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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.
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Keywords:
- electron trajectory /
- H2+ /
- strong laser pulse /
- enhanced ionization
[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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[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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