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Physical Review A

Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems

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

Published Oct 14, 2003• 43 citations
Publisher

Abstract

We investigate realistic atomic systems whose dispersion at line center switches from positive to negative and vice versa, as a particular experimental parameter is changed. We concentrate on those systems which have low probe absorption or gain at line center leading to a high figure of merit, and simultaneously have low pump absorption. For this purpose, we study both open and artificially closed ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ and ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=2$ transitions in ${}^{87}\mathrm{Rb},$ in the absence and presence of an applied magnetic field. We find that the preferred system for observing switchover in the sign of the dispersion from positive to negative, as the pump Rabi frequency increases, is the open near-degenerate ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ system. In the presence of Doppler broadening, the dispersion is positive for all realistic experimental parameters. Thus the switchover in the sign of the dispersion is only observable in the absence of Doppler broadening.

DOI
10.1103/physreva.68.043818

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We investigate realistic atomic systems whose dispersion at line center switches from positive to negative and vice versa, as a particular experimental parameter is changed. We concentrate on those systems which have low probe absorption or gain at line center leading to a high figure of merit, and simultaneously have low pump absorption. For this purpose, we study both open and artificially closed Fg=1\ensuremath→Fe=1{F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1Fg​=1\ensuremath→​Fe​=1 and Fg=1\ensuremath→Fe=2{F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=2Fg​=1\ensuremath→​Fe​=2 transitions in 87Rb,{}^{87}\mathrm{Rb},87Rb, in the absence and presence of an applied magnetic field. We find that the preferred system for observing switchover in the sign of the dispersion from positive to negative, as the pump Rabi frequency increases, is the open near-degenerate Fg=1\ensuremath→Fe=1{F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1Fg​=1\ensuremath→​Fe​=1 system. In the presence of Doppler broadening, the dispersion is positive for all realistic experimental parameters. Thus the switchover in the sign of the dispersion is only observable in the absence of Doppler broadening.
We extend our previous study of a nearly degenerate Λ three-level system that exhibits population trapping when driven by a single pump and produces an absorption or gain doublet in the probe absorption spectrum. In particular, we show that the probe dispersion is positive or negative between the doublet lines, and can survive Doppler broadening. For certain values of the pump Rabi frequency, the sign of the dispersion can be changed by altering the ratio of the splitting between the lower levels to the Doppler width.
We investigate the dispersion and absorption in the coherently prepared two-level degenerate systems. Driven by a parallel polarized light and probed by a transverse polarized light, in the degeneracy case, only the positive dispersion is obtained at the zero pump-probe detuning, as well as electromagnetic induced transparency. When magnetic field breaks the degeneracy, we find that the dispersion is shifted from positive, via negative, to positive when varying the drive Rabi frequency, which means a transition between the superluminal and subluminel group velocity. Simultaneously, in these systems, the electromagnetic induced transparency, electromagnetic induced absorption and Mollow absorption spectrum are shown in the absorption spectra.
We study the absorption and dispersion in the near-degenerate closed three-level V system, in which a single coherent driving field is tuned resonant with the average frequency of two dipole-allowed transitions. Firstly, the switching from positive to negative dispersion can be achieved simply by increasing the driving field intensity. This is the same as in the driven Λ system. Secondly, the common feature originates from the fact that both V and Λ systems have the same transitions in terms of atomic dressed states under given conditions. These dressed transitions interfere destructively in the central spectrum while the sideband resonance transitions determine the possible appearance of two pairs of absorption doublet lines and two pairs of gain doublet lines in the sideband spectrum. Thirdly, there are two minor differences between these two systems. For large driving field intensity, a narrow steep structure is always present in the central negative dispersion spectrum in the V system but it disappears in the Λ system. The driving field intensity for the appearance of the outer sideband absorption or gain peaks is larger in the V system than in the Λ system.
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.
Abstract The present study addresses light propagation in both the positive- and negative-group-index regimes in a degenerate atomic system with four energy levels. Both the static magnetic field and the Doppler shifts play essential roles. Operating in an electromagnetically induced transparency configuration, we demonstrate that probe absorption characteristics and the group velocity index can be manipulated by combined control of the static magnetic field and two coupling laser fields. By selectively engaging one or both coupling fields, the magnetic field serves as a switching mechanism, toggling the atomic medium's optical behavior between transparent and absorptive states. Consequently, both the magnitude and sign of the group index can be adjusted, transitioning from positive to negative values or the reverse, based on whether the magnetic field is applied or removed. Additionally, temperature significantly influences both the optical properties and group index characteristics of the atomic medium. Given that our proposed system operates at room temperature, it is well-suited to practical experimental conditions and offers potential for deployment in optical storage technologies and quantum information processing applications.
In this study, optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of [Formula: see text]Rb D2 transition, which involves the Doppler broadening effect, are solved. The calculated spectra agree well with the experimental results obtained based on the coupling-probe scheme with orthogonal linear polarizations of the coupling and probe fields. The mechanisms of electromagnetically induced absorption (electromagnetically induced transparency) for the open [Formula: see text] and 3 transitions (open [Formula: see text] and 3 transitions) are determined to be the effect of the strong closed [Formula: see text] transition line (strong closed [Formula: see text] transition line); this finding is based on a comparison between the calculated absorption profiles of the DTLS without neighboring states and those of all levels with neighboring states, depending on the coupling and probe power ratios. Furthermore, based on the aforementioned comparison, the crucial factors that enhance or reduce the coherence effects and lead to the transformation between electromagnetically induced absorption and electromagnetically induced transparency, are (1) the power ratios between the coupling and probe beams, (2) the openness of the excited state, and (3) effects of the neighboring states due to Doppler broadening in a real atomic system.