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Physical Review A

Semiclassical evaluation of the two-photon cross–Kerr effect

Kazuki Koshino

Published Nov 22, 2006• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.74.053818

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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.
In order to discuss the two-photon nonlinearity theoretically, both photons and nonlinear materials should be treated quantum mechanically, which usually is a heavy theoretical task. Contrarily, nonlinear optics for classical light has been developed well and a detailed analysis is possible for realistic complex nonlinear systems. Here we show that the two-photon nonlinearity can be evaluated from the linear and third-order nonlinear output fields against a classical input pulse, which contains 2(-1/2) photons on average.
Abstract In order to analyze the dynamics of single photons, a full‐quantum analysis is indispensable in principle, where both the photon field and the material system are treated quantum‐mechanically. However, the semiclassical optical response theory can be utilized to infer the photon dynamics, bypassing the full‐quantum analyses. This fact is demonstrated for a concrete problem of evaluation of the Kerr effect appearing in two photons. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock-state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock-state or coherent-state inputs. We particularly investigate light transport properties and the Kerr and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized description of the Kerr and cross-Kerr effect for different types of inputs is formulated using the first-order correlation function to compare the Kerr and cross-Kerr nonlinearity between two photons in these models.
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.
Abstract. The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyze the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will degrade the performance of the parity gate proposed by Munro, Nemoto, and Spiller [1].Continuous-time cross-phase modulation and quantum computation 2 1.