Pulse shape effects on photon-photon interactions in non-linear optical quantum gates

TL;DR

This paper investigates how pulse shape influences photon-photon interactions in non-linear optical quantum gates, highlighting the importance of multi-mode effects and proposing a semi-classical approach to analyze the system's dynamics.

Contribution

It introduces a semi-classical method to analyze temporal multi-mode effects on photon interactions, emphasizing the role of pulse shape in non-linear quantum gate performance.

Findings

Significant two photon state transformations can be derived from semi-classical descriptions.

Non-linear effects may transfer photons to orthogonal modes with distinct temporal and spectral features.

Single mode phase shifts might not be the most efficient non-linear effect for quantum gates.

Abstract

Ideally, strong non-linearities could be used to implement quantum gates for photonic qubits by well controlled two photon interactions. However, the dependence of the non-linear interaction on frequency and time makes it difficult to preserve a coherent pulse shape that could justify a single mode model for the time-frequency degree of freedom of the photons. In this paper, we analyze the problem of temporal multi-mode effects by considering the pulse shape of the average output field obtained from a coherent input pulse. It is shown that a significant part of the two photon state transformation can be derived from this semi-classical description of the optical non-linearity. The effect of a non-linear system on a two photon state can then be determined from the density matrix dynamics of the coherently driven system using input-output theory. As an example, the resonant non-linearity of a single two level atom is characterized. The results indicate that the most efficient non-linear effect may not be the widely studied single mode phase shift, but the transfer of one of the photons to an orthogonal mode distinguished by its temporal and spectral properties.