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Chinese Physics B

Quantum coherent effects in multi-Zeeman-sublevel atomic systems

Yabin Dong, Gao Jiang-Rui, Dong You-er

Published Sep 1, 2008• 5 citations
Publisher

Abstract

This paper reports the experimental results on electromagnetically induced absorption (EIA) spectra observed in the system which does not satisfy completely the conditions given by Lezama et al [1999 Phys. Rev. A 59 4732]. EIA signals on the transitions in the Cs D 2 line are able to be observed, where F g ↔ F e = F g — 1 as open systems. Theoretical model of Lezama et al is good for the case F g ↔ F e = F g + 1, considering spontaneous transfer of atomic coherences or populations this model is not able to explain our experimental results obtained in the case F g ↔ F e = F g — 1. This paper offers a theoretical model which is able to well explain the case F g ↔ F e = F g — 1. It also uses this theoretical model to explain the split and shift of EIA peaks, which have been obtained in experiments.

DOI
10.1088/1674-1056/17/9/027

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This paper reports the experimental results on electromagnetically induced absorption (EIA) spectra observed in the system which does not satisfy completely the conditions given by Lezama et al [1999 Phys. Rev. A 59 4732]. EIA signals on the transitions in the Cs D 2 line are able to be observed, where F g ↔ F e = F g — 1 as open systems. Theoretical model of Lezama et al is good for the case F g ↔ F e = F g + 1, considering spontaneous transfer of atomic coherences or populations this model is not able to explain our experimental results obtained in the case F g ↔ F e = F g — 1. This paper offers a theoretical model which is able to well explain the case F g ↔ F e = F g — 1. It also uses this theoretical model to explain the split and shift of EIA peaks, which have been obtained in experiments.
We report experimental results on electromagnetically induced absorption spectra observed in the system which does not satisfy completely the conditions given by Lezama [Phys. Rev. A 59, 4732 (1999)]. We were able to observe electromagnetically induced absorption signals on all transitions in the Rb D1{D}_{1}D1​ line, where ${F}_{g}\ensuremath{\leftrightarrow}{F}_{e}{=F}_{g}\ifmmode\pm\else\textpm\fi{}1$ or Fg{F}_{g}Fg​ as well as open systems. These signals were only observed in certain Rabi frequency ranges for the coupling field. Present theoretical models, which are good for the case ${F}_{g}\ensuremath{\leftrightarrow}{F}_{e}{=F}_{g}+1,$ considering spontaneous transfer of atomic coherences or populations have not been able to explain our experimental results obtained in both cases ${F}_{g}\ensuremath{\leftrightarrow}{F}_{e}{=F}_{g}\ensuremath{-}1$ and Fe=Fg.{F}_{e}{=F}_{g}.Fe​=Fg​.
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 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.
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.
The probe absorption spectra in single and multiple tripod systems formed when a weak sigma polarized pump and a tunable pi polarized probe interact with a Zeeman split F(g)-->F(e)=F(g)-1 atomic transition are characterized by two interfering stimulated Raman features separated by an electromagnetically induced absorption (EIA) peak at the line center. These Raman features can appear as either sharp stimulated emission peaks or electromagnetically induced transparency windows. In the multitripod systems, the EIA and stimulated emission peaks derive from the combined effects of interference between the stimulated Raman features and transfer of coherence from the excited to ground states.
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.