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Physical Review A

Effects of spontaneously generated coherence on the pump-probe response of a Λ system

Sunish Menon, G. S. Agarwal

Published May 1, 1998• 219 citations
Publisher

Abstract

Near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.

DOI
10.1103/physreva.57.4014

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Near-degenerate lower levels in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.
Due to interaction with the vacuum of the radiation field, near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term, the spontaneously generated coherence term. In this paper, we investigate effects of spontaneouly generated coherence on inversionless gain in the presence of a weak probe, a strong coherent field, and an incoherent pump. We find that the inversionless gain stems from both spontaneously generated coherence and dynamically induced coherence, but the former contributes more to the inversionless gain. In particular, we can modulate the inversionless gain just by changing the relative phase between the two fields.
Due to interaction with the vacuum of the radiation field, near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term, the spontaneously generated coherence term. In this paper, we investigate the effects of this kind of coherence on the transient process in the presence of a weak probe and a strong coherent field, with or without an incoherent pump. We find that the transient gain (absorption) properties can be dramatically affected by the spontaneously generated coherence. The transient gain can be greatly enhanced due to the effect of spontaneously generated coherence, and the transient absorption can be completely eliminated just by choosing the proper relative phase between the two fields.
Phase Dependence of the Inversionless Gain in a Λ\LambdaΛ System with Near-Degenerate Levels
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.
We present an analysis of coherent population trapping in a three-level Λ system when excited by an ultrashort pulse train near the one- and two-photon resonances. Numerical results using Bloch equations give the transient response of the system and clearly reveal a comb of electromagnetically induced transparency (EIT) lines. An analytical solution to describe the EIT lines is derived in the steady-state regime and in the weak field limit. Moreover, numerical results indicate that selective velocity spectroscopy makes possible the observation of the comb of EIT lines in Doppler broadening media.