T^p chi KHOA HOC OHSP TPHCM S647 nam 2013
BIEU HIEN BAO HOA TRONG P H 6 SONG DIEU HOA K^C CAO CilA PHAN TU" HI DAO D O N G
DO THI THU HA", N G U Y E N NGQC TY"
T 6 M TAT
BSng viic gidi sd phuong trinh Schrddinger phu thudc thai gian (TDSE - time- dependent Schrddinger equation), chiing tdi thu duac phd sdng dieu hda bgd cao phat ra tic phdn ta Hi dang dao ddng tuang tdc vai chiim laser cuang dp cao. Kit qud cho thdy, dng vdi cdc bgc dao ddng hgt nhdn thdp, khi phdn tii H^ dao ddng cdng mgnh sdng diiu hda bdc caa phdt ra cd cudng dp cdng cao. Tuy nhien vai cdc bdc dao dpng cao, phd song diiu hoa cho thdy cd su bdo hda; cuang dp sdng khdng thay ddi khi cdc mice dao ddng tiip tuc tdng.
Tit khoa: phuong pliap TDSE, laser cudng dp cao, sdng dieu hda bac cao, dao dpng phdn tu, gidi sd.
ABSTRACT
Saturation performance in high-order harmonic generation of vibrational molecule H^
By solving numerically the time-dependent Schrddinger equation, we obtain the high-order harmonic spectra emitted from the vibrating molecule H^ exposed to an intense laser pulse. The results show that with some first vibrational levels, harmonics generating f^om the molecule with a higher state are more intense. However, with highly vibrational levels, the harmonic spectra perform a saturation which implies that the intensity of harmonics does not change when molecular vibration level increases fi^om a certain value.
Keywords: TDSE method, intense laser pulse, HHG, molecular vibration, numerical solution.
1. Gidi thifu
Trong ban hai thdp ki qua cimg vdi sy phdt trien ctia ki thudt laser, cdc tuong tdc giiSa chiim laser manh, xung ngin vdi nguyen tit, phdn tit da dugc nghien cihi rpng rai [8, 10). Mdt ttong cdc nghien cihi dd la su phdt xa sdng dilu hda bac cao (High-order Harmonic generation, vilt tit Id FIHG) [4]. HHG la hieu iing quang phi tuyln xdy ra ttong qud trinh tucmg tdc gifta laser vd nguyen tir, phdn tur. Ndm 1987, MCPherson va cdng su da ldn diu tien thu dugc HHG cd bac 17, budc sdng 248nm ttong khi neon _HVCH, Trudng B^i hpc Su phgm TPHCM
" TS, Tru'dng Ogi hoc Su phgm TPHCM
Tap chi KHOA HOC OHSP TPHCM BS Thi Thu Hi vi tgk
[12]. Nam 1994, Lewenstein da dl xuit md hinh ba budc mang ten dng dl gidi thich sy phdt xj sdng dilu hda bdc cao vdi nguyen tti [11]. Theo dd, dipn til bj ion hda theo phuong thirc xuyen him ttong budc thir nhit; trong budc tilp tiieo dien hi sS hi gia tdc bdi tiordng dien cua laser; cudi ciing, khi dien tradng ddi chilu, dien tti bj keo ttd Ijti kit hgp vdi ion mp vd phdt ra photon, chinh Id HHG. Dya tten md hinh ndy, cdc nha khoa hgc da md rpng md hinh su phdt xa sdng dilu hda bac cao cua phdn tii ttong tuong tdc vdi tradng laser cyc ngin, cudng dp cao [7]. Kit qud cho thiy cudng dp HHG nhay vdi sy thay ddi khodng cdch lien bait nhan ttong phdn tu [15]. Trong cdng trinh [7], cdc tdc gid da gia djnh rang cdc hjt nhdn ttong phdn tir diing yen nen vipc khao sdt dnh hudng ciia chuyin ddng hat nhdn len cudng dp HHG chua dugc xet din.
Trong cdng trinh [3], bing cdch them vdo md hinh ba budc cdc hdm sdng md td chuyin dpng hat nhdn de khdo sat sy dnh hudng cita chuyin ddng hat nhdn len HHG. Kit qua cho thdy cudng dp HHG phdt ra nhay vdi chuygn ddng ciia hat nhdn.
