Propagation of small fluctuations in electromagnetically induced transparency. Influence of Doppler width

TL;DR

This paper investigates how small quantum fluctuations and noise properties of light are affected during propagation through an EIT medium, highlighting the effects of atomic detuning and Doppler broadening on quantum noise and correlations.

Contribution

It provides a detailed analysis of quantum noise propagation in EIT media, including the impact of atomic detuning and Doppler width on squeezing and noise correlations.

Findings

Oscillatory exchange of noise between probe and pump fields.

Propagation sensitivity to atomic detuning δ.

Significant influence of Doppler width on squeezed state propagation.

Abstract

The propagation of a pair of quantized fields inside a medium of three-level atoms in $\Lambda$ configuration is analyzed. We calculate the stationary quadrature noise spectrum of the field after propagating through the medium in the case where the field has a general (but small) noise spectrum and the atoms are in a coherent population trapping state and show electromagnetically induced transparency (EIT). Although the mean values of the field remain unaltered as the field propagates, there is an oscillatory interchange of noise properties between the probe and pump fields. Also, as the field propagates, there is an oscillatory creation and annihilation of correlations between the probe and pump quadratures. We further study the field propagation of squeezed states when there is two-photon resonance, but the field has a detuning $\delta$ from atomic resonance. We show that the field propagation is very sensitive to $\delta$. The propagation in this case can be explained as a combination of a frequency dependent rotation of maximum squeezed quadrature with an interchange of noise properties between pump and probe fields. It is also shown that the effect of the Doppler width in a squeezed state propagation is considerable.