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Physical Review A

Electromagnetically induced absorption due to transfer of population in degenerate two-level systems

Chana Goren, A. D. Wilson‐Gordon, M. Rosenbluh, Harry Friedmann

Published Oct 21, 2004• 34 citations
Publisher

Abstract

We predict the occurrence of electromagnetically induced absorption (EIA) in cycling degenerate two-level transitions where ${F}_{e}={F}_{g}+1$ and ${F}_{g}>0$, interacting with pump and probe lasers with the same polarization. The EIA is due to transfer of population (TOP) between the Zeeman levels of the ground hyperfine state, rather than transfer of coherence (TOC) which occurs for perpendicularly polarized lasers. We model EIA-TOP using a double two-level system (TLS) which we compare with the four-level $N$ system, which models EIA-TOC. When the pump intensity is low, both models give an EIA peak at line center. The effect of introducing phase-changing collisions is studied, in the presence and absence of Doppler broadening, for both the double TLS and $N$ systems. In the presence of phase-changing collisions, the central EIA peaks are narrowed in both models and persist to higher pump Rabi frequencies than in the absence of collisions. In the double TLS, in the presence of Doppler broadening, the central EIA-TOP peak becomes narrower and does not develop a dip in its center, in contrast to the $N$ system. The central dip that appears in the Doppler-broadened EIA-TOC spectrum can be wiped out by adding phase-changing collisions. We demonstrate that EIA-TOP can be obtained for realistic atomic transitions interacting with lasers that have the same polarization.

DOI
10.1103/physreva.70.043814

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Electromagnetically induced absorption due to transfer of coherence and to transfer of population

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The absorption spectrum of a weak probe, interacting with a driven degenerate two-level atomic system, whose ground and excited hyperfine states are ${\mathrm{F}}_{g,e},$ can exhibit narrow peaks at line center. When the pump and probe polarizations are different, ${F}_{e}{=F}_{g}+1$ and ${F}_{g}>0,$ the electromagnetically induced absorption (EIA) peak has been shown to be due to the transfer of coherence (TOC) between the excited and ground states via spontaneous decay. We give a detailed explanation of why the TOC that leads to EIA (EIA-TOC) can only take place when ground-state population trapping does not occur, that is, when ${F}_{e}{=F}_{g}+1.$ We also explain why EIA-TOC is observed in open systems. We show that EIA can also occur when the pump and probe polarizations are identical and ${F}_{e}{=F}_{g}+1.$ This EIA is analogous to an effect that occurs in simple two-level systems when the collisional transfer of population (TOP) from the ground state to a reservoir is greater than that from the excited state. For a degenerate two-level system, the reservoir consists of the Zeeman sublevels of the ground hyperfine state, and of other nearby hyperfine states that do not interact with the pump. We will also discuss the four-wave mixing spectrum under the conditions where EIA-TOC and EIA-TOP occur.

Physical Review A•Mar 21, 2003•155 citations

Control of group velocity by phase-changing collisions

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We discuss the influence of phase-changing collisions on the group velocities in Doppler-broadened, cycling, degenerate two-level systems where ${F}_{e}={F}_{g}+1$ and ${F}_{g}>0$, interacting with pump and probe lasers, that exhibit electromagnetically induced absorption (EIA). Two model systems are considered: the $N$ system where the pump and probe are polarized perpendicularly, and EIA is due to transfer of coherence (TOC), and the double two-level system (TLS) where both lasers have the same polarization, and EIA is due to transfer of population (TOP). For the case of Doppler-broadened EIA TOC, which occurs at low pump intensity, there is a switch from positive to negative dispersion and group velocity, as the rate of phase-changing collisions is increased. For the case of EIA TOP at low pump intensity, the dispersion and group velocity remain negative even when the collision rate is increased. Pressure-induced narrowing, accompanied by an increase in the magnitude of the negative dispersion and a decrease in the magnitude of the negative group velocity, occurs in both EIA TOC and EIA TOP, at low pump intensity. When the pump intensity is increased, a switch from negative to positive dispersion and group velocity, with increasing collision rate, also occurs in the double TLS system. However, the effect is far smaller than in the case of the $N$ system at low pump intensity.