Ngodi md binh gin dung, mpt hudng tilp can khdc khi nghidn ciru qud trinh phdt xa nay la gidi chinh xdc bing sd phuong trinh Schrddinger phy thupc thdi gian (gpi Id phuong phdp TDSE). Nam 2005, Lein dl xudt vl mjt li thuylt ring cac tin hieu sdng dieu hda trong cac phdn tu lien quan den dao dpng hat nhdn vd da cung cip thdng tin vl chuyen ddng hat nhdn tir nguon sdng ndy [9]. Trong cdng trinh [1], Baker vd cpng su da thyc hipn cdc thi nghiem cd dp chinh xac cao thdm dd cdc chuyen dpng cue nhanh cua cac h^t nhdn ttong phan tir hai nguyen tu H2 vd D2, ddng thdi vdi CH4 vd CD4 tir phd HHG. Trade dd, nam 2001, khi tinh den sy chuyen ddng cua cac hat nhan, Qu va cpng sy da thay ring sy ion hda H^ trong tradng laser cudng dp cao tdng len ddng ke va cdc dinh sdng dilu hda rieng le md rgng so vdi cdc h?t nhan cd djnh [13]. Gin day ndra 2007, Shahbaz va cdng sy da kham pha ra cdc tin hieu ddc Uimg hat nhan trong sdng dieu hda cua cdc nguyen tir hydro muonic vd doteri. Vj tti diem dimg va cudng dp HHG ttong mien phing deu dugc tdng cucmg ddng ke vdi nguyen til hydro muonic do khoi lugng vd kich thudc hjt nhan cua nd nhd so vdi nguyen tit doteri muonic [14].
Cac nghidn cim nay da dl xuit ring HHG se cd nhttng thay ddi dang kl khi xem xet chuyin ddng hjt nhdn.
Cdc kit qua tten da md ra mpt mdng nghien cilu mdi ve HHG khi cd xem xet den chuyin ddng hat nhdn. Nam 2008, Jing Zhao and Zengxiu Zhao dd nghien cihi sy phu thupc ciia HHG vdo cdc trang didi dao dpng ban diu v = 0,1,2 (v id chi sd lugng tu itjc trung cho mirc dao ddng h?t nhdn) vd mdi tuong quan giQa HHG vdi khoang cdch lien hat nhan [16]. Ciing ttong ndm 2008, Baker va cdng sy da nghien ciiu tiiyc nghidm vl sy giao thoa hai tdm ttong HHG cua phan tir cd xet din chuyin dpng h?t nhan. Vd cdc tdc gid da dua ra kit ludn ring cac dao ddng hjt nhan gdy ra sy giao thoa xdy ra d cdc bdc sdng dilu hda thip hon so vdi tradng hgp hat nhdn dimg yen [2]. Nam 2010, Ya-Hui Guo va cdng su ciing nghien cihi vl mdi tuong quan ciia HHG vd cac dao dgng
T?p chi KHOA HOC OHSP TPHCM SS 47 nim 2013
hat nhdn vdi cdc ttang thdi v = 0,1,2,3 cua chuyin ddng h?t nhan. Cdc tdc gid da dua ra nhdn xet ring khi cdc phdn til ban ddu ttong trang thai dao ddng cao hon, hat nhdn dao ddng mdnh liet, hieu suit phdt xa ciia HHG dugc tang cudng [6]. Chinh vi vdy, viec nghien cim sy dnh hudng ciia dao ddng hat nhan len HHG dang dugc phdt trien rdng rai vd cd y nghia khoa hgc. Tuy nhien, trong cdc bdi bao [2, 6, 16], cac tdc gid mdi chi khdo sdt cho cdc tradng hgp bac dao ddng hat nhdn tir 0 din 3 ma chua khao sdt cho cdc bdc dao ddng cao hon vd ddng thdi cac tac gid mdi chi dua ra kdt luan rdng chuyen ddng hat nhdn nhanh ddn din su phdt xa sdng dilu hda dugc tang cudng nhung chua chi ra cy the sy phdt xa sdng dilu hda tang nhu the ndo khi V tdng.
