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).