# Transfer of temporal coherence in parametric down-conversion

## TL;DR

This paper demonstrates that the temporal coherence of a partially coherent pump field in parametric down-conversion is fully transferred to the entangled photon pairs, impacting quantum communication applications.

## Contribution

It provides a theoretical framework for understanding how pump coherence properties influence the entanglement and coherence of down-converted photon pairs.

## Key findings

- Coherence functions factorize into pump and signal-idler components.
- Explicit expressions derived for Gaussian Schell-model pump fields.
- Concurrence of entangled states bounded by pump coherence.

## Abstract

We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency-bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely-fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.