Trong bdi bdo ndy, chiing tdi nghien cim dnh hudng cua dao ddng hat nhan len HHG khi ion phan tit H2 tucmg tdc vdi chiim laser cudng dp cao xung cyc ngdn.
Chung tdi dp dyng phuong phdp TDSE de tinh HHG cua Hi vdi dao ddng hat nhdn bac 0 den 30 khi tuong tac vdi nhieu trudng laser cd cac thdng sd khac nhau de khdo sdt su phu thudc ciia HHG vao chi sd v dac trung cho dao dpng hat nhan.
Bd cyc bai bao gdm 3 phin: Trong phdn 2 tilp theo, chiing tdi gidi thieu vl phucmg phdp TDSE cho H^ vdi hat nhan dao ddng tit do tinh HHG. Tilp theo, trong phin 3, chiing tdi trinh bay cdc kit qud thu dugc vl su phy thudc cua HHG tir H^ vdo chi sd dao ddng v vdi cac tradng laser khac nhau. Cudi ciing, chung tdi tdm l^i cdc kit qua vd thdo ludn.
2. Phuong phdp TDSE cho H^ cd xet din dao dOng h^t nhan
Trong phin ndy, chung tdi dp dyng phuang phdp TDSE cho ion phan til H* mdt chieu de tinh HHG khi xet din dao ddng hat nhdn. Phuong trinh Schrddinger cho ion phdn tti H* tuong tdc vdi tracmg laser ttong he don vj nguyen tit (h = e = m,,=l) dugc viet nhu sau:
il^iz,R,t) = [-^-^,V,iz,R).V(.,t)]n^,R,t) Trong dd, z Id tga do cua dien tir, R la khoang cdch giOa hai hat nhan, ^ Id khdi lugng nit gpn cua hai hat nhdn, V^{z,R) la thi Coulomb cua he, V(z,t) Id thi ndng tuong tdc giu-a dien til vdi tmcmg laser. Dl tranh dilm ki dj trong thi Coulomb, mpt hang sd se dugc them vdo, liic ndy gpi Id thi soft-Coulomb. Hing sd nay se dugc chpn sao cho nang lugng cua he ling vdi thi soft-Coulomb bdng vdi ndng lu(;mg ciia he thyc.
Ddi vdi phdn til H^ , chiing tdi chpn hing s6 "soft-Coulomb" bing 1. Do dd, the Coulomb tuong tac gitta dien tir vd bjt nhdn cd dang
T?p chi KHOA HOC OHSP TPHCM BS Thf Thu Hi vi tgk
The ndng tuong tdc giiia dien til vdi tradng laser dugc vilt bdi
F(z,() = z£,/(r)cos(fl)„(), (3) trong dd, £„, / ( / ) vd a),, lin lutjt Id cudng dp dien tradng cyc dai, hdm bao vd tin sl
cia xung laser.
Nghipm f (z, J?, /) cua phuang trinh (1) dugc vilt dudi d^ing
'i'(z,/J,*) = exp -i\Hdt\^{z,R,t = ii). (4) Trong bai bdo ndy chiing tdi se dp dyng phuong phdp tdch todn til [5] de thu dugc
hdm sdng phy thugc thdi gian theo bieu thirc (4), ttong dd hdm sdng d thdi dilm ban diu *P(z,J!,( = 0) khi chua tuong tdc vdi laser.
Vtii gan diing Bom - Oppenheimer, ham sdng ban diu khi chua tucmg tdc vdi laser cua ion phdn til H\ vdi mile dao dpng hat nhan ddc tnmg bdi chi sd lugng til v dugc vilt dudi dang
'V{z,R,t = i)) = c(,{z,R)x,{R)- (5) Trong dd cp(z,R), j;„(J?)ldn lugt Id hdm sdng ciia di^n til vd hat nhdn dao ddng.
