Study interaction between intensive circularly polarized laser and hydrogen atom using a matrix method

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1 ISBN Procdngs of 3 rd Intrnatonal Workshop on Matrx Analyss angzhou,p.r.chna.july 9-13, 2009, pp ( Wll st y th pulshr ) Study ntracton twn ntnsv crcularly polarzd lasr and hydrogn atom usng a matrx mthod L.F. Yang 1, 3, W. Xu 1+, Q. R. Zhang 2, X. L. Ca 1, 3, G. T. Fan 1, 3, G. W. Fan 1,3, W. Luo 1,3, Y. J. L 1,3, Q. Y. Pan 1, B. J. Xu 1, Y. Xu 1,3, Z. Yan 1 1 Shangha Insttut of Appld Physcs, Chns Acadmy of Scncs, , Shangha, Chna 2 Dpartmnts of Tchncal Physcs, Pkng Unvrsty, , Bjng, Chna 3 Graduat School of th Chns Acadmy of Scncs, , Bjng, Chna Astract. Rcntly th study of ntnsv lasr and atom ntracton s on of th most ntrstng topcs n lasr and atom ntrdscplnary physcs. Study of ntracton of hydrogn atom and ntns lasr usng a matrx mthod s rportd n ths papr. Ths mthod ncluds Gvns rducton for ral symmtrc trdagonal matrx form of amltonan matrx, Thomas algorthm for gnvctors, and scton algorthm wth Sturm thorm for gnvalus. Som prlmnary rsults and progrss for ths study ar prsntd. Kywords: ntnsv lasr, hydrogn atom, matrx mthod. 1. Introducton In rcnt dcads, wth dvlopmnt of hgh ntnsty lasr, th ntnsv lasr and mattr ntracton hav com a hot topc n oth xprmntal and thortcal physcs [1-2]. Bcaus th hydrogn s th smplst systm for studyng th ntracton of an atom systm wth a lasr fld, wthout ntrfrnc from multlctron ffcts, th study of ntracton twn hydrogn atom and a lasr provds a clan tst cas for thortcal calculaton.thrfor, w dvlop an approach to solv th tm dpndnt Schrödngr quaton (TDSE) of hydrogn atom n th prsnc of crcularly polarzd lasr fld [3]. Th rmanng of ths papr s organzd as follows: Scton 2 dscrs our thortcal approach. In Scton 3 th corrspondng gnvalus and gnvctors ar calculatd and chckd. Scton 4 concluds th papr and dscusss possl futur rsarch drctons. 2. Thortcal approach Consdrng th hydrogn atom n th prsnc of a rlatv long puls and crcularly polarzd lasr fld, Ths work s supportd y th On undrd Talnts Projct of Chns Acadmy of Scncs (2006) ( ), y Knowldg Innovaton Projct of Chns Acadmy of Scncs (KJCX2-SW-N13), y Pujang Talnt Projct of th Shangha Scnc and Tchnology Commtt (06PJ14114), and y th Natonal Natural Scnc Foundaton of Chna ( ). + E-mal addrss: xuwang@snap.ac.cn

2 th TDSE of th lctron can changd nto a non tm dpndnt Schrödngr quaton (NTDSE) y som rotaton and untary transformaton [4] = E (1), whr E s Egn nrgy of gnvctor and = p + V() r k pzl k A A z + lz + + px + kcl. (2) z 2μ μ 2μ 2μ 2μ r, Vr () s coulom potntal, c s lght vlocty, μ s th mass of lctron, k s wav numr, p s momntum, px and p y ar x and y drcton componnts of p rspctvly, l z = m s th z-componnt of th angular momntum, and m s th magntc quantum numr. At frst, w only consdr th part of ound statonary stat of hydrogn atom ψ ( knlm ( ) or to ass to comn th gnvctor of, and n th coordnaton t can wrttn as = C = C ψ = C R r Y θϕ, ( n l) ( ) ( ) ( ) nl lm l l+ 3/2 r +! 2 l 2 n C r 1F1 l 1 n,2l 2, r Ylm ( θϕ, ) 2l 1! 2n n l 1! n n = + + ( + ), whr C s th coffcnt of th orthogonal ass vctor ψ. Thn usng th matrx form of (NTDSE), scular Eq. 1 can wrttn as f c 1 c f c2 c 2 = ε (4) c f 1 f 2 ff f c f, n whch, = k ( nlm), (5) k k k C s arvaton of C, ε s th gnvalu of ffctv amltonan for gnvctor, and can spcfcally rwrttn as p k m A A k k km k k = () k k + V r kcm δ + Ψ kk px Ψ Ψ pz Ψ. (6) 2μ 2μ 2μ 2μ μ Fg. 2.1 shows th procss of our matrx mthod. Aftr w calculat th lmnt of ffctv amltonan th ral symmtrc trdagonal matrx form of amltonan matrx s otand y Gvns rducton [5]. Th rlatd gnvalus ar thn calculatd y scton algorthm wth Sturm thorm [6], and gnvctors ar computd y Thomas algorthm [7] wth wll-sparatd gnvalu. Fnally, w can otan som physcs quantts, such as onzaton cross scton and lasr ntnsty dpndnc [8]. In ths papr, w wll only prsnt som rsults of gnvalu and gnvctor of. k Ψ ) (3)

