Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets

An approximate analytical solution is presented, along with numerical calculations, for a system of two single-photon wave packets interacting via an ideal, localized Kerr medium. It is shown that, because of spontaneous emission into the initially unoccupied temporal modes, the cross-phase-modulati...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2010-04, Vol.81 (4), Article 043823
Main Author: Gea-Banacloche, Julio
Format: Article
Language:English
Subjects:
ABSORPTION
ANALYTICAL SOLUTION
APPROXIMATIONS
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSONS
CALCULATION METHODS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIELECTRIC PROPERTIES
ELECTRICAL PROPERTIES
ELEMENTARY PARTICLES
HAMILTONIANS
KERR EFFECT
MASSLESS PARTICLES
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MODULATION
OPACITY
OPTICAL PROPERTIES
PHASE SHIFT
PHOTONS
PHYSICAL PROPERTIES
PROBABILITY
PULSES
QUANTUM OPERATORS
SCHROEDINGER PICTURE
SORPTION
UNITARITY
WAVE PACKETS
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An approximate analytical solution is presented, along with numerical calculations, for a system of two single-photon wave packets interacting via an ideal, localized Kerr medium. It is shown that, because of spontaneous emission into the initially unoccupied temporal modes, the cross-phase-modulation in the Schroedinger picture is very small as long as the spectral width of the single-photon pulses is well within the medium's bandwidth. In this limit, the Hamiltonian used can be derived from the 'giant Kerr effect' for a four-level atom, under conditions of electromagnetically induced transparency; it is shown explicitly that the linear absorption in this system increases as the pulse's spectral width approaches the medium's transparency bandwidth, and hence, as long as the absorption probability remains small, the maximum cross-phase-modulation is limited to essentially useless values. These results are in agreement with the general, causality-based, and unitarity-based arguments of Shapiro and Razavi [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. H. Shapiro and M. Razavi, New J. Phys. 9, 16 (2007)].
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.81.043823