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.

本文描述了在由两个泵浦激光场 (P1, P2) 驱动的四能级 (Δ + ∇) 型闭合轮廓相互作用系统中原子介质对探针场的光学响应的​​理论研究，一个探针激光场 (Pr) 和两个微波或射频 (RF) 耦合场 (L, U)。在这里，L 和U 被认为连接了禁止的电偶极跃迁，即分别是Δ 子系统的两个超精细基态和∇ 子系统的两个超精细激发态。由于每个子系统都是一个闭环系统，因此认为光场（泵场和探测场）与微波或射频场之间存在相对相位。通过耦合场强度和相对相位对系统量子相干性的操纵是根据介质对探测场吸收发生的变化来证明的。通过在稳态条件下对系统的光学布洛赫方程进行数值求解，可以提取探针吸收和色散分布。在这项研究中，我们首先只用探针照射系统，然后通过一个一个地应用泵场和耦合场，研究了两种不同情况下吸收和色散探针线剖面的变化，这取决于泵场的相对强度，例如当 P2 强于 P1 时，反之亦然。此外，耦合场的强度和相位对探针吸收的个体影响，还探讨了这两种情况的透明度和放大问题。由于应用不同场而出现在探测信号中的所有变化都可以通过修改后的相互作用场或从部分穿着状态分析获得的相应有效 Rabi 频率来解释。