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Journal of Modern Optics

Group velocity of probe light pulse in an open lambda system

Cui Ni, X. J. Fan, Shufen Tian, Hui Ma, A. Y. Li, Zhenzhu Xu

Published Apr 27, 2006• 10 citations
Publisher

Abstract

The group velocity of the probe light pulse (GVPLP) propagating through an open Λ-type atomic system with a spontaneously generated coherence is investigated when the weak probe and strong driving light fields have different frequencies. It is found that adjusting the detuning or Rabi frequency of the probe light field can realize switching of the GVPLP from subluminal to superluminal. Changing the relative phase between the probe and driving light fields or atomic exit and injection rates can lead to GVPLP varying in a wider range, but cannot induce transformation of the property of the GVPLP. The absolute value of the GVPLP always increases with Rabi frequency of the driving light field increasing. For subluminal and superluminal propagation, the system always exhibits the probe absorption, and GVPLP is mainly determined by the slope of the steep dispersion.

DOI
10.1080/09500340600552331

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The group velocity of the probe light pulse (GVPLP) propagating through an open Λ-type atomic system with a spontaneously generated coherence is investigated when the weak probe and strong driving light fields have different frequencies. It is found that adjusting the detuning or Rabi frequency of the probe light field can realize switching of the GVPLP from subluminal to superluminal. Changing the relative phase between the probe and driving light fields or atomic exit and injection rates can lead to GVPLP varying in a wider range, but cannot induce transformation of the property of the GVPLP. The absolute value of the GVPLP always increases with Rabi frequency of the driving light field increasing. For subluminal and superluminal propagation, the system always exhibits the probe absorption, and GVPLP is mainly determined by the slope of the steep dispersion.
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.
In an open / type system with the spontaneously generated coherence (SGC), when the probe and driving fields have different frequencies, the switching of the group velocity of the probe pulse from subluminal to superluminal is realized not only by adjusting values of the relative phase between the probe and driving fields but also by varying values of the incoherent pumping rate. For the subluminal propagation, the system always exhibits the probe absorption, however, the superluminal propagation is always companied with gain of the probe field.
We study the dispersion and absorption spectra of a weak probe in a $\ensuremath{\Lambda}$-type three-level atomic system with closely ground sublevels driven by a strong field and damped by a broadband squeezed vacuum. We analyze the interplay between the spontaneous generated coherence and the squeezed field on the susceptibility of the atomic system. We find that by varying the intensity of the squeezed field the group velocity of a weak pulse can change from subluminal to superluminal. In addition we exploit the fact that the properties of the atomic medium can be dramatically modified by controlling the relative phase between the driving field and the squeezed field, allowing us to manipulate the group velocity at which light propagates. The physical origin of this phenomenon corresponds to a transfer of the atomic coherence from electromagnetically induced transparency to electromagnetically induced absorption. Besides, this phenomenon is achieved under nearly transparency conditions and with negligible distortion of the propagation pulse.
We analyse the group velocity of a laser pulse in an optically dressed atomic system. A Λ system with an additional close upper level and an incoherent pump is specially investigated. The group velocity of a pulse is strongly dependent on the optical properties of the system which can be modified by changing the amplitude or detuning of a strong coupling field or of an incoherent pump between the two lower levels of the system. Depending on the parameters, the medium may have alternatively absorptive or gain properties and the dispersion can be changed from anomalous into a normal one. The ranges of parameters are especially investigated in which absorption (gain) is not too strong, with dispersion being not too steep. The group velocity of a pulse propagating through a sample with such optical properties can be switched from the subinto superluminal regime. The dynamics of propagation in the case of negative group velocities of a small absolute value is especially interesting. In such a regime the peak of the transmitted pulse exits the sample before the peak of the incoming pulse reaches the medium. The transmitted pulse splits into two pulses - one of them propagates forward behind the medium and the other propagates backward and is cancelled at the entrance of the sample by the incoming pulse. Ranges of parameters are seeked in which the shape of the pulse is changed and the group velocity as a single parameter is not sufficient to describe the pulse propagation.
The propagation of a weak probe field in a four-level N-type quantum system in the presence of spontaneously generated coherence (SGC) is theoretically investigated. The optical properties of the system are studied and it is shown that the group velocity of light pulse can be controlled by relative phase of applied fields. By changing the relative phase of applied fields, the group velocity of light pulse changes from transparent subluminal to the transparent superluminal light propagation. Thus, the phase-controlled absorption-free superluminal light propagation is obtained without applying an incoherent laser fields to the system. The propagation of a weak probe light pulse is studied by solving the Maxwell's wave equation on numerical grid in space and time. Moreover, we study the third order self- and cross-Kerr susceptibility of probe field and calculate the nonlinear cross-phase shift for different values of intensity of applied fields. In addition, we take into account the effect of Doppler broadening on the light pulse propagation and it is found that a suitable choice of laser propagation directions allows us to preserve our results even in the presence of Doppler effect. It is demonstrated that by increasing the Doppler width of distribution to the room temperature, the dispersion changes from transparent subluminal to transparent superluminal light propagation which is our major motivation for this work.