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arXiv:quant-ph/0211056 · Physical Review A

Quantum coherence in a degenerate two-level atomic ensemble for a transition Fe=0↔Fg=1

Ying Gu, Qingqing Sun, Qihuang Gong

Published Jun 18, 2003• 29 citations
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Abstract

For a transition ${F}_{e}=0\ensuremath{\leftrightarrow}{F}_{g}=1$ driven by a linearly polarized light and probed by a transverse light, which has two equal circular components and is orthogonal to the linear polarization of the drive field and magnetic field, quantum coherence effects are investigated. Due to the coupling between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating with a pump-probe detuning in the steady state. At the zero pump-probe detuning, the subluminal and superluminal light propagations are predicted. Finally, there exist the large population fluctuations when we vary the pump-probe detuning.

DOI
10.1103/physreva.67.063809

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Physical Review A•Dec 12, 2006•8 citations
For a transition Fe=0\ensuremath↔Fg=1{F}_{e}=0\ensuremath{\leftrightarrow}{F}_{g}=1Fe​=0\ensuremath↔Fg​=1 driven by a linearly polarized light and probed by a transverse light, which has two equal circular components and is orthogonal to the linear polarization of the drive field and magnetic field, quantum coherence effects are investigated. Due to the coupling between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating with a pump-probe detuning in the steady state. At the zero pump-probe detuning, the subluminal and superluminal light propagations are predicted. Finally, there exist the large population fluctuations when we vary the pump-probe detuning.
We investigate the quantum coherence effects of a closed transition F e = 1 ↔ F g = 0 driven by transverse linearly polarized light field (with [sgrave] ± components) and probed by another transverse, linearly polarized light field. Owing to the competition of two-photon gain and single-photon absorption, the absorption spectrum is shown as a combination of electromagnetically induced transparency (EIT) and Mollow absorption spectrum (MAS). In the degenerate case, the MAS covers the EIT window at the pump-probe detuning centre. In the magnetic field, two single-photon absorption peaks inside the EIT windows appear when the drive Rabi frequency is smaller than the Zeeman splitting while, when the Rabi frequency is larger than the Zeeman splitting, we find four emission peaks due to the two-photon gain. A transition from positive to negative dispersion is obtained, which means a shift between the subluminal and superluminal group velocities.
For a closed transition Fe = 1 ↔ Fg = 2 driven by linearly polarized light and probed by circularly polarized light, quantum coherence effects induced by the Zeeman sublevels belonging to the different states are investigated. When the Zeeman splitting Δe of the excited level is larger than the Zeeman splitting Δg of the ground level, by increasing the drive Raby frequency, only the widening of the electromagnetically induced transparency (EIT) window with positive dispersion is found. In the opposite case, i.e. Δe ≤ Δg, in a moderate drive Rabi frequency, electromagnetically induced absorption with negative dispersion is obtained due to the shifting of the transparency points. Moreover, for the case of Δe ≤ Δg, a transition from subluminal to superluminal light propagation is predicted at the zero pump–probe detuning.
We have theoretically and experimentally studied the quantum coherence effects of a degenerate transition F g = 3↔ F e = 2 system interacting with a weak linearly polarized (with σ ± components) probe light and a strong linearly polarized (with σ ± components) coupling field. Due to the competition between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) are present at the different values of applied magnetic field in the case where the Zeeman splitting of excited state Δ e is larger than the Zeeman splitting of ground state Δ g (i.e. Δ e >Δ g ).
With saturation and probing by circularly polarized fields, quantum coherence effects are investigated for the cycling transition ${F}_{e}=0\ensuremath{\leftrightarrow}{F}_{g}=1$, which is subject to a linearly polarized field and a magnetic field. The saturation field is applied to the case of maximum coherence between the drive Rabi frequency and magnetic field, corresponding to the electromagnetically induced absorption (EIA) with negative dispersion found by Gu et al. For a small saturation Rabi frequency, holes are burned in two Autler-Towns peaks outside two symmetric electromagnetically induced transparency windows due to the two-photon resonance. However, when the saturation Rabi frequency is comparable with the drive Rabi frequency, holes caused by the coherent population oscillation appear in the EIA spectrum. Finally, when the saturation Rabi frequency is large enough, several emission peaks are observed due to the Mollow absorption effects. Furthermore, the dispersion at the pump-probe detuning center is kept negative with an increase in saturation field, which is a precursor of superluminal light propagation.
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.
The wealth of quantum coherence effects depending on the orientation of external magnetic field, the polarization of coupling and probe lights, and the Rabi frequency of the coupling beam are studied in transition ${F}_{e}=2\ensuremath{\leftrightarrow}{F}_{g}=3$ of Cs D2{\mathrm{D}}_{2}D2​ line. The split of electromagnetically induced transparency (EIT) resonances on two or three resonances determined by the different combination of the polarization of interaction lights and the direction of applied magnetic fields is obtained. The shifting and widening of the EIT resonances with the strength of the magnetic field (i.e., Zeeman splitting in the upper and lower levels) and Rabi frequency of the coupling beam increasing are also discussed. It may develop into the potential application for tunable multichannel optical information storage. On the other hand, an explanation of observed asymmetry of spectra by laser frequency offset from the optical resonance is given with theoretical calculation, which is in good agreement with the experimental results.