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Physical Review A

Multiphoton wave function after Kerr interaction

Kazuki Koshino

Published Aug 12, 2008• 5 citations
Publisher

Abstract

The multiphoton wave function after Kerr interaction is obtained analytically for an arbitrary photon number. The wave function is composed of two fundamental functions: the input mode function and the linear response function. The nonlinear effects appearing in this wave function are evaluated quantitatively, revealing the limitations of nonlinear quantum optics theories based on single-mode approximations.

DOI
10.1103/physreva.78.023820

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The multiphoton wave function after Kerr interaction is obtained analytically for an arbitrary photon number. The wave function is composed of two fundamental functions: the input mode function and the linear response function. The nonlinear effects appearing in this wave function are evaluated quantitatively, revealing the limitations of nonlinear quantum optics theories based on single-mode approximations.
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When two distinguishable photons are simultaneously input into a nonlinear system, the output photons undergo nonlinear optical effects of the cross--Kerr type. Theoretical quantification of this two-photon cross--Kerr effect requires, in principle, a fully quantum-mechanical analysis involving heavy computation. In this paper, we propose a method for evaluating the two-photon cross--Kerr effect using a semiclassical optical response theory. The semiclassical method enables precise evaluation of the cross--Kerr effect with greatly reduced computation. The validity of the method is confirmed using a model nonlinear system.
Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.
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The self-Kerr interaction is an optical nonlinearity that produces a phase shift proportional to the square of the number of photons in the field. At present, many proposals use nonlinearities to generate photon-photon interactions. For propagating fields these interactions result in undesirable features such as spectral correlation between the photons. Here we engineer a discrete network composed of cross-Kerr interaction regions to simulate a self-Kerr medium. The medium has effective long-range interactions implemented in a physically local way. We compute the one- and two-photon SSS matrices for fields propagating in this medium. From these scattering matrices we show that our proposal leads to a high-fidelity photon-photon gate. In the limit where the number of nodes in the network tends to infinity, the medium approximates a perfect self-Kerr interaction in the one- and two-photon regime.