飞秒激光场中原子所受光学偶极力研究
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摘要
通过求解全波矢布洛赫方程研究了两能级原子与飞秒超快激光脉冲的相互作用过程,计算了不同拉比频率取值下原子所受光学偶极力和粒子数布居随时间的演化情况,分析了光场失谐量对光学势分布情况的影响.研究发现:由飞秒激光场产生的横向光力的时间平均值并不等于零,而是随着拉比频率的增加呈现振荡的增大趋势;纵向光力的时间平均作用也并非是拉比频率的单调函数,而是随着拉比频率的增加呈现周期性的振荡分布特性;光学势的分布对光场的失谐量具有明显的依赖性,随着失谐量的变化,光学势的性质也随之发生了改变.
In 2011, Kumar et al.(2011 Phys. Rev. A 84 043402) studied the light force acting on a beam of neutral two-level atoms superimposed on a few-cycle-pulse Gaussian laser field under both resonant and off-resonant conditions by solving the optical Bloch equation beyond the rotating-wave approximation, and they found that under resonant condition the transverse component of the light force shows oscillatory behavior but vanishes when a time average is taken, and the time averaged longitudinal force is nonzero only when the Rabi frequency is smaller than the resonant frequency and vanishes when the Rabi frequency is equal to or larger than the resonant frequency.In this paper, we investigate further the strong nonlinear optical interaction between a two-level atomic system and a femtosecond Gaussian laser pulse by solving numerically the full-wave optical Bloch equations through using the predictor-corrector method. It is found that the light forces and the light potentials are sensitive to the value of the Rabi frequency and the detuning of the laser field. Under the resonant condition,the instant light forces induced by the femtosecond laser pulse change their signs as a function of time. The instant longitudinal light force changes its sign at twice the Rabi frequency, while the instant transverse light force changes its sign at twice the light carrier-wave frequency. However, none of the time-averaged light forces is zero, showing periodical oscillation characters as a function of Rabi frequency. Both of the time-averaged longitudinal and transverse light forces oscillate at the Rabi frequency corresponding to the pulse area of 2 π.The time-averaged transverse light force shows also a trend of enhancement with Rabi frequency increasing, and the time-averaged longitudinal light force shows also a saturation trend with the increase of the Rabi frequency.The optical potential depends strongly on the detuning. It changes gradually from repulsive potential to attractive potential when the detuning defined here changes from negative to positive detuning. When the field is nearly resonant, the optical potential then oscillates between repulsive and attractive potentials. Therefore,neutral atoms can be focused, defocused, trapped, splitted or steered by the femtosecond laser field with appropriate detuning and Rabi frequency.
In 2011, Kumar et al.(2011 Phys. Rev. A 84 043402) studied the light force acting on a beam of neutral two-level atoms superimposed on a few-cycle-pulse Gaussian laser field under both resonant and off-resonant conditions by solving the optical Bloch equation beyond the rotating-wave approximation, and they found that under resonant condition the transverse component of the light force shows oscillatory behavior but vanishes when a time average is taken, and the time averaged longitudinal force is nonzero only when the Rabi frequency is smaller than the resonant frequency and vanishes when the Rabi frequency is equal to or larger than the resonant frequency.In this paper, we investigate further the strong nonlinear optical interaction between a two-level atomic system and a femtosecond Gaussian laser pulse by solving numerically the full-wave optical Bloch equations through using the predictor-corrector method. It is found that the light forces and the light potentials are sensitive to the value of the Rabi frequency and the detuning of the laser field. Under the resonant condition,the instant light forces induced by the femtosecond laser pulse change their signs as a function of time. The instant longitudinal light force changes its sign at twice the Rabi frequency, while the instant transverse light force changes its sign at twice the light carrier-wave frequency. However, none of the time-averaged light forces is zero, showing periodical oscillation characters as a function of Rabi frequency. Both of the time-averaged longitudinal and transverse light forces oscillate at the Rabi frequency corresponding to the pulse area of 2 π.The time-averaged transverse light force shows also a trend of enhancement with Rabi frequency increasing, and the time-averaged longitudinal light force shows also a saturation trend with the increase of the Rabi frequency.The optical potential depends strongly on the detuning. It changes gradually from repulsive potential to attractive potential when the detuning defined here changes from negative to positive detuning. When the field is nearly resonant, the optical potential then oscillates between repulsive and attractive potentials. Therefore,neutral atoms can be focused, defocused, trapped, splitted or steered by the femtosecond laser field with appropriate detuning and Rabi frequency.