Physical Review A•Aug 29, 2005•1 citation

Pump-probe spectroscopy in degenerate two-level atoms with arbitrarily strong fields

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We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.

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Electromagnetically induced absorption due to transfer of coherence and to transfer of population

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Enhancement of electromagnetically induced absorption and four-wave mixing in a double two-level system

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Abstract We present a theoretical investigation of the electromagnetically induced absorption (EIA) due to transfer of population (TOP) in the double two-level system (TLS). It shows that one TLS is responsible for the sub-natural absorption part of EIA, and the other TLS is responsible for the natural absorption part of EIA. We propose a scheme in which the sub-natural absorption part of EIA is governed by the effect of coherent hole burning (CHB) and achieves an enhancement of at least two orders of magnitude with the detuned coupling field, while the natural absorption part is dominated by the effect of Mollow absorption (MA) and does not change with the detuned coupling field. Due to the effects of CHB and MA, the magnitude of four-wave mixing (FWM) achieves a significant increase for double TLS. We show in detail the evolution of the magnitude of the FWM signal with coupling detuning and Rabi frequency. It is demonstrated that strong resonances occur in the FWM profile at frequencies symmetrically displaced from the frequency of the coupling field by coupling detuning.

Chinese Physics B•Jun 26, 2025•0 citations
We predict the occurrence of electromagnetically induced absorption (EIA) in cycling degenerate two-level transitions where Fe=Fg+1{F}_{e}={F}_{g}+1Fe​=Fg​+1 and Fg>0{F}_{g}>0Fg​>0, interacting with pump and probe lasers with the same polarization. The EIA is due to transfer of population (TOP) between the Zeeman levels of the ground hyperfine state, rather than transfer of coherence (TOC) which occurs for perpendicularly polarized lasers. We model EIA-TOP using a double two-level system (TLS) which we compare with the four-level NNN system, which models EIA-TOC. When the pump intensity is low, both models give an EIA peak at line center. The effect of introducing phase-changing collisions is studied, in the presence and absence of Doppler broadening, for both the double TLS and NNN systems. In the presence of phase-changing collisions, the central EIA peaks are narrowed in both models and persist to higher pump Rabi frequencies than in the absence of collisions. In the double TLS, in the presence of Doppler broadening, the central EIA-TOP peak becomes narrower and does not develop a dip in its center, in contrast to the NNN system. The central dip that appears in the Doppler-broadened EIA-TOC spectrum can be wiped out by adding phase-changing collisions. We demonstrate that EIA-TOP can be obtained for realistic atomic transitions interacting with lasers that have the same polarization.
The absorption spectrum of a weak probe, interacting with a driven degenerate two-level atomic system, whose ground and excited hyperfine states are Fg,e,{\mathrm{F}}_{g,e},Fg,e​, can exhibit narrow peaks at line center. When the pump and probe polarizations are different, Fe=Fg+1{F}_{e}{=F}_{g}+1Fe​=Fg​+1 and Fg>0,{F}_{g}>0,Fg​>0, the electromagnetically induced absorption (EIA) peak has been shown to be due to the transfer of coherence (TOC) between the excited and ground states via spontaneous decay. We give a detailed explanation of why the TOC that leads to EIA (EIA-TOC) can only take place when ground-state population trapping does not occur, that is, when Fe=Fg+1.{F}_{e}{=F}_{g}+1.Fe​=Fg​+1. We also explain why EIA-TOC is observed in open systems. We show that EIA can also occur when the pump and probe polarizations are identical and Fe=Fg+1.{F}_{e}{=F}_{g}+1.Fe​=Fg​+1. This EIA is analogous to an effect that occurs in simple two-level systems when the collisional transfer of population (TOP) from the ground state to a reservoir is greater than that from the excited state. For a degenerate two-level system, the reservoir consists of the Zeeman sublevels of the ground hyperfine state, and of other nearby hyperfine states that do not interact with the pump. We will also discuss the four-wave mixing spectrum under the conditions where EIA-TOC and EIA-TOP occur.
We discuss the influence of phase-changing collisions on the group velocities in Doppler-broadened, cycling, degenerate two-level systems where Fe=Fg+1{F}_{e}={F}_{g}+1Fe​=Fg​+1 and Fg>0{F}_{g}>0Fg​>0, interacting with pump and probe lasers, that exhibit electromagnetically induced absorption (EIA). Two model systems are considered: the NNN system where the pump and probe are polarized perpendicularly, and EIA is due to transfer of coherence (TOC), and the double two-level system (TLS) where both lasers have the same polarization, and EIA is due to transfer of population (TOP). For the case of Doppler-broadened EIA TOC, which occurs at low pump intensity, there is a switch from positive to negative dispersion and group velocity, as the rate of phase-changing collisions is increased. For the case of EIA TOP at low pump intensity, the dispersion and group velocity remain negative even when the collision rate is increased. Pressure-induced narrowing, accompanied by an increase in the magnitude of the negative dispersion and a decrease in the magnitude of the negative group velocity, occurs in both EIA TOC and EIA TOP, at low pump intensity. When the pump intensity is increased, a switch from negative to positive dispersion and group velocity, with increasing collision rate, also occurs in the double TLS system. However, the effect is far smaller than in the case of the NNN system at low pump intensity.
We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.
In this paper, we present the theoretical study of double electromagnetically induced transparency (EIT) in a four-level V-type system which is formed by two co-propagating laser fields and the Zeeman sublevels of hyperfine transitions of 87Rb D2 line. The density matrix equations for the four-level V-type system are derived from the Liouville’s equation of motion and numerically solved under steady state condition to get the EIT signals. We consider both the probe and pump transmission spectra for the observation of double EIT signals under both Doppler free and Doppler broadened conditions. In case of Doppler free medium, two EIT peaks are formed in the two Lorentzian shape dips present in the both Doppler free probe and pump transmission spectra. When the medium becomes Doppler broadened, the two EIT peaks are formed in the probe transmission spectrum having Doppler broadened background, but the pump transmission spectrum gives two EIT peaks in the Doppler free background. The effect of probe intensity variation on the two EIT peaks is studied in case of Doppler broadened probe transmission spectrum. It is found that the heights of the EIT peaks decrease as the probe intensity increases, and interestingly one EIT peak converts into EIA (electromagnetically induced absorption) dip at some strong probe intensity value. The depth of the EIA dip is significantly increased as the intensity of the probe field increases. We also present the effect of probe intensity variation on the EIT peaks in the pump transmission spectrum and found that the EIT peak heights are increased as the probe intensity increases.
Abstract We present a theoretical investigation of the electromagnetically induced absorption (EIA) due to transfer of population (TOP) in the double two-level system (TLS). It shows that one TLS is responsible for the sub-natural absorption part of EIA, and the other TLS is responsible for the natural absorption part of EIA. We propose a scheme in which the sub-natural absorption part of EIA is governed by the effect of coherent hole burning (CHB) and achieves an enhancement of at least two orders of magnitude with the detuned coupling field, while the natural absorption part is dominated by the effect of Mollow absorption (MA) and does not change with the detuned coupling field. Due to the effects of CHB and MA, the magnitude of four-wave mixing (FWM) achieves a significant increase for double TLS. We show in detail the evolution of the magnitude of the FWM signal with coupling detuning and Rabi frequency. It is demonstrated that strong resonances occur in the FWM profile at frequencies symmetrically displaced from the frequency of the coupling field by coupling detuning.