Physical meaning of the radial index of Laguerre-Gauss beams

The Laguerre-Gauss modes are a class of fundamental and well-studied optical fields. These stable, shape-invariant photons - exhibiting circular-cylindrical symmetry - are familiar from laser optics, micro-mechanical manipulation, quantum optics, communication, and foundational studies in both classical optics and quantum physics. They are characterized, chiefly, by two modes numbers: the azimuthal index indicating the orbital angular momentum of the beam - which itself has spawned a burgeoning and vibrant sub-field - and the radial index, which up until recently, has largely been ignored. In this manuscript we develop a differential operator formalism for dealing with the radial modes in both the position and momentum representations, and - more importantly - give for the first time the meaning of this quantum number in terms of a well-defined physical parameter: the "intrinsic hyperbolic momentum charge".Comment: 12 pages, 4 figures, comments encourage

Quantum orbital angular momentum of elliptically-symmetric light

We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields --- the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity and discover several compelling features, including: non-monotonic behavior, stable beams with real continuous (non-integer) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may have application to quantum key distribution, atom trapping, and quantum informatics in general --- as the ellipticity opens up a new way of navigating the photonic Hilbert space.Comment: 9 Pages, 4 Figures, Comments Welcom

L00L and p00p entanglement

We demonstrate the generation of unbalanced two-photon entanglement in the Laguerre-Gaussian (LG) transverse-spatial degree-of-freedom, where one photon carries a fundamental (Gauss) mode and the other a higher-order LG mode with a non-zero azimuthal ($\ell$) or radial ($p$) component. Taking a cue from the $N00N$ state nomenclature, we call these types of states $LOOL$ (L00L) or $p00p$-entangled. They are generated by shifting one photon in the LG mode space and combining it with a second (initially uncorrelated) photon at a beamsplitter, followed by coincidence detection. In order to verify two-photon coherence, we demonstrate a two-photon ``twisted'' quantum eraser, where Hong-Ou-Mandel interference is recovered between two distinguishable photons by projecting them into a rotated LG superposition basis. Using an entanglement witness, we find that our generated $LOOL$ and $p00p$ states have fidelities of 95.31\% and 89.80\% to their respective ideal maximally entangled states. Besides being of fundamental interest, this type of entanglement will likely have a significant impact on tickling the average quantum physicist's funny bone.Comment: Written for submission to the AVS Quantum Science special issue in memory of Jon Dowlin

Quantum metrology with two-mode squeezed vacuum: Parity detection beats the heisenberg limit

We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (n̄ photons on average). We show that superresolution and sub-Heisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves n̄ times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/n̄, and we saturate the quantum Cramer-Rao bound. © 2010 The American Physical Society