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Majorana Representation in Quantum Optics: SU(2) Interferometry and Uncertainty Relations
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.ORCID iD: 0000-0003-3123-0389
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The algebra of SU(2) is ubiquitous in physics, applicable both to the atomic spin states and the polarisation states of light. The method developed by Majorana and Schwinger to represent pure, symmetric spin-states of arbitrary value as a product of spin-1/2 states is a powerful tool that allows for a great conceptual and practical simplification. Foremost, it allows the representation of a qudit on the same geometry as a qubit, i.e., the Bloch sphere.

An experimental implementation of the Majorana representation in the realm of quantum optics is presented. The technique allows the projection of arbitrary quantum states from a coherent state input. It is also shown that the method can be used to synthesise arbitrary interference patterns with unit visibility, and without resorting to quantum resources. In this context, it is argued that neither the shape nor the visibility of the interference pattern is a good measure of quantumness. It is only the measurement scheme that allows for the perceived quantum behaviour.

The Majorana representation also proves useful in delineating uncertainty limits of states with a particular spin value. Issues with traditional uncertainty relations involving the SU(2) operators, such as trivial bounds for certain states and non-invariance, are thereby resolved with the presented pictorial solution.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. , p. 66
Series
TRITA-FYS, ISSN 0280-316X ; 2017:25
Keywords [en]
Majorana representation, Quantum optics, interferometry, SU(2) group, angular momentum, arbitrary optical gates
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-206222ISBN: 978-91-7729-367-5 (print)OAI: oai:DiVA.org:kth-206222DiVA, id: diva2:1091994
Public defence
2017-05-12, FA31, AlbaNova University Center, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20170428

Available from: 2017-04-28 Created: 2017-04-28 Last updated: 2017-04-28Bibliographically approved
List of papers
1. Synthesis of arbitrary, two-mode, high-visibility N-photon interference patterns
Open this publication in new window or tab >>Synthesis of arbitrary, two-mode, high-visibility N-photon interference patterns
2013 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, no 5, p. 053821-Article in journal (Refereed) Published
Abstract [en]

Using coherent states, linear optics, and N-photon detection we demonstrate the synthesis of arbitrary interference patterns and establish that neither the shape nor the visibility of N-photon interference patterns can be used as a quantum signature in general. Specific examples include saw-curve and rectangle-curve interference patterns and phase super-resolution with period shortening of up to 60 times compared to ordinary interference. The former two have visibility close to 100% and the latter has visibility in excess of 57%.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-124042 (URN)10.1103/PhysRevA.87.053821 (DOI)000319113300009 ()2-s2.0-84878047338 (Scopus ID)
Funder
Swedish Research Council, 621-2011-4575
Note

QC 20130627

Available from: 2013-06-27 Created: 2013-06-25 Last updated: 2017-12-06Bibliographically approved
2. Arbitrary interference curves by coincidence detection: Theory and experiment
Open this publication in new window or tab >>Arbitrary interference curves by coincidence detection: Theory and experiment
2013 (English)In: Optical Society of America. Journal A: Optics, Image Science, and Vision, ISSN 1084-7529, E-ISSN 1520-8532, Vol. 30, no 10, p. 1921-1928Article in journal (Refereed) Published
Abstract [en]

We discuss how to use coincidence detection to generate unusual, nonsinusoidal interference curves by using not a single detector, but several in coincidence. The method works for both strong (classical) and weak (on the fewphoton level) light, although in the latter case the detection becomes probabilistic with low efficiency. Using the method, one can tailor the coincidence measurement setup to obtain essentially any interference pattern. We then use the method to experimentally demonstrate phase-difference state interference patterns in the few-photon regime that are highly nonsinusoidal. We also discuss optimal implementation of the method with regard to fluctuations and success probability, and we analyze the origin and magnitude of errors.

National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-133197 (URN)10.1364/JOSAA.30.001921 (DOI)000325214200003 ()2-s2.0-84885332632 (Scopus ID)
Funder
Swedish Research Council, 621-2011-4575
Note

QC 20131028

Available from: 2013-10-28 Created: 2013-10-28 Last updated: 2017-04-28Bibliographically approved
3. Non-monotonic projection probabilities as a function of distinguishability
Open this publication in new window or tab >>Non-monotonic projection probabilities as a function of distinguishability
2014 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, no 1, article id 013006Article in journal (Refereed) Published
Abstract [en]

Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference a non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more photons. We show that such a non-monotonic behavior of projection probabilities is not unnatural, and can also occur for single-photon and even semiclassical states. Thus, while the effect traces its roots from indistinguishability and thus interference, the states for which this can be observed do not need to have particular quantum features.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2014
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-206217 (URN)10.1088/1367-2630/16/1/013006 (DOI)000330574800001 ()2-s2.0-84892740861 (Scopus ID)
Note

QC 20170502

Available from: 2017-04-28 Created: 2017-04-28 Last updated: 2017-11-29Bibliographically approved
4. Reply to comment on ‘non-monotonic projection probabilities as a function of distinguishability’
Open this publication in new window or tab >>Reply to comment on ‘non-monotonic projection probabilities as a function of distinguishability’
2014 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, no 11, article id 118004Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2014
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-206218 (URN)10.1088/1367-2630/16/11/118004 (DOI)000346762500002 ()2-s2.0-84918511905 (Scopus ID)
Note

QC 20170503

Available from: 2017-04-28 Created: 2017-04-28 Last updated: 2017-11-29Bibliographically approved
5. SU(2) uncertainty limits
Open this publication in new window or tab >>SU(2) uncertainty limits
2016 (English)In: PHYSICAL REVIEW A, ISSN 2469-9926, Vol. 93, no 5, article id 052101Article in journal (Refereed) Published
Abstract [en]

Although progress has been made recently in defining nontrivial uncertainty limits for the SU(2) group, a description of the intermediate states bound by these limits remains lacking. In this paper we enumerate possible uncertainty relations for the SU(2) group that involve all three observables and that are, moreover, invariant under SU(2) transformations. We demonstrate that these relations however, even taken as a group, do not provide sharp, saturable bounds. To find sharp bounds, we systematically calculate the variance of the SU(2) operators for all pure states belonging to the N = 2 and N = 3 polarization excitation manifold (corresponding to spin 1 and spin 3/2). Lastly, and perhaps counter to expectation, we note that even pure states can reach the maximum uncertainty limit.

Place, publisher, year, edition, pages
American Psychological Association (APA), 2016
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-188065 (URN)10.1103/PhysRevA.93.052101 (DOI)000375523600001 ()2-s2.0-84964912088 (Scopus ID)
Note

QC 20160627

Available from: 2016-06-27 Created: 2016-06-03 Last updated: 2017-05-03Bibliographically approved

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