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Journal of Physics B Atomic Molecular and Optical Physics

Control over group velocity in a three-level closed Λ system via spontaneously generated coherence and dynamically induced coherence

Sulagna Dutta, Krishna Rai Dastidar

Published Oct 22, 2007• 21 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/40/21/014

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Control of probe response and dispersion in a three level closed Λ system: Interplay between spontaneously generated coherence and dynamically induced coherence

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The dispersion and the absorption properties of a closed three-level Λ system with incoherent pumping have been studied when both dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role. We analyze the interplay between the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) on the absorption spectrum to induce different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). By changing the probe field Rabi frequency the response of the system can switch over from one nonlinear process to other and hence the probe field Rabi frequency can be used as a knob for switching different nonlinear responses. By changing the relative phase of two fields the response of the system switches over from EIA to EIT or EIT to AWI which can be used as optical switch. Choosing appropriate value of the relative phase and the probe field Rabi frequency, the dispersion and hence the propagation of the probe pulse can be controlled efficiently. Therefore these parameters can be used as a knob to manipulate light propagation from subluminal to superluminal. 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. Any restrictions over the system parameters have been avoided to make it applicable to various atomic and molecular systems.

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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.

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The probe response and dispersion of a three-level closed ? system considering spontaneously generated coherence (SGC) have been investigated with and without an incoherent pumping. One can get electromagnetically induced transparency (EIT) whatever be the value of the SGC parameter and phase difference when an incoherent pump is absent. But by turning the incoherent pump rate on, one can control the light propagation from subluminal to superluminal and also the nonlinear response from EIT to electromagnetically induced absorption (EIA) by controlling the SGC parameter and phase difference. Using the incoherent pump rate as an optical tool, the desired configuration around the resonance can be realized. Exact analytical expressions for the coherences in the steady-state limit have been derived in the absence of an incoherent pump rate (keeping all orders of the system parameters) to generalize the analysis, and any restriction on the system parameters has been avoided to make it applicable to various atomic and molecular systems.

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Abstract We present a comparative study of the control of group velocity in three-level atomic systems including Λ-, Ladder-, and V-types via spontaneously generated coherence (SGC) and relative phase of laser fields. In the steady regime, expressions of group index are derived as an analytical function of controllable parameters related to SGC and relative phase. It is shown that the group velocity can be further slowed down or speeded up under SGC in which modifications of group velocity due to the SGC in Λ- and V-systems are stronger than that in Ladder-system. In particular, when interference strength of SGC p increases from 0.7 to 1.0, the light propagation is switched from superluminal to subluminal modes (for Λ- and Ladder-systems) or from subluminal to superluminal modes (for V-system). In the presence of relative phase, the group velocity changes between subluminal and superluminal modes with a period of 2π. In resonant region, the largest positive value of group index reaches at the relative phase φ = π while the largest negative value of group index reaches at φ = 0 and 2π for the Λ- and Ladder-systems, otherwise, for the V-system the largest positive group index occurs at φ = 0 and 2π, and the largest negative group index occurs at φ = π .

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Broadening of EIT window by incoherent pumping in a three-level Λ system: Effect of homogeneous and inhomogeneous broadening

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The interplay between dynamically induced coherence (DIC) and spontaneously generated coherence (SGC) can induce electromagnetically induced transparency (EIT) in a three-level closed Λ system. When the contributions from these two coherences are equal in magnitude and opposite in sign at the resonances of both the coherent and probe fields, transparency of the probe light occurs at the resonance with absorption humps away from the resonance. We have demonstrated here that the broadening of the EIT window can be controlled by changing the strength of incoherent pumping. This is a new approach for achieving wide EIT window for lossless and distortionless transmission of light of large spectral width. The most attractive feature of this new method is that the FWHM (full width at half-maximum) of the EIT window is further increased when the broadening due to homogeneous/inhomogeneous decay is taken into consideration. This scheme can be applied in atoms/molecules where SGC can be invoked by dressing two closely spaced levels ( e.g. hyperfine levels in atoms or rovibrational levels in molecules) by an external field. This effect has been demonstrated in a heteronuclear molecule ( e.g. LiH) and examined the role of incoherent pumping for controlling the width of the EIT window in the presence and absence of homogeneous/inhomogeneous decay. The experimental realization of the widening of the EIT window in molecules has been discussed.

