Cross-Kerr nonlinearity between continuous-mode coherent states and single photons

TL;DR

This paper develops a comprehensive theory for the interaction between continuous-mode photonic pulses, specifically a single photon and a coherent state, analyzing the validity of the single-mode approximation in quantum information applications.

Contribution

It introduces a general framework for continuous-mode interactions and evaluates the accuracy of the single-mode approximation using fidelity and conditional phase metrics.

Findings

High fidelities and non-zero conditional phases are achievable with high photon numbers.

The single-mode approximation is valid when pulses fully pass through each other and transverse-mode effects are minimized.

The theory provides insights into optimizing cross-Kerr nonlinearities for quantum information processing.

Abstract

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, non-zero 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.