc&sig=Hd__eQsXuQVnNLppiHK7-4_clX8&hl=en&ei=hKiWSsnBFNXktgeV5-2-Dg&sa=X&oi=book_result&ct=result&resnum=8#v=onepage&q=%22virtual%20state%22%20%20maria&f=false Douglas C. Neckers, William S. Jenks, Thomas Wolff Advances in Photochemistry, Volume 29 John Wiley and Sons, 2006] {{ISBN|0-471-68240-3}} {{ISBN|978-0-471-68240-0}} page 116</ref> and/or [[Nuclear physics|nuclear]] processes.<ref>{{cite journal | vauthors = Breit G | title = Virtual coulomb excitation in nucleon transfer | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 57 | issue = 4 | pages = 849–55 | date = April 1967 | pmid = 16591541 | pmc = 224623 | doi = 10.1073/pnas.57.4.849 }}</ref>
 == See also ==