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Subluminal and superluminal light propagation in two kinds of V-type system

Olimpia Budrigă

We study the change of the probe field group velocity from subluminal to superluminal range for two kinds of closed three-level V-type system with spontaneously generated coherence and incoherent pumping field. For the first kind of the V-type system we deduce the analytical formula of the group velocity, while for the second kind of the V-type system we solve numerically the density matrix equations system and apply it to a real system from the LiH molecule. We find that the group index of the probe field can be changed from positive to negative within the appropriate choice of the relative phase between the probe and coupling field phases, the incoherent pumping rate and probe detuning.

arXiv:1406.5288•Jun 20, 2014•1 citation
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.
The dispersion and the absorption properties of a closed three-level Λ system with incoherent pumping have been studied when both dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role. We analyze the interplay between the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) on the absorption spectrum to induce different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). By changing the probe field Rabi frequency the response of the system can switch over from one nonlinear process to other and hence the probe field Rabi frequency can be used as a knob for switching different nonlinear responses. By changing the relative phase of two fields the response of the system switches over from EIA to EIT or EIT to AWI which can be used as optical switch. Choosing appropriate value of the relative phase and the probe field Rabi frequency, the dispersion and hence the propagation of the probe pulse can be controlled efficiently. Therefore these parameters can be used as a knob to manipulate light propagation from subluminal to superluminal. 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. Any restrictions over the system parameters have been avoided to make it applicable to various atomic and molecular systems.
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.
The probe response and dispersion of a three-level closed ? system considering spontaneously generated coherence (SGC) have been investigated with and without an incoherent pumping. One can get electromagnetically induced transparency (EIT) whatever be the value of the SGC parameter and phase difference when an incoherent pump is absent. But by turning the incoherent pump rate on, one can control the light propagation from subluminal to superluminal and also the nonlinear response from EIT to electromagnetically induced absorption (EIA) by controlling the SGC parameter and phase difference. Using the incoherent pump rate as an optical tool, the desired configuration around the resonance can be realized. Exact analytical expressions for the coherences in the steady-state limit have been derived in the absence of an incoherent pump rate (keeping all orders of the system parameters) to generalize the analysis, and any restriction on the system parameters has been avoided to make it applicable to various atomic and molecular systems.
Abstract We present a comparative study of the control of group velocity in three-level atomic systems including Λ-, Ladder-, and V-types via spontaneously generated coherence (SGC) and relative phase of laser fields. In the steady regime, expressions of group index are derived as an analytical function of controllable parameters related to SGC and relative phase. It is shown that the group velocity can be further slowed down or speeded up under SGC in which modifications of group velocity due to the SGC in Λ- and V-systems are stronger than that in Ladder-system. In particular, when interference strength of SGC p increases from 0.7 to 1.0, the light propagation is switched from superluminal to subluminal modes (for Λ- and Ladder-systems) or from subluminal to superluminal modes (for V-system). In the presence of relative phase, the group velocity changes between subluminal and superluminal modes with a period of 2π. In resonant region, the largest positive value of group index reaches at the relative phase φ = π while the largest negative value of group index reaches at φ = 0 and 2π for the Λ- and Ladder-systems, otherwise, for the V-system the largest positive group index occurs at φ = 0 and 2π, and the largest negative group index occurs at φ = π .
The interplay between dynamically induced coherence (DIC) and spontaneously generated coherence (SGC) can induce electromagnetically induced transparency (EIT) in a three-level closed Λ system. When the contributions from these two coherences are equal in magnitude and opposite in sign at the resonances of both the coherent and probe fields, transparency of the probe light occurs at the resonance with absorption humps away from the resonance. We have demonstrated here that the broadening of the EIT window can be controlled by changing the strength of incoherent pumping. This is a new approach for achieving wide EIT window for lossless and distortionless transmission of light of large spectral width. The most attractive feature of this new method is that the FWHM (full width at half-maximum) of the EIT window is further increased when the broadening due to homogeneous/inhomogeneous decay is taken into consideration. This scheme can be applied in atoms/molecules where SGC can be invoked by dressing two closely spaced levels ( e.g. hyperfine levels in atoms or rovibrational levels in molecules) by an external field. This effect has been demonstrated in a heteronuclear molecule ( e.g. LiH) and examined the role of incoherent pumping for controlling the width of the EIT window in the presence and absence of homogeneous/inhomogeneous decay. The experimental realization of the widening of the EIT window in molecules has been discussed.
We study the change of the probe field group velocity from subluminal to superluminal range for two kinds of closed three-level V-type system with spontaneously generated coherence and incoherent pumping field. For the first kind of the V-type system we deduce the analytical formula of the group velocity, while for the second kind of the V-type system we solve numerically the density matrix equations system and apply it to a real system from the LiH molecule. We find that the group index of the probe field can be changed from positive to negative within the appropriate choice of the relative phase between the probe and coupling field phases, the incoherent pumping rate and probe detuning.