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The Forgotten Quantum Number: The Radial Modes of Laguerre-Gauss Beams

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

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The Forgotten Quantum Number: The Radial Modes of Laguerre-Gauss Beams

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  1. The Forgotten Quantum Number: The Radial Modes of Laguerre-Gauss Beams William Plick, PhD IQOQI Vienna APS March Meeting, March 7th, 2014

  2. Laguerre-Gauss Modes

  3. Orbital Angular Momentum 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) L. Marrucci, C. Manzo, and D. Paparo Phys. Rev. Lett. 96, 163905 (2006)

  4. The “Forgotten” Quantum Number • A Google Scholar search for “orbital angular momentum of light” yielded about 1,560 results a couple weeksago. • 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.

  5. Operator Formalism • Mathematically we can find that: • 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? Plick et al.arXiv:1306.6517 (2013). Karimi, and Santamato Opt. Lett. 37, 2484 (2012).

  6. 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).

  7. Acknowledgements Mario Krenn Sven Ramelow Anton Zeilinger ERC Advanced Grant: QIT4QAD

  8. Thank you! Plicket al. arXiv:1306.6517 (2013).

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