引文
[1]Meystre P 2001 Atom Optics(New York:Springer)p1
[2]Yin J P 2012 Atomic Optics:Basic Concepts,Principles,Techniques and Applications(Shanghai:Shanghai Jiao Tong University Press)p12(in Chinese)[印建平2012原子光学-基本概念、原理、技术及其应用(上海:上海交通大学出版社)p12]
[3]Ashkin A 1970 Phys.Rev.Lett.24 156
[4]H?nsch T W,Schawlow A L 1975 Opt.Commun.13 68
[5]Chu S,Hollberg L,Bjorkholm J E,Cable A,Ashkin A 1985Phys.Rev.Lett.55 48
[6]Anderson M H,Ensher J R,Matthews M R,Wieman C E,Cornell E A 1995 Science 269 198
[7]Davis K B,Mewes M O,Andrews M R,van Druten N J,Durfee D S,Kurn D M,Ketterle W 1995 Phys.Rev.Lett.753969
[8]Cheuk L W,Nichols M A,Okan M,Gersdorf T,Ramasesh VV,Bakr W S,Lompe T,Zwierlein M W 2015 Phys.Rev.Lett.114 193001
[9]Parsons M F,Huber F,Mazurenko A,Chiu C S,Setiawan W,Wooley-Brown K,Blatt S,Greiner M 2015 Phys.Rev.Lett.114 213002
[10]Haller E,Hudson J,Kelly A,Cotta D A,Peaudecerf B,Bruce G D,Kuhr S 2015 Nat.Phys.11 738
[11]Wang Y Q 2007 Laser Cooling and Trapping of Atoms(Beijing:Beijing University Press)p101(in Chinese)[王义遒2007原子的激光冷却与陷俘(北京:北京大学出版社)p101]
[12]Metcalf H 2017 Rev.Mod.Phys.89 041001
[13]van der Straten P,Metcalf H 2016 Atoms and Molecules Interacting with Light(Cambridge:Cambridge University Press)p1
[14]Jiang Y,Narushima T,Okamoto H 2010 Nat.Phys.6 1005
[15]Garbin V,Cojoc D,Ferrari E,Proietti R Z,Cabrini S,Fabrizio E D 2005 Jpn.J.Appl.Phys.44 5773
[16]Eichmann U,Nubbemeyer T,Rottke H,Sandner W 2009Nature 461 1261
[17]Kumar P,Sarma A K 2012 Phys.Rev.A 86 053414
[18]Kumar P,Sarma A K 2014 Phys.Rev.A 89 033422
[19]Cai X,Lin Q 2013 Eur.Phys.J.D 67 246
[20]Allen L,Eberly J H 1987 Optical Resonance and Two-Level Atoms(New York:Dover Publications,Inc)p41
[21]Zhang Q,Jin K,Tang Y H,Qu G H 2011 Acta Phys.Sin.60053204(in Chinese)[张琴,金康,唐远河,屈光辉2011物理学报60 053204]
[22]Wang Z L,Yin J P 2008 Chin.Phys.B 17 2466
[23]Xing J,Chen X,Zhu S,Zhang R 2003 Chin.Opt.Lett.1 122
[24]Kumar P,Sarma A K 2011 Phys.Rev.A 84 043402
[25]Lembessis V E,Ellinas D 2005 J.Opt.B:Quant.Sem.Opt.7319
[26]Liu B,Jin G,Sun R,He J,Wang J 2017 Opt.Express 2515861
[27]Han Y C 2017 J.Phys.B:At.Mol.Opt.Phys.50 225401
[28]Liu J C,Wang C K,Gel’mukhanov F 2007 Phys.Rev.A 76043422
