Physics – Mathematical Physics
Scientific paper
2008-10-04
J. Math. Phys. 50, 023501 (2009)
Physics
Mathematical Physics
30 pages, 3 figures. Small corrections, mostly in Section V. To appear in the Journal of Mathematical Physics
Scientific paper
10.1063/1.3072670
Gabriel F. Calvo and Antonio Picon defined a class of operators, for use in quantum communication, that allows arbitrary manipulations of the three lowest two-dimensional Hermite-Gaussian modes {|0,0>,|1,0>,|0,1>}. Our paper continues the study of those operators, and our results fall into two categories. For one, we show that the generators of the operators have infinite deficiency indices, and we explicitly describe all self-adjoint realizations. And secondly we investigate semiclassical approximations of the propagators. The basic method is to start from a semiclassical Fourier integral operator ansatz and then construct approximate solutions of the corresponding evolution equations. In doing so, we give a complete description of the Hamilton flow, which in most cases is given by elliptic functions. We find that the semiclassical approximation behaves well when acting on sufficiently localized initial conditions, for example, finite sums of semiclassical Hermite-Gaussian modes, since near the origin the Hamilton trajectories trace out the bounded components of elliptic curves.
No associations
LandOfFree
Manipulation of Semiclassical Photon States does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Manipulation of Semiclassical Photon States, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Manipulation of Semiclassical Photon States will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-541819