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Chinese Optics Letters
Vol. 15, Issue 9, 090201 (2017)

Simultaneous electromagnetically induced transparency and absorption in thermal atomic medium

Shangqing Liang¹, Yunfei Xu¹, and Qiang Lin^2、*

Author Affiliations

¹Institute of Optics, Department of Physics, Zhejiang University, Hangzhou 310027, China

²Center for Optics & Optoelectronics Research, College of Science, Zhejiang University of Technology, Hangzhou 310023, China

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DOI: 10.3788/COL201715.090201 Cite this Article Set citation alerts

Shangqing Liang, Yunfei Xu, Qiang Lin. Simultaneous electromagnetically induced transparency and absorption in thermal atomic medium[J]. Chinese Optics Letters, 2017, 15(9): 090201 Copy Citation Text

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Abstract

A three-level lambda system driven by multicolor control, pump, and probe fields is investigated. The pump and probe fields are derived from the same laser with opposite propagating directions. Due to the Doppler effect, the zero group-velocity atoms face bichromatic fields, while other atoms face trichromatic fields. The atomic medium shows distinct characteristics and exhibits simultaneous electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) at two frequencies. EIT and EIA peaks have a fixed relationship with frequency, which is determined by the Doppler shifts.

\overset{⇀}{E} (R, t) = \overset{⇀}{E} \cos (\overset{⇀}{k} \cdot \overset{⇀}{R} - ω t),

(1)

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{\overset{⇀}{E}}_{p} (R, t) = {\overset{⇀}{E}}_{p} \cos (\overset{⇀}{k} \cdot \overset{⇀}{R} - ω t) .

(2)

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{\overset{⇀}{E}}^{'} (R, t) = {\overset{⇀}{E}}^{'} \cos ({\overset{⇀}{k}}^{'} \cdot \overset{⇀}{R} - ω^{'} t) .

(3)

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H = H_{0} - \overset{⇀}{μ} \cdot [\overset{⇀}{E} (\overset{⇀}{R}, t) + {\overset{⇀}{E}}^{'} (\overset{⇀}{R}, t) + E_{P} (\overset{⇀}{R}, t)],

(4)

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i ℏ {\dot{ρ}}_{s} = [H, ρ^{s}] + (relaxation terms) .

(5)

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ρ_{12}^{s} = ρ_{12} e^{- i (\overset{⇀}{k} \cdot \overset{⇀}{R} - ω t)},

(6a)

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ρ_{32}^{s} = ρ_{32} e^{- i ({\overset{⇀}{k}}^{'} \cdot \overset{⇀}{R} - ω^{'} t)},

(6b)

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ρ_{13}^{s} = ρ_{13} e^{- i [(\overset{⇀}{k} - {\overset{⇀}{k}}^{'}) \cdot \overset{⇀}{R} - (ω - ω^{'}) t]},

(6c)

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ρ_{13}^{s} = ρ_{13}^{s *} .

(6d)

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\dot{ρ} = - A ρ + B_{+} ρ e^{- i ({\overset{⇀}{k}}_{p} - {\overset{⇀}{k}}^{'}) \cdot \overset{⇀}{R}} e^{i Δ t} - B_{-} ρ e^{i ({\overset{⇀}{k}}_{p} - {\overset{⇀}{k}}^{'}) \cdot \overset{⇀}{R}} e^{- i Δ t} + λ,

(7)

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A = (\begin{matrix} 0 & 0 & 0 & - i χ & i χ & 0 & 0 & - γ_{2, 1} \\ 0 & - i (δ - δ^{'}) & 0 & - i χ^{'} & 0 & 0 & i χ & 0 \\ 0 & 0 & (δ - δ^{'}) & 0 & i χ^{'} & - i χ & 0 & 0 \\ - i χ & - i χ^{'} & 0 & γ - i δ & 0 & 0 & 0 & i χ \\ i χ & 0 & i χ^{'} & 0 & γ + i δ & 0 & 0 & - i χ \\ i χ^{'} & 0 & - i χ & 0 & 0 & γ - i δ^{'} & 0 & 2 i χ^{'} \\ - i χ^{'} & i χ & 0 & 0 & 0 & 0 & γ + i δ^{'} & - 2 i χ^{'} \\ 0 & 0 & 0 & i χ & - i χ & i χ^{'} & - i χ^{'} & γ_{2} \end{matrix}),

(8)

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B_{+} = i χ_{p} (\begin{matrix} 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & - 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & - 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \end{matrix}),

(9)

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B_{-} = i χ_{p} (\begin{matrix} 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ - 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & - 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & - 1 & 0 & 0 & 0 & 0 \end{matrix}),

(10)

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Δ = ω_{p 0} (1 + \frac{v}{c}) - ω_{0} (1 - \frac{v}{c}) = \frac{2 v}{c} ω_{0},

(11)

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δ = ω_{21} - ω = ω_{21} - ω_{0} (1 - \frac{v}{c}),

(12)

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δ^{'} = ω_{23} - ω^{'} = ω_{23} - ω_{0}^{'} (1 + \frac{ν}{c}) = ω_{23} - (ω_{23} - 60 γ) (1 + \frac{ν}{c}) = 60 γ + (60 γ - ω_{23}) \frac{ν}{c},

(13)

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ρ = ρ^{(0)} + ρ^{(+)} e^{- i ({\overset{⇀}{k}}_{p} - \overset{⇀}{k}) \cdot \overset{⇀}{R}} e^{i Δ t} + ρ^{(-)} e^{i ({\overset{⇀}{k}}_{p} - \overset{⇀}{k}) \cdot \overset{⇀}{R}} e^{- i Δ t} .

(14)

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References (24)

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Shangqing Liang, Yunfei Xu, Qiang Lin. Simultaneous electromagnetically induced transparency and absorption in thermal atomic medium[J]. Chinese Optics Letters, 2017, 15(9): 090201

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