[29]Cai X,Zheng J,Lin Q 2013 Phys.Rev.A 87 043401
[30]Boyd R W 2010 Nonlinear Optics(Singapore:Elsevier Pte Ltd)p158
[31]Liu J C,Guo F F,Zhao Y N,Li X Z 2018 Chin.Phys.B 27104209
[32]Liu J C,Zhang Y Q,Chen L 2014 J.Mod.Opt.61 781
[33]Liu J C,Zhao K,Song Y Z,Wang C K 2006 Acta Phys.Sin.55 1803(in Chinese)[刘纪彩,赵珂,宋玉志,王传奎2006物理学报55 1803]
[34]Liu J C,Sun Y P,Wang C K,?gren H,Gel’mukhanov F2010 Phys.Rev.A 81 043412
[35]Sun Y P,Liu J C,Wang C K,Ge’lmukhanov F 2010 Phys.Rev.A 81 013812
[36]Butt H J,Cappella B,Kappl M 2005 Surf.Sci.Rep.59 1
[37]Sukhov S V 2018 J.Commun.Technol.Electr.63 1137
[38]Florin E L,Pralle A,H?rber J K,Stelzer E H K 1997 J.Stru.Bio.119 202
[39]Munday J N,Capasso F,Parsegian V A 2009 Nature 457 170
[40]Antognozzi M,Bermingham C R,Harniman R L,Simpson S,Senior J,Hayward R,Hoerber H,Dennis M R,Bekshaev AY,Bliokh K Y,Nori F 2016 Nat.Phys.12 731
[41]Tumkur T,Yang X,Zhang C,Yang J,Zhang Y,Naik G V,Nordlander P,Halas N J 2018 Nano Lett.18 2040
[42]Guan D,Hang Z H,Marcet Z,Liu H,Kravchenko I I,Chan C T,Chan H B,Tong P 2016 Sci.Rep.5 16216
[43]Jahng J,Ladani F T,Khan R M,Li X,Lee E S,Potma E O2015 Opt.Lett.40 5058
[2]Yin J P 2012 Atomic Optics:Basic Concepts,Principles,Techniques and Applications(Shanghai:Shanghai Jiao Tong University Press)p12(in Chinese)[印建平2012原子光学-基本概念、原理、技术及其应用(上海:上海交通大学出版社)p12]
[3]Ashkin A 1970 Phys.Rev.Lett.24 156
[4]H?nsch T W,Schawlow A L 1975 Opt.Commun.13 68
[5]Chu S,Hollberg L,Bjorkholm J E,Cable A,Ashkin A 1985Phys.Rev.Lett.55 48
[6]Anderson M H,Ensher J R,Matthews M R,Wieman C E,Cornell E A 1995 Science 269 198
[7]Davis K B,Mewes M O,Andrews M R,van Druten N J,Durfee D S,Kurn D M,Ketterle W 1995 Phys.Rev.Lett.753969
[8]Cheuk L W,Nichols M A,Okan M,Gersdorf T,Ramasesh VV,Bakr W S,Lompe T,Zwierlein M W 2015 Phys.Rev.Lett.114 193001
[9]Parsons M F,Huber F,Mazurenko A,Chiu C S,Setiawan W,Wooley-Brown K,Blatt S,Greiner M 2015 Phys.Rev.Lett.114 213002
[10]Haller E,Hudson J,Kelly A,Cotta D A,Peaudecerf B,Bruce G D,Kuhr S 2015 Nat.Phys.11 738
[11]Wang Y Q 2007 Laser Cooling and Trapping of Atoms(Beijing:Beijing University Press)p101(in Chinese)[王义遒2007原子的激光冷却与陷俘(北京:北京大学出版社)p101]
[12]Metcalf H 2017 Rev.Mod.Phys.89 041001
