H2+在强激光脉冲作用下的电离率和原子核间距的关系

俞祖卿; 杨魏吉; 何峰

doi:10.7498/aps.65.204202

摘要

本文利用蒙特卡罗方法模拟电子在激光场以及分子库仑势作用下的经典轨迹，研究了氢分子离子H2+的电离率和原子核间距的关系，为电荷共振电离增强现象提供了一种基于电子经典运动的解释.当原子核间距为5–6 a.u.时，H2+的电离率显著增大.电子的运动轨迹揭示此时电子先围绕其中一个原子核运动，在逐步获得越来越多的动能后，运动轨迹受到另一个原子核的强烈影响，最后电子逃逸原子核的束缚.原子核之间的库仑势垒和激光调制的库仑势垒的高度差与电离率的大小直接相关.

关键词:

Abstract

Ionizations of atoms and molecules in strong laser fields are fundamental processes of ultrafast physics. Compared with atom ionization, molecular ionization is very complex due to the existence of multi Coulomb centers. As a simplest molecule, H2+ has been widely used to explore new phenomena of molecules in strong laser fields. One of the notable processes in H2+ ionization is charge resonance enhanced ionization (CREI), in which the ionization rate is enhanced substantially when the internuclear distances are around 6 a.u. and 10 a.u. CREI has been extensively studied by numerically simulating the time-dependent Schrödinger equation. While quantum calculations provide accurate ionization rates, the mechanism governing the CREI is not revealed in such ab-initio calculations. On the contrary, the calculations based on the classical trajectories Monte-Carlo assembly may offer an intuitive picture for CREI though some quantum information is not included. In this paper, we revisit the CREI of H2+ in a strong infrared laser field by Monte-Carlo simulation. By initializing ten-thousand classical points whose initial positions and velocities satisfy the field-free Hamiltonian of H2+, we solve the classical Newtonian equation and obtain the trajectories of all particles, from which one may analyze the particle velocities, energies, etc. We count the ionization events by diagnosing the particle energy after the laser interaction. If the sum of the kinetic energy and potential energy is larger than 0, we set it as an ionization event. The ionization rate is calculated by collecting all ionization events and normalizing it with the total particle number involved in the calculation. By setting the internuclear distances to be different values, we obtain the ionization rate as a function of internuclear distance. Our simulation shows that the ionization probability is greatly enhanced when the internuclear distance is about 5 to 6 a.u. by employing a 1064 nm, 4×1013 W/cm2, five cycles laser pulse. By tracing the particle trajectory, we find that the electron usually gains the energy from the laser field by circulating one nucleus, then passes through the interatomic barrier and moves around the other nucleus before being ionized. By looking into the relationship between the ionization probability and the laser-distorted Coulomb potential at different internuclear distances, we find that the ionization probability is maximum when the energy difference between the ground state and the interatomic Coulomb barrier, or between the ground state and the saddle value of the laser-distorted potential, is minimum. The classical calculation of the ionization of H2+ interacting with intense laser field reproduces the qualitative features of the corresponding quantum-mechanical calculation. It offers an intuitive physical picture of the tunneling ionization of molecules through investigating the classical trajectories and provides a new perspective to inspect the intriguing phenomena in quantum systems.

Keywords:

作者及机构信息

1.
上海交通大学物理与天文系, 激光等离子体教育部重点实验室, IFSA协同创新中心, 上海 200240

通信作者: 何峰, fhe@sjtu.edu.cn

基金项目: 国家自然科学基金（批准号：11322438，11574205）资助的课题．

Authors and contacts

1.
Key Laboratory for Laser Plasma(Ministry of Education), Collaborative Innovation Center of IFSA(CICIFSA), Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding author: He Feng, fhe@sjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11322438, 11574205).

