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Chinese Physics Letters

Nonlinear Theory of Light Speed Reduction in a Three-Level Λ System

Dezhong Wang, Daijun Li, Xia-Ji Liu, Shiqun Li, Yuzhu Wang

Published Jul 11, 2001• 5 citations
Publisher

Abstract

We present a nonlinear theory of light velocity reduction in a three-level Λ system based on electromagnetically induced transparency. Analysis shows that the probe field propagates with a velocity that is quite strongly dependent on its intensity instead of being merely approximately dependent on the coupling intensity. Moreover, the minimum group velocity of the probe field is analytically given for a given input power.

DOI
10.1088/0256-307x/18/8/322

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We present a nonlinear theory of light velocity reduction in a three-level Λ system based on electromagnetically induced transparency. Analysis shows that the probe field propagates with a velocity that is quite strongly dependent on its intensity instead of being merely approximately dependent on the coupling intensity. Moreover, the minimum group velocity of the probe field is analytically given for a given input power.
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Abstract We propose an analytical model to study the effect of giant Kerr nonlinearity on group velocity of probe light in a six-level inverted-Y atomic system under electromagnetically induced transparency (EIT). In this scheme, a nonlinearity of the medium is enhanced greatly around in three spectral regions corresponding to transparent windows. As a consequence, such a giant Kerr nonlinearity of the medium changes significantly group index for probe light which can obstruct light slowdown. Moreover, this model shows also that the probe propagation can switch between subluminal and superluminal modes in three EIT windows by adjusting the parameters of the signal and coupling fields. Such analytical model is not only convenient for considering the influence of laser parameters on group velocity but is also easy used to fit the experimental results.
The light propagation of a probe field in a three-level Λ system with incoherent pumping has been studied when both dynamically induced coherence (DIC) and spontaneously generated coherence (SGC) play a significant role. We have investigated the group velocity of probe field and hence the group index of a three-level Λ system with incoherent pumping when both DIC and SGC play a significant role. We have shown that by varying the probe field Rabi frequency one can control the interference between these two coherences which leads to different nonlinear response (amplification without inversion, electromagnetically induced transparency and electromagnetically induced absorption) leading to different (positive and negative) dispersion. Hence control over switching of group velocity from subluminal to superluminal and vice versa can be achieved. We have also shown that when the contributions from both the coherences are comparable, the dependence of group velocity of probe field in a three-level Λ system with incoherent pumping on phase difference between probe and coherent fields is different from that obtained under the weak probe field condition. Going beyond the weak probe field approximation we have derived analytical expressions for group velocity and hence the group index in the steady state limit (keeping all orders of system parameters) to generalize the analysis, and these expressions can be used for any set of system parameters without any restriction. The numerical values obtained by solving the density matrix equations agree well with these exact analytical values at a large time limit. We have proposed a scheme for experimental realization of EIT and hence subluminal light propagation in molecules by invoking spontaneously generated coherence.
We have observed the reduction of group velocity of light via electromagnetically induced transparency (EIT) and measured the dependence of pulse delay on the one-photon detuning in a three-level Λ-type atomic system. The results show that due to the effect of Doppler broadening the light speed reduction is signif icant in a range of ±600MHz one-photon detuning. Under the condition of consid ering the Doppler shift of frequency, the pulse delay as a function of the one-p hoton detuning is numerically calculated. The experimental measurements are in g ood agreement with the theoretical results. These researches provide theoretical and experimental references for controlling the group velocity of light by mean s of one-photon detuning.
We studied the electromagnetically induced transparency, where the three-level atom of Λ-type is put in two statistically independent squeezed vacuums. We start from the master equation containing the decay of the atom to the squeezed vacuums, and solve the non-diagonal density matrix element analytically, finding that it is strongly dependent on the squeezing degree and the phase of the squeezed vacuum. There is also a dependence on the intensity and phase of the probe beam, which would not appear in the normal vacuum case. By coupling with squeezed vacuums, the atom would not only experience electromagnetically induced transparency and slow group velocity, but also induce a fast group velocity,backward group velocity and a gain in the probe light field. Besides, the absorption and gain can be modulated by the intensity of probe light.
We analyze the energy transformation of light propagating with slow group velocity in a three-level medium. Depending on the excitation scheme, the energy of the probe can be transformed into the coupling field or into the atomic excitation. As a result a zero-energy adiabaton develops for the lambda scheme or an energy carrying adiabaton is formed for the ladder scheme. In both cases slow light is produced by the atoms, also feeding this light by the energy stored in the metastable state (ladder scheme) or borrowing the energy from the coupling field (lambda scheme).