Narrowband biphoton generation in the group delay regime

TL;DR

This paper investigates narrow-band biphoton generation via four-wave mixing in cold atoms, comparing theoretical models, and shows how laser beam profiles influence the biphoton waveform, enabling potential waveform shaping.

Contribution

It extends theoretical formalisms to account for atomic density and laser field non-uniformities, revealing how laser spatial profiles affect biphoton temporal waveforms.

Findings

Two formalisms agree at low gain but differ at high gain.

Biphoton waveform is independent of atomic density distribution.

Laser beam spatial profiles significantly influence the biphoton temporal waveform.

Abstract

We study narrow-band biphoton generation from spontaneous four-wave mixing with electromagnetically induced transparency in a laser cooled atomic ensemble. We compare two formalisms in the interaction and Heisenberg pictures, and find that they agree in the low gain regime but disagree in the high gain regime. We extend both formalisms accounting the non-uniformity in atomic density and the driving laser fields. We find that for a fixed optical depth and a weak and far-detuned pump laser beam, the two-photon waveform is independent of the atomic density distribution. However, the spatial profiles of the two driving laser beams have significant effects on the biphoton temporal waveform. We predict that waveform shaping in time domain can be achieved by controlling the spatial profiles of the driving laser fields.