参考文献

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[7]	Gibson G N, Li M, Guo C, Neira J 1997 Phys. Rev. Lett. 79 2022
[8]	He F, Ruiz C, Becker A 2007 Phys. Rev. Lett. 99 083002
[9]	He F, Becker A, Thumm U 2008 Phys. Rev. Lett. 101 213002
[10]	He F, Thumm U 2010 Phys. Rev. A 81 053413
[11]	He F 2012 Phys. Rev. A 86 063415
[12]	Rankin R, Capjack C E, Burnett N H, Corkum P B 1991 Opt. Lett. 16 835
[13]	Fittinghoff D N, Bolton P R, Chang B, Kulander K C 1992 Phys. Rev. Lett. 69 2642
[14]	Paulus G G, Nicklich W, Zacher F, Lambropoulos P, Walther H 1996 J. Phys. B 29 L249
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[18]	Ben-Itzhak I, Wang P Q, Sayler A M, Carnes K D, Leonard M, Esry B D, Alnaser A S, Ulrich B, Tong X M, Litvinyuk I V, Maharjan C M, Ranitovic P, Osipov T, Ghimire S, Chang Z, Cocke C L 2008 Phys. Rev. A 78 063419
[19]	Xu H, He F, Kielpinski D, Sang R T, Litvinyuk I V 2015 Sci. Rep. 5 13527
[20]	Xin L, Qin H C, Wu W Y, He F 2015 Phys. Rev. A 92 063803
[21]	Liu H, Li M, Xie X G, Wu C, Deng Y K, Wu C Y, Gong Q H, Liu Y Q 2015 Chin. Phys. Lett. 32 063301
[22]	Bocharova I, Karimi R, Penka E F, Brichta J P, Lassonde P, Fu X, Kieffer J C, Bandrauk A D, Litvinyuk I, Sanderson J, Légaré F 2011 Phys. Rev. Lett. 107 063201
[23]	Lötstedt E, Kato T, Yamanouchi K 2012 Phys. Rev. A 85 041402
[24]	Xi C, Chu S 2000 Phys. Rev. A 63 013414
[25]	Plummer M, McCann J F 1996 J. Phys. B:At. Mol. Opt. Phys. 29 4625
[26]	Tsogbayar T, Horbatsch M 2013 J. Phys. B 46 085004
[27]	Rzaewski K, Mewenstein, Salières P 1994 Phys. Rev. A 49 1196
[28]	Grobe R, Law C K 1991 Phys. Rev. A 44 R4114
[29]	Qu W X, Hu S X, Xu Z Z 1998 Acta Phys. Sin. 47 571 (in Chinese)[屈卫星, 胡素兴, 徐至展1998 47 571]
[30]	Balcou Ph, L'Huillier A, Escande D 1996 Phys. Rev. A 53 3456
[31]	Bandarage G, Maquet A, Cooper J 1990 Phys. Rev. A 41 1744
[32]	Cocke S, Reichl L E 1996 Phys. Rev. A 53 1746
[33]	Chelkowski S, Foisy C, Bandrauk A D 1998 Phys. Rev. A 57 1176
[34]	Li M, Geng J W, Liu H, Deng Y, Wu C, Peng L Y, Gong Q H, Liu Y Q 2014 Phys. Rev. Lett. 112 113002
[35]	Duan Y W, Liu W K, Yuan J M 2000 Phys. Rev. A 61 053403

施引文献

[1]	Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
[2]	L'Huillier, Schafer K J, Kulander K C 1991 J. Phys. B 24 3315
[3]	Zhou X X, Li B W 2001 Acta Phys. Sin. 50 1902 (in Chinese)[周效信, 李白文2001 50 1902]
[4]	Sukharev M E, Krainov V P 1998 J. Opt. Soc. Am. B:Opt. Phys. 15 2201
[5]	Winter M, Schmidt R, Thumm U 2009 Phys. Rev. A 80 031401
[6]	Guo C, Li M, Nibarger J P, Gibson G N 1998 Phys. Rev. A 58 R4271
[7]	Gibson G N, Li M, Guo C, Neira J 1997 Phys. Rev. Lett. 79 2022
[8]	He F, Ruiz C, Becker A 2007 Phys. Rev. Lett. 99 083002
[9]	He F, Becker A, Thumm U 2008 Phys. Rev. Lett. 101 213002
[10]	He F, Thumm U 2010 Phys. Rev. A 81 053413
[11]	He F 2012 Phys. Rev. A 86 063415
[12]	Rankin R, Capjack C E, Burnett N H, Corkum P B 1991 Opt. Lett. 16 835
[13]	Fittinghoff D N, Bolton P R, Chang B, Kulander K C 1992 Phys. Rev. Lett. 69 2642
[14]	Paulus G G, Nicklich W, Zacher F, Lambropoulos P, Walther H 1996 J. Phys. B 29 L249
[15]	Yu X G, Wang B B, Chen T W, Li X F, Fu P M 2005 Acta Phys. Sin. 54 3542 (in Chinese)[余晓光, 王兵兵, 程太旺, 李晓峰, 傅盘铭2005 54 3542]
[16]	Zuo T, Bandrauk A D 1995 Phys. Rev. A 52 R2511
[17]	Staudte A, Pavičič D, Chelkowski S, Zeidler D, Meckndel M, Niikura H, Schöffler M, Schössler S, Ulrich B, Rajeev P P, Weber Th, Jahnke T, Villeneuve D M, Bandrauk A D, Cocke C L, Corkum P B, Dörner R 2007 Phys. Rev. Lett. 98 073003
[18]	Ben-Itzhak I, Wang P Q, Sayler A M, Carnes K D, Leonard M, Esry B D, Alnaser A S, Ulrich B, Tong X M, Litvinyuk I V, Maharjan C M, Ranitovic P, Osipov T, Ghimire S, Chang Z, Cocke C L 2008 Phys. Rev. A 78 063419
[19]	Xu H, He F, Kielpinski D, Sang R T, Litvinyuk I V 2015 Sci. Rep. 5 13527
[20]	Xin L, Qin H C, Wu W Y, He F 2015 Phys. Rev. A 92 063803
[21]	Liu H, Li M, Xie X G, Wu C, Deng Y K, Wu C Y, Gong Q H, Liu Y Q 2015 Chin. Phys. Lett. 32 063301
[22]	Bocharova I, Karimi R, Penka E F, Brichta J P, Lassonde P, Fu X, Kieffer J C, Bandrauk A D, Litvinyuk I, Sanderson J, Légaré F 2011 Phys. Rev. Lett. 107 063201
[23]	Lötstedt E, Kato T, Yamanouchi K 2012 Phys. Rev. A 85 041402
[24]	Xi C, Chu S 2000 Phys. Rev. A 63 013414
[25]	Plummer M, McCann J F 1996 J. Phys. B:At. Mol. Opt. Phys. 29 4625
[26]	Tsogbayar T, Horbatsch M 2013 J. Phys. B 46 085004
[27]	Rzaewski K, Mewenstein, Salières P 1994 Phys. Rev. A 49 1196
[28]	Grobe R, Law C K 1991 Phys. Rev. A 44 R4114
[29]	Qu W X, Hu S X, Xu Z Z 1998 Acta Phys. Sin. 47 571 (in Chinese)[屈卫星, 胡素兴, 徐至展1998 47 571]
[30]	Balcou Ph, L'Huillier A, Escande D 1996 Phys. Rev. A 53 3456
[31]	Bandarage G, Maquet A, Cooper J 1990 Phys. Rev. A 41 1744
[32]	Cocke S, Reichl L E 1996 Phys. Rev. A 53 1746
[33]	Chelkowski S, Foisy C, Bandrauk A D 1998 Phys. Rev. A 57 1176
[34]	Li M, Geng J W, Liu H, Deng Y, Wu C, Peng L Y, Gong Q H, Liu Y Q 2014 Phys. Rev. Lett. 112 113002
[35]	Duan Y W, Liu W K, Yuan J M 2000 Phys. Rev. A 61 053403

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