Combined effect of spontaneously generated coherence and dynamically induced coherence in a three-level closed Λ system

Abstract

In a three-level closed Λ system with incoherent pumping, both the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role in inducing different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). These two coherences can interfere destructively and constructively giving rise to different nonlinear processes (EIT, EIA, AWI) when the strength of these two coherences is comparable. Therefore the system can switch over from one nonlinear process to the other and the desired response of the system can be achieved by controlling the system parameters. It has been shown that this switching can occur by changing the relative strength of Rabi frequencies for the coherent and probe fields and the mode of incoherent pumping (unidirectional and bidirectional) for a chosen SGC parameter. Further control over the response can be achieved by changing the phase between two radiation fields. But the dependence on phase is different when both the coherences contribute than that obtained only from SGC. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis and any restrictions over the system parameters (e.g. spontaneous decay widths on probe and coherent transitions are equal) have been avoided to make it applicable to various atomic and molecular systems. However the approximate expressions can be derived from these exact values. Numerical values obtained by solving the density matrix equations agreed well with these exact analytical values.

Study of group velocity in the negative refractive index region in three level closedΛsystem via spontaneously generated coherence

“…In Figure 2(b), the variation of Im( r ) with the probe detuning has been shown. It shows the EIT profile which occurs due the destructive interference of absorptions induced by two types of coherences, DIC and SGC [38].…”

“…In our previous work [38,39], we analytically solved the density matrix Equations (1)-(6) in the steady state limit without any approximation, i.e. keeping all the orders of both the probe field and coherent field Rabi frequencies, spontaneous decay rates and incoherent pumping and obtain the exact analytical steady state value of the polarizations 13 and 23 .…”

“…keeping all the orders of both the probe field and coherent field Rabi frequencies, spontaneous decay rates and incoherent pumping and obtain the exact analytical steady state value of the polarizations 13 and 23 . We have shown that EIT arises due to the destructive interference of absorptions induced by SGC and DIC in the presence of incoherent pumping (see Equation (21) of [38]). The first term in the numerator of Equation (21) is proportional to G and the second term is proportional to the product of O and P, with the other parameters remaining the same.…”

“…This is true when the dipole transition moments on the probe and coherent field transitions are orthogonal. However, the situation is completely different when the dipole transition moments from the upper level to two closely lying lower levels are nonorthogonal [38][39][40][41][42][43]. In this case another coherence, i.e.…”

“…When the dipole transition moments are non-orthogonal, both the coherences SGC and DIC act together to determine the probe response and dispersion. Previously [38] we have shown that when the probe field Rabi frequency is comparable to the coherent field Rabi frequency, one can obtain the electromagnetically induced transparency (EIT) in the three-level à system due to the destructive interference of absorptions induced by spontaneously generated coherence (SGC) and dynamically induced coherence (DIC). In another paper, we showed how the control over the susceptibility and the group velocity in a closed three-level à system can be achieved in the presence of SGC and DIC in the positive refractive index region [40].…”