Vacuum induced transparency and photon number resolved Autler-Townes splitting in a three-level system

TL;DR

This paper investigates how a three-level quantum system exhibits vacuum-induced transparency and Autler-Townes splitting, revealing photon number resolution effects and drawing parallels to PT symmetry transitions.

Contribution

It introduces a threshold condition to distinguish VIT and vacuum-induced ATS and explores photon number resolved spectra in a three-level system with a quantized control field.

Findings

VIT occurs at zero photons, ATS appears with finite photon numbers

Photon number resolved spectrum is observed only in ATS regime

Parameter change from VIT to ATS resembles PT symmetry transition

Abstract

We study the absorption spectrum of a probe field by a {\Lambda}-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler- Townes splitting (ATS). We also find that the parameter change from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization.