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New Journal of Physics

Coherent processes in electromagnetically induced absorption: a steady and transient study

Jelena Dimitrijević, D. Arsenović, B. M. Jelenkovic

Published Mar 8, 2011• 11 citations
Publisher

Abstract

A perturbation method was used to solve optical Bloch equations (OBEs) for the transition F g =1→ F e =2, in order to describe the role of ground-level Zeeman coherences in the formation of electromagnetically induced absorption (EIA). A narrow Lorentzian peak, centered at zero value of the scanning magnetic field, appears in the analytical expression of the second-order correction of a density-matrix element for ground-level Zeeman coherences, (ρ g −1 , g +1 ) x 2 . Through analytical expressions for lower-order corrections of density-matrix elements, we were able to establish clear relations between the narrow Lorentzian in (ρ g − 1 , g +1 ) x 2 and higher-order corrections of optical coherences, i.e. EIA. We see from analytical expressions that these two resonances have opposite signs and that EIA becomes electromagnetically induced transparency (EIT) in the limit of low efficiency of spontaneous transfer of coherences from excited-level to ground-level Zeeman sublevels. The transient behavior of EIA follows the time evolution of (ρ g − 1 , g +1 ) x 2 . After the coupling laser is turned on, both the Lorentzian peak in (ρ g − 1 , g +1 ) x 2 and EIA reach steady state via over-damped oscillations.

DOI
10.1088/1367-2630/13/3/033010

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Acta Physica Sinica•Jan 1, 2008•10 citations
A perturbation method was used to solve optical Bloch equations (OBEs) for the transition F g =1→ F e =2, in order to describe the role of ground-level Zeeman coherences in the formation of electromagnetically induced absorption (EIA). A narrow Lorentzian peak, centered at zero value of the scanning magnetic field, appears in the analytical expression of the second-order correction of a density-matrix element for ground-level Zeeman coherences, (ρ g −1 , g +1 ) x 2 . Through analytical expressions for lower-order corrections of density-matrix elements, we were able to establish clear relations between the narrow Lorentzian in (ρ g − 1 , g +1 ) x 2 and higher-order corrections of optical coherences, i.e. EIA. We see from analytical expressions that these two resonances have opposite signs and that EIA becomes electromagnetically induced transparency (EIT) in the limit of low efficiency of spontaneous transfer of coherences from excited-level to ground-level Zeeman sublevels. The transient behavior of EIA follows the time evolution of (ρ g − 1 , g +1 ) x 2 . After the coupling laser is turned on, both the Lorentzian peak in (ρ g − 1 , g +1 ) x 2 and EIA reach steady state via over-damped oscillations.
We study phenomenon of electromagnetically induced absorption (EIA) in the Hanle configuration by applying a perturbative method to solve linear system of optical Bloch equations (OBEs) for the case of closed F g = 1 → F e = 2 transition. The method is applied assuming stationary case and a weak laser fields (Ω ≪ Γ, i.e., Rabi frequency small compared to spontaneous emission rate). This way, we calculate (both numerically and analytically) higher order corrections to density matrix. Odd corrections give contributions to optical coherences, while even corrections contribute to populations and Zeeman coherences. The method gives insight into mechanism of transfer of coherences and transfer of populations between Zeeman sublevels. We have found that the ground-state coherences (2nd correction to coherences) are crucial for the 4th correction to the change of populations which brings EIA type behavior of the Hanle spectrum. Using exact analytical expressions we further discuss further the role of decoherence of the ground-state sublevels when forming EIA.
We study phenomenon of electromagnetically induced absorption in the Hanle configuration by solving time-dependent optical Bloch equations for the case of the closed multilevel F g = 1 → F e = 2 transition.Our model gives optical Bloch equations as a non-homogeneous system of ordinary linear differential equations.For weak laser fields (Ω Γ i.e.Rabi frequency small compared to spontaneous emission rate), a perturbative method to solve linear differential equations can be applied.Perturbative method is realized by solving (in the time-domain) higher-order corrections to the density matrix which in the sum converge to the exact solution of optical Bloch equations.By its form, each successive correction is also system of ordinary linear differential equations which depends on the solution of previous ones.Corrections are partitioned such that odd give corrections to optical coherences, while even give corrections to populations and Zeeman coherences.We present numerical results for the behavior of density matrix elements with successive corrections, and compare them with exact solution of optical Bloch equations.Electromagnetically induced absorption is observed as a 4th and higher (even) correction to populations, when behavior in respect to both time and magnetic field is viewed.Since in our method each correction depends on the solution of previous ones, we can analyze how (through mechanism of transfer of coherences and transfer of populations between Zeeman sublevels) electromagnetically induced absorption is formed.We also discuss qualitative differences in the behavior (with respect to time) of certain density matrix elements for magnetic fields "inside" and "outside" electromagnetically induced absorption resonance.
The temporal evolution of electromagnetically induced transparency (EIT) and absorption (EIA) coherence resonances in pump-probe spectroscopy of degenerate two-level atomic transition is studied for light intensities below saturation. Analytical expressions for the transient absorption spectra are given for simple model systems and a model for the calculation of the time-dependent response of realistic atomic transitions, where the Zeeman degeneracy is fully accounted for, is presented. EIT and EIA resonances have a similar (opposite sign) time-dependent line shape, however, the EIA evolution is slower and thus narrower lines are observed for long interaction time. Qualitative agreement with the theoretical predictions is obtained for the transient probe absorption on the 85Rb{}^{85}\mathrm{Rb}85Rb D2{D}_{2}D2​ line in an atomic beam experiment.
We have investigated atomic coherence changes caused by optical pumping applied to electromagnetically induced absorption (EIA) occurring at the open system, which consists of the transition between the F g = 2 ground state and the F e = 3 excited state in the 85 Rb D1-line. For optical pumping, another laser resonantly tuned to the transition between the F g = 3 ground state and the F e = 2 excited state was used. We found that the atomic coherence for EIA can be changed not by increasing the pumping rate but by pumping differently populations into the Zeeman sublevels in the F g = 2 ground state, which is realized by changing the polarization of the pumping laser. The experimental results were able to be analysed by density matrix equations in the simple model system.
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.
Electromagnetically induced transparency (EIT) resonance is obtained in a well-studied lambda three level system where an optical coupling field and a probing field interact with two optical transitions. However, both electromagnetically induced absorption (EIA) and EIT can be obtained in a modified quasi-lambda four level system consisting of an optical-radio two-photon coupling field and a probing field. By solving the density matrix equation of motion, a physical account of EIA and EIT is given in terms of a dressed state picture. It can be seen that the optical coupling field in this quasi-lambda four level system has a crucial effect on the forming of EIA and EIT. An EIA is observed under a resonant optical coupling and it evolves into an EIT when there is a detuning. Furthermore, the width of EIA or EIT increases as the optical coupling Rabi frequency increases.