[13]van der Straten P,Metcalf H 2016 Atoms and Molecules Interacting with Light(Cambridge:Cambridge University Press)p1
[14]Jiang Y,Narushima T,Okamoto H 2010 Nat.Phys.6 1005
[15]Garbin V,Cojoc D,Ferrari E,Proietti R Z,Cabrini S,Fabrizio E D 2005 Jpn.J.Appl.Phys.44 5773
[16]Eichmann U,Nubbemeyer T,Rottke H,Sandner W 2009Nature 461 1261
[17]Kumar P,Sarma A K 2012 Phys.Rev.A 86 053414
[18]Kumar P,Sarma A K 2014 Phys.Rev.A 89 033422
[19]Cai X,Lin Q 2013 Eur.Phys.J.D 67 246
[20]Allen L,Eberly J H 1987 Optical Resonance and Two-Level Atoms(New York:Dover Publications,Inc)p41
[21]Zhang Q,Jin K,Tang Y H,Qu G H 2011 Acta Phys.Sin.60053204(in Chinese)[张琴,金康,唐远河,屈光辉2011物理学报60 053204]
[22]Wang Z L,Yin J P 2008 Chin.Phys.B 17 2466
[23]Xing J,Chen X,Zhu S,Zhang R 2003 Chin.Opt.Lett.1 122
[24]Kumar P,Sarma A K 2011 Phys.Rev.A 84 043402
[25]Lembessis V E,Ellinas D 2005 J.Opt.B:Quant.Sem.Opt.7319
[26]Liu B,Jin G,Sun R,He J,Wang J 2017 Opt.Express 2515861
[27]Han Y C 2017 J.Phys.B:At.Mol.Opt.Phys.50 225401
[28]Liu J C,Wang C K,Gel’mukhanov F 2007 Phys.Rev.A 76043422
[29]Cai X,Zheng J,Lin Q 2013 Phys.Rev.A 87 043401
[30]Boyd R W 2010 Nonlinear Optics(Singapore:Elsevier Pte Ltd)p158
[31]Liu J C,Guo F F,Zhao Y N,Li X Z 2018 Chin.Phys.B 27104209
[32]Liu J C,Zhang Y Q,Chen L 2014 J.Mod.Opt.61 781
[33]Liu J C,Zhao K,Song Y Z,Wang C K 2006 Acta Phys.Sin.55 1803(in Chinese)[刘纪彩,赵珂,宋玉志,王传奎2006物理学报55 1803]
[34]Liu J C,Sun Y P,Wang C K,?gren H,Gel’mukhanov F2010 Phys.Rev.A 81 043412
[35]Sun Y P,Liu J C,Wang C K,Ge’lmukhanov F 2010 Phys.Rev.A 81 013812
[36]Butt H J,Cappella B,Kappl M 2005 Surf.Sci.Rep.59 1
[37]Sukhov S V 2018 J.Commun.Technol.Electr.63 1137
[38]Florin E L,Pralle A,H?rber J K,Stelzer E H K 1997 J.Stru.Bio.119 202
[39]Munday J N,Capasso F,Parsegian V A 2009 Nature 457 170
[40]Antognozzi M,Bermingham C R,Harniman R L,Simpson S,Senior J,Hayward R,Hoerber H,Dennis M R,Bekshaev AY,Bliokh K Y,Nori F 2016 Nat.Phys.12 731
[41]Tumkur T,Yang X,Zhang C,Yang J,Zhang Y,Naik G V,Nordlander P,Halas N J 2018 Nano Lett.18 2040
[42]Guan D,Hang Z H,Marcet Z,Liu H,Kravchenko I I,Chan C T,Chan H B,Tong P 2016 Sci.Rep.5 16216
[43]Jahng J,Ladani F T,Khan R M,Li X,Lee E S,Potma E O2015 Opt.Lett.40 5058