Hdm sdng dipn til p(z,.R)dugc xdc djnh bing phuang phdp thdi gian do gidi phuong trinh Schrddinger cila di$n tit chuyin dOng iing vdi mdi khodng cdch hat nhdn R co djnh
Sau khi gidi phuang trinh Schrddinger ndy chiing tdi ciing thu dugc cac trj ridng ndng lugng cita dipn til £,,(/?) va sil dyng ndng lugng nay ta gidi phuong tiinh Schrddinger cho h?t nhdn
T^p chi KHOA HOC OHSP TPHCM S6 47 nim 2013
cOng bdng phuong phdp thdi gian do dl thu dugc ham sdng cOa h?it nhdn dao dgng
xM)-
Sau khi thu dugc ham sdng phy thugc thdi gian, ta tinh gia toe cua moment bdi bilu tiiirc a{t) = -E(t)-l^{z,R,t)^Vc{z,R\'V[z,R,t)) vd tin hipu sdng dieu hda thu dugc bang each bien ddi Fourier \a (ffl) = I a{t)e "'(/n
3. Kit qud
Trong phdn nay chiing tdi se trinh bay kit qud vl sy phy thugc cila HHG tit H^
theo so lugng til dao ddng v ciia h?t nhdn ma chiing tdi da khao sdt vtji cdc laser cudng dp, budc sdng vd chu ki khac lihau.
Su dyng quy tiinh tinh HHG nhu da trinh bdy ttong phin ttdn, chiing tdi tinh cudng dd HHG vdi cac ttang thai ban diu cd mile dao dOng hjt nhan khdc nhau. Kit qua cho thiy, cdc ttang thdi ban diu cd mile dao dOng hjt nhdn cao hon se phdt ra HHG cd cudng do cao hon. Trong hinh 1, chiing tdi trinh bdy kit qua HHG phdt ra tir i?2 ttng voT' '^^ ttiilc dao dpng v = 0,1,2,3 tuong tdc vdi xung laser cudng dp 2x10'*
W/cm^, d$ ddi xung 13 fs (5 chu ki quang hpc), budc sdng 800 nm. Trong hinh 1 ta thay, cudng dd HHG vdi v = 1 cao hem khoang hai bdc so vdi v = 0, nhung vdi v = 2 cudng dp HHG chi cao hon v = 1 khodng 1,5 bdc vd khi v = 3 thi cudng dg HHG chi tang khoang mdt bdc so vdi miic v = 2. Nhu vdy, vdi cdc bdc dao d$ng v cdng tdng flii mirc dp tang cua cudng dp HHG cdng gidm.
Hinh 1. HHG cua HI khi tucmg tdc vai xung laser cuang dp 2xl0" W/crrf, dg ddi xung 13fs, buac song 800 nm Ong vol cdc mUc dao dpng v = 0,1,2,3 Chiing tdi tilp tyc tdng cdc chi sd v dl khdo sdt sy phy tiiuOc cudng dp HHG vdo mile dp dao ddng hat nhan. Theo kit qua dugc ttinh bdy tiong hinh 2 ta tiiiy ring khi v tdng til 0 din 5, cudng dp HHG tang mdt cdch tiiyln tinh. Tuy nhidn, vdi cac chi so V ldn ban 5 (5 <v < 21) cudng do HHG gin nhu khdng fliay ddi, cd bilu hipn giong nhu
T?p chl KHOA HOC OHSP TPHCM Bo Thi Thu Hi vi tgk
mOt qui tiinh bao hda. Sy tdng tayIn tmh vdi cdc bdc dao dpng nhd vd bilu hipn bao bda d cdc bdc dao dpng v ldn dugc kilm chiing vdi tit ca cdc bac ttong miln phing cda pho HHG. Trong hinh 2, chiing tdi chi vS sy phu thudc vdo chi sd dao dgng v cho cdc bdc Id til 23 din 31.
