Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime

TL;DR

This paper develops comprehensive models to accurately describe high-gain frequency conversion and type-II parametric down-conversion, addressing multi-photon and time-dependent effects that are crucial for quantum optics applications.

Contribution

It introduces both a rigorous numerical model and a simplified analytical model for high-gain nonlinear optical processes, improving theoretical understanding and prediction accuracy.

Findings

Simplified model closely matches the rigorous model in many regimes.

Rigorous model predicts decreased FC performance in quantum pulse gates.

Enhanced EPR-state generation rate for high squeezing values above 12 dB.

Abstract

Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein-Podolsky-Rosen-states (EPR-states). FC gives rise to technologies enabling efficient atom-photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered.