铯原子高里德堡态Stark结构
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摘要
Stark效应是原子分子能级在电场作用下发生分裂和移动的现象,已有许多关于原子的Stark效应的研究报道,也有许多应用Stark效应的研究报道。由于Stark效应与主量子数n有关,n越大,效应越明显,所以高n的里德堡态是Stark效应的主要研究对象。本文从理论和实验两方面详细研究了碱金属铯原子的Stark能级结构,给出了详细的计算方法,对实验结果进行了详细分析讨论。
理论计算采用量子力学中的微扰理论。碱金属原子高里德堡态的电子行为与氢原子非常类似,最大的差别在于前者为多电子原子,其能级公式要加入量子亏损进行修正,这导致碱金属原子的径向波函数不同于氢原子,而角度波函则完全相同。我们采用了目前最新的(最精确的)无外场时的能级数据,使用Fortran90和Mathematic软件编程计算。对氢原子的径向波函数做了数值计算以便与解析结果对比验证计算的精确度。铯原子是重原子,精细结构分裂较大,所以在计算中考虑了电子自旋使能级的分裂。n=15附近的计算结果与Daniel Kleppner的结果一致。n越大,计算时需要考虑的波函数(能级)越多,大约是n的几十倍,所以高n的计算需要对角化更高阶的矩阵。我们计算的n=35,磁量子数丨m丨=1/2的结果中大约当电场小于35V/cm时,外加静电场使能级产生分裂和移动,移动大小与场强近似成线性关系,相邻的能级开始靠近。当场强大于35V/cm时,产生非线性Stark效应,相邻能级靠的很近,但并未交叉。而氢原子的Stark能级是可以交叉的。这是两者的最大差别之一。
目前的实验研究一般都是先将原子激发到nS_(1/2)态,然后再激发到主量子数n较高的里德堡态。根据选择规则Δm=0,±1,则Stark高里德堡态将是丨m丨=1/2,3/2的态。若最后激发光的偏振方向平行于电场方向,则获得丨m丨=1/2的态,若垂直于电场方向,则获得m=3/2的Stark态。更普遍的情况是首先将原子激发到非S的态,譬如P,D,F,G等原子态,然后再激发到高里德堡态,那么根据选择规则多个丨m丨不等的态将被同时观察到。本文的实验工作是在超冷铯原子中完成,采用垂直于电场方向的偏振光激发。由于俘获光和再泵浦光已将原子激发到6P_(3/2)态,所以用偏振方向垂直于电场的脉冲燃料激光激发原子可以到达丨m丨=1/2,3/2和5/2的高里德堡态,这些态的原子再吸收一个燃料激光光子即被电离,这种方法称为共振增强多光子电离。通过探测离子信号获得丨m丨=1/2,3/2和5/2的高里德堡态信号。由于丨m丨=1/2,3/2和5/2的态对光谱的共同贡献,观察到的谱线产生了较大加宽。在适当的场强下,精细结构分量变的可以分辨。对铯原子n=14到n=19范围内的能级结构的数值计算结果与实验结果获得很好一致。
The Stark effect is the phenomena that the energy-levels of atoms or molecules split and shift in an external electric field.This makes it is easy to carry out the energy resonance transfer,which have been extensively applied in molecular refrigeration and quantum calculation realm.There are many reports about Stark effect and its application.Because Stark effect is related with main quantum number n,the bigger n,the more evidence effect,high n Rydberg states are chose as object of studying.This paper investigates the cesium atom Stark structures not only theoretically but also experimentally in an ultracold gas.The detailed calculate method was present and the calculated and experimental results were analyzed and discussed in detail.
The calculation method uses the perturbation theories of quantum mechanics.The alkali metals atom at high n Rydberg state is very similar in the electronic behavior with the hydrogen atom.The main difference is alkali metal atoms have more electrons,and the quantum deficiency has to be used to correct energy formula,which makes the radial wave function of the alkali metal atom different from the hydrogen atom,however the angle wave function is the same.We used latest(the most accurate) zero field energy level data and Fortran90 and Mathematic4.0 software to perform the calculation.The comparisons between numerical and analyzed calculation results for the radial wave function and Stark structure of hydrogen atom were made in order to verify our numerical calculation accuracy.The cesium atom is a heavy atom,the fine structure splitting need to be considered.Our calculated Stark structure for cesium atom n=15 is in good agreement with Daniel Kleppner's.The bigger n is,the more wave functions(energy level) need to be considered,so the calculation of higher n Stark structure needs to diagonalize the much higher order matrix.In the Stark structure of n=35 and |m|=1/2,when electric field is smaller than 35 V/cm,the shifting and splitting is appreciatively in direct proportion to the static electric field.When field is greater than 35 V/cm,nonlinear Stark effects generate.The neighbor n levels become very close,but not cross.
