20 research outputs found
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 () or radial () component. Taking a cue from the
state nomenclature, we call these types of states (L00L) or
-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 and 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