Self-modulation of optical pulses in a Kerr medium and limits of the single-mode approximation

Ashat M. Basharov, Andrei I. Maimistov

Ludwig Kunz, Matteo G. A. Paris, Konrad Banaszek

We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon, accompanying the standard unitary Kerr transformation of the optical field, is described with high accuracy as Gaussian phase diffusion with parameters given by closed expressions in terms of the system properties. We show that the irreversibility of the nonlinear phase noise ultimately limits the ability to transmit classical information in the phase variable over a lossy single-mode bosonic channel with Kerr-type nonlinearity. Our model can be also used to estimate the amount of squeezing attainable through self- phase modulation in a Kerr medium with distributed attenuation.

В. В. Козлов, Evald E. Fradkin

Dmitri A. Kouznetsov, Eduardo García Gómez

Any nonlinear interaction, in principle, can produce non-classical state. The Kerr nonlinearity seems to be the simplest one. Since papers [1-3], it seemed that as the squeezed states, as the Schriidinger cat ones can be produced by the self-modulation. The squeezing was really observed [ 3] in such a scheme. As for cats, Ref. {4,5] mention the large distance of propagation and linear absorption as factors which make the experimental realization unlike. Note that neither the large distance of propagation nor the linear absorption are fundamental reasons why the Schrödinger cat cannot be obtained by such a manner.

Naohiro Tanno

Julio R. Gea-Banacloche

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 Schr\"odinger 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)].