In general,experimental studying takes two or much steps to excite atoms to S state,and then re-excite them to higher n Rydberg state.Because of the select ruleΔm=0,±1,the final Stark states is m=0,±1 state.If the last exciting light polarization is parallel to the electric field direction,we will obtain |m|=1/2 states.If light polarization is perpendicular to the electric field direction,then m=3/2 Stark state will be observed.The more usual circumstance is that the atom populate to non-S state first,like P,D,F,G etc., then excited to high n Rydberg state.So according to select rules different |m| the state will be observed in the meantime.Our experiment works are performed in an untracold cesium atom.At first we excited atoms at ground state to 6~2p_(3/2) state by trapping laser or re-pumping laser,and then re-excite them to high n states by a tunable pulsed dye laser which has a perpendicular polarization to the static electric field direction.The |m|=1/2,3/2,and 5/2 mixing Stark spectra were observed by resonance enhanced multiphoton ionization method.Because the spectra are compose of |m|=1/2,3/2 and 5/2 components,spectra linewidth become wider.At appropriate field intensity, the fine structure component can be distinguished.The n=14 to n=19 Stark structures are investigated.Our theoretical and experimental results are in good agreement within error.
理论计算采用量子力学中的微扰理论。碱金属原子高里德堡态的电子行为与氢原子非常类似,最大的差别在于前者为多电子原子,其能级公式要加入量子亏损进行修正,这导致碱金属原子的径向波函数不同于氢原子,而角度波函则完全相同。我们采用了目前最新的(最精确的)无外场时的能级数据,使用Fortran90和Mathematic软件编程计算。对氢原子的径向波函数做了数值计算以便与解析结果对比验证计算的精确度。铯原子是重原子,精细结构分裂较大,所以在计算中考虑了电子自旋使能级的分裂。n=15附近的计算结果与Daniel Kleppner的结果一致。n越大,计算时需要考虑的波函数(能级)越多,大约是n的几十倍,所以高n的计算需要对角化更高阶的矩阵。我们计算的n=35,磁量子数丨m丨=1/2的结果中大约当电场小于35V/cm时,外加静电场使能级产生分裂和移动,移动大小与场强近似成线性关系,相邻的能级开始靠近。当场强大于35V/cm时,产生非线性Stark效应,相邻能级靠的很近,但并未交叉。而氢原子的Stark能级是可以交叉的。这是两者的最大差别之一。
目前的实验研究一般都是先将原子激发到nS_(1/2)态,然后再激发到主量子数n较高的里德堡态。根据选择规则Δm=0,±1,则Stark高里德堡态将是丨m丨=1/2,3/2的态。若最后激发光的偏振方向平行于电场方向,则获得丨m丨=1/2的态,若垂直于电场方向,则获得m=3/2的Stark态。更普遍的情况是首先将原子激发到非S的态,譬如P,D,F,G等原子态,然后再激发到高里德堡态,那么根据选择规则多个丨m丨不等的态将被同时观察到。本文的实验工作是在超冷铯原子中完成,采用垂直于电场方向的偏振光激发。由于俘获光和再泵浦光已将原子激发到6P_(3/2)态,所以用偏振方向垂直于电场的脉冲燃料激光激发原子可以到达丨m丨=1/2,3/2和5/2的高里德堡态,这些态的原子再吸收一个燃料激光光子即被电离,这种方法称为共振增强多光子电离。通过探测离子信号获得丨m丨=1/2,3/2和5/2的高里德堡态信号。由于丨m丨=1/2,3/2和5/2的态对光谱的共同贡献,观察到的谱线产生了较大加宽。在适当的场强下,精细结构分量变的可以分辨。对铯原子n=14到n=19范围内的能级结构的数值计算结果与实验结果获得很好一致。
The Stark effect is the phenomena that the energy-levels of atoms or molecules split and shift in an external electric field.This makes it is easy to carry out the energy resonance transfer,which have been extensively applied in molecular refrigeration and quantum calculation realm.There are many reports about Stark effect and its application.Because Stark effect is related with main quantum number n,the bigger n,the more evidence effect,high n Rydberg states are chose as object of studying.This paper investigates the cesium atom Stark structures not only theoretically but also experimentally in an ultracold gas.The detailed calculate method was present and the calculated and experimental results were analyzed and discussed in detail.