Hinh 2. Sif phu thupc ciia HHG vdp sd luang tu dao ddng v ciia hgt nhdn khi H\
tucmg tdc vai xung laser cuang dp 2x10''' W/cn^, 13 fs, budc sdng 800 nm xet vdi cdc bgc HHG 23, 25, 27, 29, 31
Chiing tdi tilp tyc khdo sdt hien tut^ng ndy khi cho phdn tit tuong tdc vdi cdc chum laser cd cdc thdng sl cudng dd, dd ddi xung vd budc sdng khdc nhau. Sy phy thugc cda cudng dO HHG vdo sl lugng til dao dgng v d bac 23 vdi cdc thdng sd laser khdc nhau dugc thi hi^n ttong hinh 3. Kit qua tten hinh cho thiy hien tugng da dl cdp vin xdy ra vdi tradng htjrp cac thdng sd laser khdc nhau. Dilu ndy cho thdy sy tdng tuyln tinh vd bdo hda ttong phd HHG khi xet din dao ddng hat nhan Id bdn chit ciu tnic cda phdn til.
3 -•
I • I n / —^—2" 10 liu —•" ^"'^
" l\u ~~°~ ^"'^
/ * • — o — 3 x 1 0 / — ' ^ 3 x 1 0
. S — • — 3 x 1 0
*• W / c m ^
• w , ™ ^
" W / c m ^
•* W / c m '
" w / c m
^ W / c r a ^ I 3 f s , 6 0 0 n m •
1 3 f s , g 0 0 n m 13 f&.IOOO n m 5 fs. BOO n m g f s , 8 0 0 Dm 1 3 f s , 8 0 0 n m .
Hinh 3. Stf phy thupc cua HHG vdo sd luang td dao ddng v cua hgt nhdn khi HI tucmg tdc vai cdc xung laser vdi thdng sd khdc nhau xet vdi cdc bgc HHG 23
189
Tgp chi KHOA HOC OHSP TPHCM Sd 47 nam 2013
Hmh 4. a) Thi ion hda cua H* theo khodng cdch lien hgt nhdn R b) Tri trung binh ciia khodng cdch lien hgt nhdn R theo sd luang tir dao ddng v
D I gidi thich hi^n tugng tren, chung tdi dya vao dnh hudng cua khoang cdch lien hat nhdn len tdc do ion hda. Hinh 4 bieu diln su phu thudc cua thi ion hda I^ cua H^
vao khodng cdch lien h?t nhdn R vd su thay ddi ciia khodng cdch ndy khi hat nhdn d trong cdc mirc dao ddng cao hem. Trong hinh 4b, khi b^t nhdn H^ a trong cac trang thdi dao dpng cao hon thi khoang cdch lien hat nhdn cung se tdng len, titc la phan til bj keo gian. Ddng thdi ttong hinh 4a, d giai dojn diu, chiing ta cd thi thdy khi khodng cdch lien h?t nhan tdng thi tdc dp ion hda gidm, khi dd hifu suit phdt x? sdng dilu hda tang. Dilu ndy gidi thich cho sy tdng tuyln tinh cita cucmg dO HHG vdi v tit 0 din 5.
Khi khodng cdch lien hat nhdn tdng tdi mgt gidi ban nhit djnh thi the ion hda thay ddi khdng nhieu. Dieu ndy cd the la nguyen nhan gay ra bieu hipn bao hda ciia HHG d cdc bdc dao ddng v ldn.
4, Ket luan
Chung tdi da su dyng phucmg phdp gidi sd TDSE trong dd cd dp dyng phuong phdp thdi gian do vd phucmg phap tach todn til dl khdo sat sy phu thugc cua HHG vao bdc dao ddng v cita hat nhdn vdi phan tit //j* khi tucmg tdc vdi cac xung laser cd cudng dp, dp ddi xung vd chu ki khdc nhau. Ddi vdi cdc bdc dao dpng v nhd, khi bdc dao dgng v trong khoang tit 0 din 5 thi HHG tang mgt each tuyln tinh. Ddi vdi cac bdc dao ddng v cao han, cudng dp HHG gin nhu khdng thay ddi, cd bilu hipn gidng nhu mdt qua trinh bao hda. Hien tugng nay dugc chiing tdi gidi thich dya tren sy gidm cua thi ion hda khi hat nhan phdn tti d cdc tr?ng thai dao ddng cao hon.
