Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: 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 potential
of OAM entanglement of photons by controlling the parameters in both the generation
and measurement systems. We show the experimental procedures and apparatus involved
in generating and measuring entangled photons in two-dimensions. We verify important
quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle
correlations, as well as a violation of a Bell-type inequality. By performing a full state
tomography, we characterise our quantum state and show we have a pure, highly entangled
quantum state. We demonstrate that this method can be extended to higher dimensions. 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
which to increase the spiral bandwidth of our generated quantum state. We alter the shape
of the pump beam in spontaneous parametric down-conversion and demonstrate an effect 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 entanglement
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
demonstrate that BG modes can be entangled in higher dimensions compared with the commonly
used helical modes by calculating and comparing the linear entropy and fidelity 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
on OAM entanglement measured in the BG basis. We investigate the self-healing property
of BG beams and show that the classical property is translated to the quantum regime. By
calculating the concurrence, we see that measured entanglement recovers after encountering
an obstruction. / AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton.
Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum
kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse
van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in
die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die
potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering
en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke
is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons
verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en
die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n
volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n
suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei
kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet
van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse.
Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane
parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die
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 gemeetde
spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van
die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër
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 kwantumverstrengling
akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie,
wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies
in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek
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),
sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/95868 |
| Date | 12 1900 |
| Creators | McLaren, Melanie |
| Contributors | Forbes, Andrew, Rohwer, Erich G., Roux, Filippus Stefanus, Stellenbosch University. Faculty of Science. Dept. of Physics. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Rights | Stellenbosch University |
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