Analytical solution of three-dimensional Fourier transform frequency spectrum for three-level potassium atomic gas

Chao-Ying Zhao; Wei-Han Tan

doi:10.7498/aps.69.20190964

Journals >Acta Physica Sinica >Volume 69 >Issue 2 >Page 020201-1 > Article

Acta Physica Sinica
Vol. 69, Issue 2, 020201-1 (2020)

Analytical solution of three-dimensional Fourier transform frequency spectrum for three-level potassium atomic gas

Chao-Ying Zhao^1、2、* and Wei-Han Tan³

Author Affiliations

¹School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China

²State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

³Department of Physics, Shanghai University, Shanghai 200444, China

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DOI: 10.7498/aps.69.20190964 Cite this Article

Chao-Ying Zhao, Wei-Han Tan. Analytical solution of three-dimensional Fourier transform frequency spectrum for three-level potassium atomic gas[J]. Acta Physica Sinica, 2020, 69(2): 020201-1 Copy Citation Text

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Fig. 1. Four wave mixing schematic.四波混频原理图

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(a) 2D time; (b) frequency coordinates for photon echo signals; (c) 2D time projection onto the diagonal corresponding to a slice along ; (d) 2D time projection onto the cross diagonal corresponding to a slice along .(a) 二维时域; (b) 光子回波信号的频率坐标; (c) 二维时域投影在对应于沿的切片的对角线上; (d)沿的切片对应的交叉对角线上的二维时域投影

Fig. 2. (a) 2D time; (b) frequency coordinates for photon echo signals; (c) 2D time projection onto the diagonal corresponding to a slice along ; (d) 2D time projection onto the cross diagonal corresponding to a slice along . (a) 二维时域; (b) 光子回波信号的频率坐标; (c) 二维时域投影在对应于沿的切片的对角线上; (d)沿的切片对应的交叉对角线上的二维时域投影

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Fig. 3. The three-dimensional Fourier transform spectrum with , , : (a) Real part; (b) imaginary part; (c) module. 当 , , 时频谱图　(a)实部; (b)虚部; (c)模

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Fig. 4. The three-dimensional Fourier transform spectrum with , , : (a) Real part; (b) imaginary part; (c) module. 当 , , 时频谱图　(a)实部; (b)虚部; (c)模

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Fig. 5. The three-dimensional Fourier transform spectrum with , , 0.05 THz, : (a) Real part; (b) imaginary part; (c) module. 当 , , , 时频谱图　(a)实部; (b)虚部; (c)模

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Fig. 6. The three-dimensional Fourier transform spectrum with , , 0.05 THz, (a) Real part; (b) imaginary part; (c) module. 当 , , , 时频谱图　(a)实部; (b)虚部; (c)模

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Fig. 7. Three-dimensional Fourier transform spectrum: (a) Fig. 5(a) in Ref. [11], , 0.2 THz; (b) ; (c) . 三维傅里叶转换频谱图　(a) 参考文献[11]中的图5(a), , , (b) ; (c)

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Fig. 8. The three-dimensional Fourier transform spectrum with , , for different R: (a) ; (b) . R不同时, 三维傅里叶转换频谱, , , 　(a) ; (b)

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	x	y	z
${\text{δ}} {\omega _{10}} = {\text{δ}} {\omega _{20}}$, $R = {\rm{1}}$	0	${\rm{4}}{\text{δ}} \omega _{10}^2$	0
${\text{δ}} {\omega _{10}} = {\text{δ}} {\omega _{20}}$, $R \ne {\rm{1}}$	$2\left( {1 - R} \right){\text{δ}} \omega _{10}^2$	$2\left( {{\rm{1}} + R} \right){\text{δ}} \omega _{10}^2$	0
${\text{δ} } {\omega _{10} } = m{\text{δ} } {\omega _{20} },$$R = {\rm{1}}$	${\left(1 - \dfrac{1}{m}\right)^2}{\text{δ}} \omega _{10}^2$	${\left(1 + \dfrac{1}{m}\right)^2}{\text{δ}} \omega _{10}^2$	$\left(1- \dfrac{1}{{{m^2}}}\right){\text{δ}} \omega _{10}^2$
${\text{δ} } {\omega _{10} } = m{\text{δ} } {\omega _{20} },$$R \ne {\rm{1}}$	$\dfrac{{({m^2} - 2 Rm + 1)}}{{{m^2}}}{\text{δ}} \omega _{10}^2$	$\dfrac{{({m^2} + 2 Rm + 1)}}{{{m^2}}}{\text{δ}} \omega _{10}^2$	$\left(1 - \dfrac{1}{{{m^2}}}\right){\text{δ}} \omega _{10}^2$

Table 1. The relation between in-homogeneous line-width and the diagonal correlation coefficient.

Chao-Ying Zhao, Wei-Han Tan. Analytical solution of three-dimensional Fourier transform frequency spectrum for three-level potassium atomic gas[J]. Acta Physica Sinica, 2020, 69(2): 020201-1

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