# Spectral shaping of the biphoton state from multiplexed thermal atomic ensembles

## TL;DR

This paper presents a theoretical method to spectrally shape biphoton states from multiplexed thermal atomic ensembles, enhancing entanglement and spectral mode capacity for quantum communication applications.

## Contribution

It introduces a multiplexing scheme that increases spectral entanglement and mode capacity of biphoton states generated via four-wave mixing in thermal atomic ensembles.

## Key findings

- Spectral entanglement increases with more multiplexed vapor cells.
- Eigenvalues in Schmidt bases approach degeneracy, indicating higher mode capacity.
- The scheme can produce low-entanglement states suitable for pure single-photon sources.

## Abstract

We theoretically investigate the spectral property of a biphoton state from multiplexed thermal atomic ensembles. This biphoton state originates from the cascade emissions, which can be generated by two weak pump fields under four-wave mixing condition. Under this condition, a signal photon from the upper transition, chosen in a telecommunication bandwidth, can be generated along with a correlated idler photon from the lower infrared transition. We can spectrally shape the biphoton state by multiplexing the atomic ensembles with frequency-shifted emissions, where the entropy of entanglement can be analyzed via Schmidt decompositions. We find that this spectral entanglement increases when more vapor cells are multiplexed with correlated or anti-correlated signal and idler fields. The eigenvalues in Schmidt bases approach degenerate under this multiplexing scheme, and corresponding Schmidt numbers can be larger than the number of the multiplexed vapor cells, showing the enlarged entropy of entanglement and excess correlated modes in continuous frequency spaces. We also investigate the lowest entropy of entanglement allowed in the multiplexing scheme, which is preferential for generating a pure single photon source. This shows the potentiality to spectrally shape the biphoton source, where high-capacity spectral modes can be applied in long-distance quantum communication and multimode quantum information processing.