三能级钾原子气体三维傅里叶变换频谱的解析解  

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

作　　者：赵超樱[1,2] 谭维翰 Zhao Chao-Ying;Tan Wei-Han(School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,China;State Key Laboratory of Quantum Optics and Quantum Optics Devices,Institute of Opto-Electronics,Shanxi University,Taiyuan 030006,China;Department of Physics,Shanghai University,Shanghai 200444,China)

机构地区：[1]杭州电子科技大学理学院,杭州310018 [2]山西大学光电研究所,量子光学与光量子器件国家重点实验室,太原030006 [3]上海大学物理系,上海200444

出　　处：《物理学报》2020年第2期46-53,共8页Acta Physica Sinica

基　　金：国家自然科学基金青年科学基金(批准号:11504074);教育部量子光学重点实验室(批准号:KF201801)资助的课题~~

摘　　要：利用投影切片定理、傅里叶位移定理和误差函数给出三能级钾原子气体三维傅里叶变换频谱在T=0界面的解析解.固定均匀线宽,非均匀展宽和对角线相关系数可以定量地识别,通过在适当方向上拟合三维傅里叶变换频谱谱峰的切片来确定.结果表明,非均匀展宽增大,频谱图沿着对角线方向延伸,对角线相关系数增大,频谱图逐渐变圆,振幅也逐渐变小.With the development of laser technology in the field of optics,ultra-fast optics has become an important research field.Compared with the traditional technology,ultrafast optics can be realized not only under shorter pulse function,but also on a smaller scale,which can more quickly reflect the dynamic process.We present an analytical calculation of the full three-dimensional(3 D)coherent spectrum with a finite duration twodimensional(2 D)Gaussian pulse envelope.Our starting point is the solution of the optical Bloch equations for three-level potassium atomic gas in the 3 D time domain by using the projection-slice theorem,error function and Fourier-shift theorem of 3 D Fourier transform.These principles are used to calculate and simplify the third-order polarization equation generated by the device,and the analytical calculation of three-dimensional Fourier transform frequency spectrum at T=0 is obtained.We simulate the analytic solution by using mathematics software.By comparing the simulations with the experimental results,with the homogeneous linewidth fixed,we can obtain the relationship among the in-homogeneous broadening,the correlation diagonal coefficients and the three-dimensional spectrum characteristics,which can be identified quantitatively by fitting the slices of three-dimensional Fourier transform spectrum peaks in an appropriate direction.The results show that the three-dimensional Fourier transform spectrum will extend along the diagonal direction with the increasing of the in-homogeneous broadening,and the spectrogram progressively becomes a circle with the increasing of the diagonal correlation coefficient,and the amplitude also gradually turns smaller.According to the analytical solution,we give a complete two-dimensional spectrum of the T=0 interface.The results can be fit to the experimental 3 D coherent spectrum for arbitrary inhomogeneity.

关 键 词：傅里叶变换谱 四波混频 原子气体 

分 类 号：O562.3[理学—原子与分子物理]