Abstract
We study the absorption spectrum of a probe field by a Λ-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 changing 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.
Highlights
We study the absorption spectrum of a probe field by a Λ-type three-level system, which is coupled to a quantized control field through the two upper energy levels
If the classical control field in such system is replaced by a quantized control field, the so-called vacuum induced transparency (VIT), resulted from the quantum interference has been theoretically and experimentally studied when the quantized control field is in vacuum and the coupling strength between three-level system and quantized control field is in the weak coupling regime28,29
When the quantized control field is in vacuum, we first derive a threshold condition to discern VIT from vacuum induced Autler-Townes splitting (ATS), we further analyze how VIT is changed to vacuum induced ATS when the decay rate of the cavity field or the coupling strength between the quantized control field and three-level system is varied
Summary
We find that the absorption spectrum of the probe field in coherent pumping is very similar to that of the incoherent pumping when the coupling strength between the three-level system and the quantized control field is in the parameter regime of VIT. If the coupling strength between the three-level system and the quantized control field is in the parameter regime of vacuum induced ATS, as shown in Fig. 8(b) for the strong pumping case (the green dotted curve), we have photon number resolved spectrum. Such difference between the coherent and incoherent pumping is due to the statistical distributions for coherent and thermal states
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