the forgotten quantum number: the radial modes of laguerre-gauss beams
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The Forgotten Quantum Number: The Radial Modes of Laguerre-Gauss Beams . William Plick , PhD IQOQI Vienna. APS March Meeting, March 7 th , 2014 . Laguerre-Gauss Modes. Orbital Angular Momentum. Applications: Access to higher dimensional Hilbert Spaces Tests of Quantum Foundations - PowerPoint PPT PresentationTRANSCRIPT
The Forgotten Quantum Number: The Radial Modes of Laguerre-Gauss
Beams
William Plick, PhDIQOQI Vienna
APS March Meeting, March 7th, 2014
Laguerre-Gauss Modes
Orbital Angular Momentum
L. Marrucci, C. Manzo, and D. PaparoPhys. Rev. Lett. 96, 163905 (2006)
Applications: Access to higher dimensional Hilbert Spaces
Tests of Quantum Foundations
Higher Alphabet QKD
Doing physical work (micromechanical systems, trapping, etc)
L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, Phys. Rev. A 45, 8185 (1992) G.F. Calvo, A. Picon, and E. Bagan; Phys. Rev. A, 73, 013805 (2006)
The “Forgotten” Quantum Number
• A Google Scholar search for “orbital angular momentum of light” yielded about 1,560 results a couple weeks ago.
• I only know of 5 or 6 papers that address, directly, the OTHER quantum number of LG beams, the so-called “radial index”.
• All of these are just from the past couple years.
• The radial number is usually considered to be unwanted noise.
Operator Formalism
• But what IS this quantum number?
• Does it relate to a physical observable?
• Does it have a conjugate variable?
• Is it really even a quantum number?
• Mathematically we can find that:
Plick et al. arXiv:1306.6517 (2013).Karimi, and Santamato Opt. Lett. 37, 2484 (2012).
The “Forgotten” Quantum Number (3)
• But what IS this quantum number?
• Does it relate to a physical observable?
• Does it have a conjugate variable?
• Is it really even a quantum number?
???????????????
Probably: Her., Terms “Familiar”
Oh God! Don’t ask!
YES! Karimi et al. Phys. Rev. A 89, 013829 (2014).
Acknowledgements
Mario
Krenn
Anton Zeilinger
Sven Ramelow
ADVANCEDGRANT: QIT4QADERC
Thank you!
Plick et al. arXiv:1306.6517 (2013).