Nhu vdy, cdc ket qua thu dugc cho thdy sy tdng tuyen tinh vd dat gid tri bao hda trong phd HHG nguyen nhdn do ban chit ciu tnic ndng lugng cita phdn tit khi xet den dao dgng hat nhan.
Tjp chi KHOA HOC OHSP TPHCM BS Thj Thu Ha va tgk
TAI L l f u THAM KHAO
1. Baker S., Robinson J. S., Haworth C. A., Teng H., Smith R. A., Chirila C. C, Lein M., Tisch J. W. G., Marangos J. P. (2006), "Probing Proton Dynamics in Molecules on an Attosecond Time Scale", Science 312, 424.
2. Baker S., Robinson J. S., Lein M., Chirila C. C, Torres R., Bandulet H. C, Comtois D., Kiefier J. C, Villeneuve D. M., Tisch J. W. G., va Marangos J. P. (2008),
"Dynamic Two-Center Interference in High-Order Harmonic Generation from Molecules with Attosecond Nuclear Motion", Phys. Rev. Lett. 101, 053901.
3. 'Chirila C. C. and Lein M. (2005), "High-order harmonic generation in vibrating molecules". Journal of Modem Optics 53, 113-124.
4. Corkum P.B. (1993), "Plasma Perspective on Strong Field Multiphoton Ionization", Phys. Rev. Lett. 71, 1994.
5. Feit M. D., Fleck J. A., and A Steiger (1982), "Solution ofthe Schrddinger equation by a spectral method", J. Comput. Phys. 47, 412-433.
6. Guo Y. H., He H. X., Liu J. Y., He G. Z. (2010), "Sensitivity of High-order Harmonic Generation to Nuclear Motion", Journal of Molecular Structure:
THEOCHEM 947, \ 19.
7. Hay N., Velotta R., Lein M., de Nalda R., Heesel E., Castillejo M., and Marangos J.
P. (2002), "High-order harmonic generation in laser-aligned molecules", Phys. Rev.
A 65, 053805-8.
8. Kanai T., Takahashi E. J., Nabekawa Y., and Midorikawa K. (2008), "Observing molecular structures by using high-order harmonic generation in mixed gases", Phys.
Rev. A 77, 041402(R)-4.
9. Lein M. (2005), "Attosecond Probing of Vibrational Dynamics with High-Harmonic Generation", Phys. Rev. Lett. 94, 053004.
10. Lein M. (2007), "Molecular imaging using recolliding electtons", J. Phys. B: At Moi. Opt Phys. 40, R135-R173.
11. Lewenstein M., Balcou Ph., Ivanov M. Y., L'Huillier A., Corkum P. B. (1994),
"Theory of High-Harmonic Generation by Low-Frequency Laser Fields", Phys.
Rev.Lett. 49, 2\n.
12. McPherson A., Gibson G., Jara U., Johann H., Luk T. S., Mclntyre 1. A., Boyer K., and Rhodes C. K. (1987), "Sttidies of Multiphoton Production of Vacuum-ultraviolet Radiation in the Rare Case", Journal ofthe Optical Society of America B 4(4), 595.
13. Qu W. X., Chen Z. Y., Xu Z. Z., Keitel C. H. (2001), "Nuclear Correlation in Ionization and Harmonic Generation of //;* in Short Intense Laser Pulses", Phys.
«ev. ,4 65,013402.
Tgp chi KHOA HOC OHSP TPHCM SS 47 nim 2013
14. Shahbaz A., Muller C , Staudt A., Burvenich T. J., and Keite C. H. (2007), "Nuclear Signatures in High-Order Harmonic Generation from Laser-Driven Muonic Atoms", Phys. Rev. Lett 98,263901.
15. Zao T., Chelkowski S., Bandrauk A. D. (1993), "Harmonic generation by the HI molecular ion in intense laser fields", Phys. Rev. A 48, 3837.
16. Zhao J. and Zhao Z. (2008), "Probing //^ Vibrational Motions with High-order Harmonic Generation", Phys. Rev. A 78, 053414.
(Ngiy Toa soan nhin duvc bii: 05-6-2013: ngay phin bifn Mnh gii: 19-8-2013:
ngiy chip nh$n ding: 21-6-2013)
