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In this theoretical work, we study the optical behaviour of a microwave driven four-level tripod-type atomic system, configured by Zeeman sub-levels in D1line of 87Rb atom. The non-optical microwave field (L) reasonably assists the optical pumping by a linearly polarized (π) laser field (P1) and a right-handed circularly polarized (σ+) laser field (P2), in presence as well as absence of a static magnetic field (MF). The optical responses of the system to the left-handed circularly polarized (σ−) optical probe laser field (Pr) under three specific P1-P2 strength conditions depict substantial variations in the Doppler-free and Doppler-broadened absorption peaks, accompanied with single EIT or double EIT windows. The origin of Doppler-free Pr absorption peaks are explained by analyzing the resonant poles for the scanning Pr which attribute to the decaying-dressed-states. Perceptible changes of resonant pole positions on the complex planes of the poles w.r.t. the applied MF and L signify that one can externally alter the optical responses of the medium. The related Pr dispersion and its controllability are discussed as well. It is found that the interaction length of the Doppler-free medium has a prominent effect on the Pr absorption and transmission when both MF and L are present in the medium. Furthermore, we have shown the modifications in the Doppler-free Pr absorption profiles in presence of MF and L by considering P2 as an elliptically polarized laser field. Interestingly, Pr absorption turns into Pr gain at suitable polarization rotation angles of the elliptically polarized P2 field for different P1-P2 strength ratios.

This paper describes a theoretical study of the optical responses of an atomic medium to the probe field in a four-level (Δ + ∇)-type closed-contour interaction system driven by two pump laser fields (P1, P2), one probe laser field (Pr) and two microwave or radio frequency (RF) coupling fields (L, U). Here, L and U are considered to connect the forbidden electric dipole transitions, i.e. two hyperfine ground states of the Δ subsystem and two hyperfine excited states of the ∇ subsystem, respectively. Since each subsystem is a closed-loop system, relative phases are thought to be present between the optical fields (pump and probe fields), and the microwave or RF fields. The manipulation of the quantum coherence of the system by the strengths of coupling fields along with the relative phases is demonstrated in terms of the changes occurring in the absorption of the probe field by the medium. The probe absorption and dispersion profiles are extracted by numerically solving the optical Bloch equations for the system under steady-state conditions. In this study, we start by illuminating the system with the probe only, and then, by applying the pump fields and the coupling fields one by one, the changes in the absorptive and dispersive probe line profiles are investigated for two distinct cases that depend on the relative strengths of the pump fields, e.g. when P2 is stronger than P1 and vice versa. Furthermore, the individual effects of the strengths and phases of the coupling fields on the probe absorption, transparency and amplification are also explored for both cases. All the changes that appear in the probe signal as a result of the application of different fields are explained by the modified interaction fields or the corresponding effective Rabi frequencies obtained from the partial dressed-state analysis.