The calculation method uses the perturbation theories of quantum mechanics.The alkali metals atom at high n Rydberg state is very similar in the electronic behavior with the hydrogen atom.The main difference is alkali metal atoms have more electrons,and the quantum deficiency has to be used to correct energy formula,which makes the radial wave function of the alkali metal atom different from the hydrogen atom,however the angle wave function is the same.We used latest(the most accurate) zero field energy level data and Fortran90 and Mathematic4.0 software to perform the calculation.The comparisons between numerical and analyzed calculation results for the radial wave function and Stark structure of hydrogen atom were made in order to verify our numerical calculation accuracy.The cesium atom is a heavy atom,the fine structure splitting need to be considered.Our calculated Stark structure for cesium atom n=15 is in good agreement with Daniel Kleppner's.The bigger n is,the more wave functions(energy level) need to be considered,so the calculation of higher n Stark structure needs to diagonalize the much higher order matrix.In the Stark structure of n=35 and |m|=1/2,when electric field is smaller than 35 V/cm,the shifting and splitting is appreciatively in direct proportion to the static electric field.When field is greater than 35 V/cm,nonlinear Stark effects generate.The neighbor n levels become very close,but not cross.
In general,experimental studying takes two or much steps to excite atoms to S state,and then re-excite them to higher n Rydberg state.Because of the select ruleΔm=0,±1,the final Stark states is m=0,±1 state.If the last exciting light polarization is parallel to the electric field direction,we will obtain |m|=1/2 states.If light polarization is perpendicular to the electric field direction,then m=3/2 Stark state will be observed.The more usual circumstance is that the atom populate to non-S state first,like P,D,F,G etc., then excited to high n Rydberg state.So according to select rules different |m| the state will be observed in the meantime.Our experiment works are performed in an untracold cesium atom.At first we excited atoms at ground state to 6~2p_(3/2) state by trapping laser or re-pumping laser,and then re-excite them to high n states by a tunable pulsed dye laser which has a perpendicular polarization to the static electric field direction.The |m|=1/2,3/2,and 5/2 mixing Stark spectra were observed by resonance enhanced multiphoton ionization method.Because the spectra are compose of |m|=1/2,3/2 and 5/2 components,spectra linewidth become wider.At appropriate field intensity, the fine structure component can be distinguished.The n=14 to n=19 Stark structures are investigated.Our theoretical and experimental results are in good agreement within error.
引文
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[2]Okada T,Andou H,Moriyama Y et al.Sensitive photon detector based on selective laser ionization.Opt.Lett.,1989,14,987.
[3]Liu B,Wang J,Liu Wet al.The Theoretical and Experimental Investigation of Stark Structure in Sodium Rydberg States Atoms.Chinese Journal of Lasers,1993,B2,429.
[4]H.L.Bethlem and G.Meijer,Int.Rev.Phys.Chem.2003 22,73.
[5]E.Vliegen,S.D.Hogan,H.Schmutz,and F.Merkt,Phys.Rev.A.2007 76,023405.
[6]B.J.Bichsel,M.A.Morrison,N.Shafer-Ray,and E.R.I.Abraham,Phys.Rev.A 2007 75,023410.
[7]V.P.Gavrilenko,H.J.Kim,T.Ikutake,J.B.Kim,Y.W.Choi,M.D.Bowden and Muraoka,Phys.Rev.E,2000 62,7201.
[8]T.Kampschulte,J.Schulze,D.Luggenholscher,M.D.Bowden and U.Czarnetzki,New J.Phys.2007 9,18.
[9]T.Jiang,M.D.Bowden,E.Wagenaars,E.Stoffels and G.M.W.Kroesen,New J.Phys.2006 8,202.
[10]U.Czarnetzki,D.Luggenh(o丨¨)lscher and H.F.D(o丨¨)bele,Phys.Rev.Lett.1998 81,4592.
[11]S.Ritter,P.Gartner,N.Baer,and F.Jahnke,Phys.Rev.B 2007 76,165302.
[12]S.N.Pisharody,J.G.Zeibel,and R.R.Jones,Phys.Rev.A,2000 61,063405.
[13]胡正发,柳晓军,周士康,龚顺生,詹明生.里德堡态铯原子的Stark效应的实验研究.量子电子学报,2000,17,301.
[14]Zimmerman M L,Littman M G,Kash M M et al.Stark Structure of the Rydberg State of Alkali-metal Atoms.Phys.Rev.A,1979,20,2251.
[15]Littman M G,Kash M M,Kleppner K.Field-ionization Processes in Excited Atom.Phys.Rev.Lett.,1978,41,103.
[16] Feneuille S, Liberman S, Pinard J et al. Observation of fano profiles in photoionization of Rubidium in the presence of a dc field. Phys. Rev. Lett., 1979,42,1404.
[17] T. F. Gallagher. Rydberg Atoms. Cambridge, Cambridge University Press, 1994. [18] S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable. A. Ashkin. Atomic velocity selection using stimulated Raman transitions. Phys. Rev. Lett., 1985,66,2297.
[19] D. Sesko, C. G. Fan, C. E. Wieman. Production of a cold atomic vapor using diode-laser cooling. J. Opt. Soc. Am. B ,1988,5,1225.
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