3 Fg Flowchart of our approach. Tal 3.1. A fv ordr squar matrx M0. 3. Som rsults Bfor gvng som rsults of gnvalu and gnvctor of, w would lk to chck th rlalty and accuracy for Gvns rducton and Bscton algorthm usd n our approach. W compar th gnvalus and gnvctors from our approach to a known rsult. Th matrx usd for comparson s a fv ordr squar matrx M0 [5] (shown n Tal 3.1). Tal 3.2 Egnvalu. Egnvalu No No.1 No.2 No.3 No.4 No.5 Matrx calculator V V V V V Gvns+Bscton* V V V V V Tal 3.3 No1. Egnvctor. Mthod Gvns+ Matrx Thomas calculator ndx No.1 No E Tal 3.4 No3. Egnvctor. Mthod Gvns+ Matrx Thomas Calculator ndx No.3 No E Excpt No.1 and No.3 gnvctors, othr gnvctors ar compltly sam. Only No.1 and No3 gnvctors wth som slght dffrncs ar shown n Tal 3.3 and Tal 3.4, rspctvly. Thrfor, w can asly conclud that th rsult of our modl has a 5-dgt prcson for gnvctor and has mor than 5- dgt prcson for gnvalu As w st lasr paramtrs A = V s/ m, and k = / m (wav lngthy λ = m ), th gnvalu E of amltonan, and corrspondng gnvctor n th prsnc of ths lasr fld ar calculatd asd on our approach. Tal 3.5 shows th frst tn tms of gnvctor ψ = 4.65 of E V

4 amltonan (whch has a largst componnt of ground stat of atomc hydrogn) asd on th ass of ound stats of hydrogn atom, and ts corrspondng gn nrgy E= 4.65V. Tal 3.5. Data for th frst tn tms of gnvctorψ = Indx of c Valu of c Indx of c Valu of c E ψ = Usng data n Tal 3.5, on can plot E 4.65 mathmatc softwar. Z 7, Ψ E 4.65 V 2 y 10 V E, an gnvctor of ffctv amltonan 10 V Z 7, Ψ E 13.6 V 2 y wth x 0 x Fg Proalty forψ E = 4.65V, an gnvctor of ffctv amltonan (lft pctur), and th proalty for ground stat of atomc hydrogn wth lasr off (rght pctur). Wht color rprsnts a larg proalty and lu rprsnts a low proalty n oth pcturs. ψ = Bcaus E 4.65V has a largst componnt of ground stat of atomc hydrogn wthout lasr among all gnvctors of, th ground stat ψ E = 13.6V of atomc hydrogn wll most lkly transt to gnvctor 5 7 ψ E = 4.65V of ffctv amltonan as a lasr fld ( A = V s/ m, and k = / m) s mployd. Th transton proalty s calculatd as 0.57 y our approach. owvr, from oth plots n Fg. 3.6, on can clarly s that th sphrcal symmtry of th ground stat of atomc hydrogn s rokn as th crcularly polarzd lasr fld s mployd.

5 4. Concluson and outlook In ths papr, w hav rfly dscrd th procss of how to stalsh th approach, and chckd ts rlalty and accuracy wth an xampl whn th gnvalus ar wll-sparatd. On of th gnvctor of wth a largst componnt of ground stat of hydrogn atom has n studd. In th futur, w wll study th gnvctors whn th corrspondng gnvalus ar not wll-sparatd, onzaton cross scton, transton rat twn two dscrt stats, and spcally th ffct of contnuum part of hydrogn atom wav functon on our approach n th prsnc of th crcularly polarzd lasr fld. 5. Rfrncs [1] M. Protopapas, C.. Ktl and P.L. Knght, Atomc physcs wth supr-hgh ntnsty lasrs, Rp. Prog. Phys, 60(1997), pp [2] C.J. Joachan, M. Dörr, and N.J. Kylstra, gh-ntnsty lasr-atom physcs, Adv. At, Mol, and Opt. Phy, pp , [3] Q.R. Zhang, Intnsty dpndnt of th th photolctrc ffct nducd y crcularly polarzd lasr am, Phys. Ltt. A, pp , [4] D. Zhang, Q.R. Zhang, Th Photoonzaton of Atomc ydrogn n an Intns Crcularly Polarzd Lasr Fld, Comm.Thor.Phys, pp ,2001. [5] J.. Wlknson, Th Algrac Egnvalu Prolm, Oxford Unvrsty Prss,1965. [6] W. Barth, R. S. Martn, and J.. Wlknson, Calculaton of th Egnvalus of a Symmtrc Trdagonal Matrx y th Mthod of Bscton, Numrsch Mathmatk 9 (1967), pp [7] S.D. Cont, C.W. D Boor, Elmntary Numrcal Analyss. McGraw-ll Educaton, [8] Q.R. Zhang, Non-ntgr Quantum Transton, a Tru Non-prturaton Ect n Lasr-Atom Intracton Commun. Thor. Phys, 47 (2007), pp