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arXiv:quant-ph/0209011 · Physical Review A

Temporal buildup of electromagnetically induced transparency and absorption resonances in degenerate two-level transitions

Paulo Valente, H. Failache, A. Lezama

Published Jan 23, 2003• 22 citations
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Abstract

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 ${}^{85}\mathrm{Rb}$ ${D}_{2}$ line in an atomic beam experiment.

DOI
10.1103/physreva.67.013806

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The temporal evolutions of electromagnetically induced transparency (EIT) and absorption (EIA) were observed in a Hanle absorption experiment carried on the ${D}_{2}$ lines of ${}^{87}\mathrm{Rb}$ vapor by suddenly turning the magnetic field on or off. The main features of the experimental observations are well reproduced by a theoretical model based on Bloch equation where the atomic level degeneracy has been fully accounted for. Similar (opposite phase) evolutions were observed at low optical-field intensities for Hanle-EIT or Hanle-EIA resonances. Unlike the Hanle-EIA transients that are increasingly shorter for driving field intensities approaching saturation, the $B\ensuremath{\ne}0$ transient of the Hanle-EIT signal at large driving field intensities present a long decay time approaching the atomic transit time. Such counterintuitive behavior is interpreted as a consequence of the Zeno effect.

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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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Simultaneous observations of electromagnetically induced transparency (EIT) and absorption (EIA) in a multi-level V-type system of 87Rb and theoretical simulation of the observed spectra using a multi-mode approach

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We report here simultaneous experimental observation of Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Absorption (EIA) in a multi-level V-type system in D2 transition of Rb87, i.e., F=2→F′ with a strong pump and a weak probe beam. We studied the probe spectrum by locking the probe beam to the transition F=2→F′=2 while the pump is scanned from F=2→F′. EIA is observed for the open transition (F=2→F′=2) whereas EIT is observed in the closed transition (F=2→F′=3). Sub natural line-width is observed for the EIA. To simulate the observed spectra theoretically, Liouville equation for the three-level V-type system is solved analytically with a multi-mode approach for the density matrix elements. We assumed both the pump and the probe beams can couple the excited states. A multi-mode approach for the coherence terms facilitates the study of all the frequency contributions due to the pump and the probe fields. Since the terms contain higher harmonics of the pump and the probe frequencies, we expressed them in Fourier transformed forms. To simulate the probe spectrum, we have solved inhomogeneous difference equations for the coherence terms using the Green’s function technique and continued fraction theory. The experimental line-widths of the EIT and the EIA are compared with our theoretical model. Our system can be useful in optical switching applications as it can be precisely tuned to render the medium opaque and transparent simultaneously.

The Journal of Chemical Physics•Dec 14, 2016•18 citations
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.
The temporal evolutions of electromagnetically induced transparency (EIT) and absorption (EIA) were observed in a Hanle absorption experiment carried on the D2{D}_{2}D2​ lines of 87Rb{}^{87}\mathrm{Rb}87Rb vapor by suddenly turning the magnetic field on or off. The main features of the experimental observations are well reproduced by a theoretical model based on Bloch equation where the atomic level degeneracy has been fully accounted for. Similar (opposite phase) evolutions were observed at low optical-field intensities for Hanle-EIT or Hanle-EIA resonances. Unlike the Hanle-EIA transients that are increasingly shorter for driving field intensities approaching saturation, the $B\ensuremath{\ne}0$ transient of the Hanle-EIT signal at large driving field intensities present a long decay time approaching the atomic transit time. Such counterintuitive behavior is interpreted as a consequence of the Zeno effect.
The temporal evolutions of coherent resonances corresponding to electromagnetically induced transparency (EIT) and absorption (EIA) were observed in a Hanle absorption experiment carried on the D2D_{2}D2​ lines of % ^{87}Rb vapor by suddenly turning the magnetic field on or off. The main features of the experimental observations are well reproduced by a theoretical model based on Bloch equation where the atomic level degeneracy has been fully accounted for. Similar (opposite phase) evolutions were observed at low optical field intensities for Hanle/EIT or Hanle/EIA resonances. Unlike the Hanle/EIA\ transients which are increasingly shorter for driving field intensities approaching saturation, the B≠0B\neq 0B=0 transient of the Hanle/EIT signal at large driving field intensities present a long decay time approaching the atomic transit time. Such counterintuitive behavior is interpreted as a consequence of the Zeno effect.
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.
Employing an intense laser field coupling to the degenerate two-level system of cesium 6 2S_ 1/2(F=4)- 6 2P_ 3/2(F′=5) transition in a cesium vapor cell, electromagnetically induced absorption (EIA) has been demonstrated via probe absorption spectra, at the same time, electromagnetically induced transparency (EIT) of V-type three-level scheme has been demonstrated on the F=4-F′=3 and F=4-F′=4 transition frequency. The EIA is affected by the intensity and detuning of the coupling laser. By analyzing the effect of optical pumping between Zeeman sub-levels on the EIA and the coherent interactions between multiple degenerate two-level atoms, it is shown that the optical pumping affects the population of different Zeeman sub-levels and the number of the involved two-level atoms, the coherent time between the sub-levels is then changed and the linewidth and intensity of the EIA are affected accordingly.
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.
We report here simultaneous experimental observation of Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Absorption (EIA) in a multi-level V-type system in D2 transition of Rb87, i.e., F=2→F′ with a strong pump and a weak probe beam. We studied the probe spectrum by locking the probe beam to the transition F=2→F′=2 while the pump is scanned from F=2→F′. EIA is observed for the open transition (F=2→F′=2) whereas EIT is observed in the closed transition (F=2→F′=3). Sub natural line-width is observed for the EIA. To simulate the observed spectra theoretically, Liouville equation for the three-level V-type system is solved analytically with a multi-mode approach for the density matrix elements. We assumed both the pump and the probe beams can couple the excited states. A multi-mode approach for the coherence terms facilitates the study of all the frequency contributions due to the pump and the probe fields. Since the terms contain higher harmonics of the pump and the probe frequencies, we expressed them in Fourier transformed forms. To simulate the probe spectrum, we have solved inhomogeneous difference equations for the coherence terms using the Green’s function technique and continued fraction theory. The experimental line-widths of the EIT and the EIA are compared with our theoretical model. Our system can be useful in optical switching applications as it can be precisely tuned to render the medium opaque and transparent simultaneously.