Quantum Entanglement in Electron Optics: Generation, Characterization, and Applications PDF
Preview Quantum Entanglement in Electron Optics: Generation, Characterization, and Applications
Springer Series on Atomic, Optical and Plasma Physics 67 N. Chandra R. Ghosh Quantum Entanglement in Electron Optics Generation, Characterization, and Applications SpringerSerieson atomic, optical, and plasma physics 67 Editor-in-Chief: G.W.F. Drake Department of Physics U niversity of Windsor 401 Sunset, Windsor N9B3P4 Ontario Canada Editorial Board: U we Becker, Fritz-Haber-Institut, Berlin, Germany Philip George Burke, Q ueen’ s U niversity, Belfast, Ireland Robert N Compton, Oak Ridge National Laboratory, Oak Ridge, U SA M.R. Flannery, Georgia Institute of Technology, Atlanta, U SA Charles J. Joachain, U niversite´Libre Bruxelles, Bruxellas, Belgium B.R. Judd, The Johns Hopkins U niversity, Baltimore, U SA Peter Lambropoulos, Foundation of Research and Technology-Hellas (F.O.R.T.H.), Heraklion, Greece Gerd Leuchs, Friedrich-Alexander-U niversitä t Erlangen-Nürnberg, Erlangen, Germany Pierre Meystre, The U niversity of Arizona, Tuscon, U SA SpringerSerieson atomic, optical, and plasma physics TheSpringerSeriesonAtomic,Optical,andPlasmaPhysicscoversinacompre- hensivemannertheoryandexperimentintheentirefieldofatomsandmolecules andtheirinteractionwithelectromagneticradiation.Booksintheseriesprovide arichsourceofnewideasandtechniqueswithwideapplicationsinfieldssuchas chemistry,materialsscience,astrophysics,surfacescience,plasmatechnology,ad- vancedoptics,aeronomy,andengineering.Laserphysicsisaparticularconnecting themethathasprovidedmuchofthecontinuingimpetusfornewdevelopments inthefield.Thepurposeoftheseriesistocoverthegapbetweenstandardunder- graduatetextbooksandtheresearchliteraturewithemphasisonthefundamental ideas,methods,techniques,andresultsinthefield. PleaseviewavailabletitlesinSpringerSeriesonAtomic,Optical,andPlasmaPhysics onserieshomepagehttp://www.springer.com/series/411 N. Chandra R. Ghosh Quantum Entanglement in Electron Optics Generation, Characterization, and Applications With 23 Figures 123 N.Chandra IndianInstituteofTechnology Department of PhysicsandMeteorology Kharagpur 721302 , West Bengal India [email protected] R.Ghosh c/o B.N.Panda 1/A--46(H.I.G.),Lingraj Vihar P okhariput 751020 , Orissa India [email protected] Additional material to this book can be downloaded from http://extra.springer.com Password: 978-3-642-24069-0 SpringerSeriesonAtomic,Optical,andPlasmaPhysics ISSN1615-5653 ISBN978-3-642-24069-0 ISBN978-3-642-24070-6 (eBook) DOI10.1007/978-3-642-24070-6 SpringerHeidelberg New York Dordrecht London LibraryofCongressControlNumber: 2012944986 © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. 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Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) “An expertis aperson who hasmadeeverypossiblemistake at leastonce.” AlbertEinstein 14March 1879 -18April1955 Thisbookisdedicatedto allthosepatient peoplewho taughtushowto read,write, think,anddo scientificresearch. Foreword Quantum entanglementis one of the most intriguing phenomenain nature. In the wordsofAlbertEinstein,itisa”spookylongdistanceinteraction”.Inessence,itis theeffectoftheinstantaneousinteractionbetweentwoquantumobjectswhentheir properties are described by quantum variables. The possible eigenvalues of these variables are for a single object completely random. Their actual values become determined by a corresponding measurement of the particular variable only. For the case of an entangled pair of two quantum objects, however, the eigenvalue of a particular variable of the second object will be completely determined by the result of the measurement performed on the first object, although the values associated with the second object are completely random, if its properties are measured independently, which means not in coincidence with the measurement ofthefirstone.Thisistheresultofthejointwavefunctionofanentangledpairof quantumobjectspossessingjointquantumvariables.Moreover,eventheselection oftheparticularquantumvariablebythemeasurementonthefirstobjectdetermines thevariableandtheireigenvaluesofthesecondobject.Thisisevenincontradiction with the laws of quantummechanics themselves, because the selected variable of the ”spooky long distance interaction” does not exist in quantum mechanics - or moreprecisely-accordingtoHeisenberg’suncertaintyprinciple.Thisisthereason that Albert Einstein argued in the famous Einstein, Podolsky and Rosen (EPR) paper that the variable must have an existence before its measurement which is determined by so-called hidden variables. This is the basis of the longstanding discussionbetweentheexponentsof”pure”quantummechanicsandtheexponents of the so-called localrealistic theorieswith hiddenvariables.The outcomeof this dispute is known. All measurements probing Bell’s inequality, a quantitative way of distinguishing between the two theories, have shown that quantum mechanics is right. One of the major problems in probing the validity of Bell’s inequality was the variable to be chosen. EPR suggested in their Gedankenexperiment that the position in ordinaryspace be taken. This is, however,even nowadaysstill not feasible.Bohmsuggestedthespin ofthe electron,butdueto thefactthatthespin oftheelectroncannotbeprobedbyaStern-Gerlachexperiment,thissuggestionhas alsoneverbeenrealized.Instead,thepolarizationpropertiesofthephoton,whichare ix
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