Tailoring Quantum Entanglement of Orbital Angular Momentum

136 Pages·2014·6.82 MB·English

Tailoring Quantum Entanglement of Orbital Angular
Momentum
by
Melanie McLaren
DissertationpresentedforthedegreeofDoctorofScienceinPhysicsinthe
FacultyofPhysicsatStellenboschUniversity
DepartmentofLaserPhysics,
UniversityofStellenbosch,
PrivateBagX1,Matieland7602,SouthAfrica.
Promoter:Prof.A.Forbes,Dr.F.S.Roux,Prof.E.Rohwer
December2014
Stellenbosch University http://scholar.sun.ac.za
Stellenbosch University http://scholar.sun.ac.za
Declaration
By submitting this dissertation electronically, I declare that the entirety of the work con-
tainedthereinismyown,originalwork,thatIamthesoleauthorthereof(savetotheextent
explicitlyotherwisestated),thatreproductionandpublicationthereofbyStellenboschUni-
versity will not infringe any third party rights and that I have not previously in its entirety
orinpartsubmitteditforobtaininganyqualification.
Signature: ...............................
M.McLaren
2014/03/20
Date: ...................................
Copyright©2014StellenboschUniversity
Allrightsreserved.
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Stellenbosch University http://scholar.sun.ac.za
Abstract
TailoringQuantumEntanglementofOrbitalAngularMomentum
M.McLaren
DepartmentofLaserPhysics,
UniversityofStellenbosch,
PrivateBagX1,Matieland7602,SouthAfrica.
Dissertation: PhDPhys
December2014
High-dimensional quantum entanglement offers an increase in information capacity per
photon; a highly desirable property for quantum information processes such as quantum
communication, computation and teleportation. As the orbital angular momentum (OAM)
modes of light span an infinite-dimensional Hilbert space, they have become frontrunners
in achieving entanglement in higher dimensions. In light of this, we investigate the poten-
tialofOAMentanglementofphotonsbycontrollingtheparametersinboththegeneration
and measurement systems. We show the experimental procedures and apparatus involved
in generating and measuring entangled photons in two-dimensions. We verify important
quantumtestssuchastheEinstein,PodolskyandRosen(EPR)paradoxusingOAMandan-
gle correlations, as wellas aviolation ofa Bell-type inequality. By performinga fullstate
tomography,wecharacteriseourquantumstateandshowwehaveapure,highlyentangled
quantumstate. Wedemonstratethatthismethodcanbeextendedtohigherdimensions. The
experimental techniques used to generate and measure OAM entanglement place an upper
bound on the number of accessible OAM modes. As such, we investigate new methods in
whichtoincrease thespiralbandwidthofour generatedquantumstate. Wealtertheshape
of the pump beam in spontaneous parametric down-conversion and demonstrate an effect
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vi ABSTRACT
on both OAM and angle correlations. We also made changes to the measurement scheme
by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate en-
tanglement in this basis. We show that this method allows the measured spiral bandwidth
to be optimised by simply varying the continuous radial parameter of the BG modes. We
demonstratethatBGmodescanbeentangledinhigherdimensionscomparedwiththecom-
monly usedhelical modes by calculating and comparing thelinear entropy andfidelity for
both modes. We also show that quantum entanglement can be accurately simulated using
classical light using back-projection, which allows the study of projective measurements
and predicts the strength of the coincidence correlations in an entanglement experiment.
Finally, we make use of each of the techniques to demonstrate the effect of a perturbation
onOAMentanglementmeasuredintheBGbasis. Weinvestigatetheself-healingproperty
of BG beams and show that the classical property is translated to the quantum regime. By
calculatingtheconcurrence,weseethatmeasuredentanglementrecoversafterencountering
anobstruction.
Stellenbosch University http://scholar.sun.ac.za
Uittreksel
Kwantumverwikkelingvanorbitalehoekmomentum
(“TailoringQuantumEntanglementofOrbitalAngularMomentum”)
M.McLaren
Departementvanlaserfisika,
UniversiteitvanStellenbosch,
PrivaatsakX1,Matieland7602,SuidAfrika.
