Phase-dependent gain without inversion in an inhomogeneous broadened quasi Λ-type four-level system with VIC

Abstract

The effect of the relative phase (φ) between the probe and driving fields on the gain without inversion (GWI) is studied in a Doppler broadened quasi ∧-type four-level atomic system with vacuum induced coherence (VIC). It is shown that: The probe detuning region in which GWI exists and size of GWI are very sensitive to variation of the relative phase, the Doppler width ( D ) also has dramatically modulation role on the phase-dependent GWI. The GWI maximum value (G max ) varies periodically with the relative phase varying, the period is 2π; but the concrete varying rule is closely related to the value of the Doppler width. In the case of D = 0 (i.e. without Doppler broadening), when 0 < φ < π, G max increases monotonously with φ increasing; when π < φ < 2π, G max decreases monotonously with φ increasing; when φ = π, G max has the largest value. Under the condition of D ≠ 0 (i.e. Doppler broadening presents), in both regions 0 < φ < π and π < φ < 2π, G max does not monotonically increase or decrease with φ increasing; the value of φ, which corresponds to the largest value of G max , decreases gradually from π with D increasing, when value of D is large enough, the value of φ, which corresponds to the largest value of G max , is about π / 2 . In general speaking, G max decreases with D increasing; but G max larger than that in the corresponding static atomic system ( D = 0 ) can be gotten by choosing suitable values of φ and D.