Proefskrif: (PhDPhys)
Desember2014
Hoë-dimensionelekwantumverstrengeldheidbied’ntoenameininligtingskapasiteitperfo-
ton. Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum
kommunikasie,berekeningenteleportasie. Omdatdieorbitalehoekmomentum(OAM)mo-
dussevanlig’noneindigdimensioneleHilbertruimtebeslaan,hetditvoorlopersgewordin
die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die
potensiaalvanOAMverstrengelingvanfotonedeurdieparametersinbeidediegenerering
en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat be-
trokke is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons
verifieerkwantumtoetse,soosdieEinstein,PodolskyenRosen(EPR)paradoksvirOAMen
diehoekkorrelasies,sowelas’nskendingvan’nBell-tipeongelykheid. Deurmiddelvan’n
volledigetoestandtomografie,karakteriseeronsdiekwantumtoestandenwysonsdatdit’n
suiwer,hoogsverstrengelkwantumtoestandis. Onstoonookdathierdiemetodeuitgebrei
kanwordnahoërdimensies. Dieeksperimenteletegniekewattydensdiegenerasieenmeet
van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM mo-
dusse. Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde
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viii UITTREKSEL
kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane
parametrieseaf-omskakelingendemonstreerdieuitwerkingdaarvanopbeideOAMendie
hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton
pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die ge-
meetdespiraalbandwydtekanoptimeerdeureenvoudigdiekontinueradialeparametervan
dieBGmodesteverander. OnsdemonstreerdatBGmodusseverstrengelkanwordinhoër
dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak
en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumver-
strengling akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie,
watdiestudievanprojeksiemetingstoelaatenvoorspeldiekragvandiesaamvalkorrelasies
in’nverstrengelingeksperiment. Tenslotte,gebruikonselkvandietegniekeomdieeffek
van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons
ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap
vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence),
sienonsdatdiegemeetdeverstrengelingherstelwordnadat’nobstruksieondervindis.
Stellenbosch University http://scholar.sun.ac.za
Acknowledgements
I would like to express my gratitude to everyone who provided support throughout the
courseofmyPhDwork. Specifically,Iwouldliketothankthefollowingpeople:
My supervisors, Prof. Andrew Forbes and Dr. Stef Roux, thank you for all the guid-
ance and support during my PhD. In particular, I am grateful to Andrew for the detailed
discussions and planning of each aspect of my PhD work. I have gained not only valu-
able experimental techniques, but have also learnt the art to expressing one’s work to the
internationalcommunity,bothinjournalsandatconferences.
IamalsogratefultotheCSIRNationalLaserCentreforprovidingmewithopportuni-
tiestoconductthisresearchwithinourownlabsaswellasthoseofourcollaboratorsaround
theworld.
These collaborators include Prof. Miles Padgett from the University of Glasgow, who
has offered a great deal of support by allowing me to visit his labs to work together with
himandhisstudents,Dr. JacquiRomeroandDanieleGiovannini. BothJacquiandDaniele
havebecomegreatfriends,whomIhopetocontinuetoworkwithinthefuture. Iwasalso
fortunate to visit the University of Ottawa and work within Prof. Robert Boyd’s group,
which at the time was coordinated by Dr. Jonathan Leach. Much of my experimental
knowledgewasgainedfromJonathanonmyfirstvisit. However, itwasduringmysecond
visit, working with Megan Agnew, Xinru Cheng, Eliot Bolduc and Jonathan, that I really
learnttoenjoymyPhDandforthatIamtrulygrateful.
While at the NLC, there were two individuals, Angela (the Doc) and Darryl, who pro-
vided a great deal of support both in and out of the lab. Experimental work is not without
itsfrustrations,butthankstoAngeandDarryl,Imanagedtomaintainmysanityandcome
outthebetterforit. IlookforwardtoseeingyournamesinForbestop100.
Lastly,I’dliketothankmyfamilyandfriendsforsupportingmethroughouttheseyears.
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x ACKNOWLEDGEMENTS
I am grateful to my Dad for enthusiastically supporting my pursuit of this degree, I know
ithasbeendifficultattimes,buthopefullyitwasallworthit. Marko,whohasputupwith
this journey from the beginning and I am incredibly thankful for all our discussions about
work,familyandthefuture,whichkeptmemotivatedthroughout.