2P106ห૏૕ㆬᛯ⊛ᝄേബ⿠ߦ߅ߌࠆᄙḰ૏ലᨐߦ㑐ߔࠆℂ⺰⊛⎇ⓥ
㧔ේሶജᯏ᭴㧕 ٤㤥ፒ⼑㧘ᮮጊ໪৻㧘ᮮጊᷕ‫ޣ‬ᐨ‫ޤ‬ㄭᐕ‫ޔ‬㊂ሶ೙ᓮߩ⠨߃ᣇ߇᭽‫‛ߥޘ‬ℂ⊛࡮ൻቇ⊛⃻⽎ߦᔕ↪ߐࠇ‫ޔ‬ᣂߒ޿೙ᓮᴺߩ৻ߟߣߒߡᵈ⋡ࠍ㓸߼ߡ޿ࠆ‫ޕ‬㘃ૃߩᕈ⾰ࠍᜬߟ‛⾰ߩᷙว‛ࠍ⚐☴ߥ‛⾰ߦಽ㔌ߔࠆߣ޿߁໧㗴ߪ‫ޔ‬නߦၮ␆⑼ቇߣߒߡ⥝๧ᷓ޿ߣ޿߁ߛߌߢߪߥߊ‫ޔ‬Ꮏᬺ⊛ߦ߽ฎߊ߆ࠄ޽ࠆ㊀ⷐߥ࠹࡯ࡑߢ޽ࠆ‫ޕ‬ᦨㄭ‫ޔ‬Rabitz╬[1]ߦࠃߞߡ㊂ሶ೙ᓮߦၮߠߊಽ㔌ᴺ߇ℂ⺰⊛ߦឭ᩺ߐࠇ‫ޔ‬Optimal Dynamic
Discrimination (ODD)ᴺߣฬઃߌࠄࠇߚ‫ޕ‬ODDᴺߪᦨㆡ೙ᓮℂ⺰(Optimal Control Theory)[2]ࠍၮ␆
ߣߒ‫ᦨޔ‬ㆡ࡟࡯ࠩ࡯ࡄ࡞ࠬߦࠃߞߡ‛⾰ߩᕈ⾰ߩᓸᅱߥᏅࠍჇ᏷ߔࠆߎߣߢᦨ⚳⊛ߦ㜞ല₸ߢߩಽ㔌ࠍ㆐ᚑߔࠆߣ޿߁߽ߩߢ޽ࠆ‫⎇ᧄޕ‬ⓥߢߪ‫࡛࠙ޔ‬ൻ࠮ࠪ࠙ࡓ(CsI)ಽሶߩห૏૕ᷙว‛(133CsI
ߣ135CsI)ࠍኻ⽎ߣߒߡ‫ޔ‬ODDߩ⠨߃ᣇߦၮߠ߈ห૏૕ㆬᛯ⊛ᝄേബ⿠ߦߟ޿ߡℂ⺰⊛ߦ⠨ኤߒߚ‫ޕ‬․ߦ‫ޔ‬⠨ᘦߔࠆᝄേḰ૏ߩᢙߣቢోㆬᛯ⊛ബ⿠ࠍ㆐ᚑߔࠆߩߦᔅⷐߥࡄ࡞ࠬᤨ㑆ߩ㑐ଥߦߟ޿ߡ⹦ߒߊ⺞ߴߚ‫ޕ‬‫ޣ‬ℂ⺰⸘▚‫⎇ᧄޤ‬ⓥߢߪ ODD ᴺߦၮߠ߈‫ޔ‬ᰴߩࠃ߁ߥ᳢㑐ᢙ J:J,! p . (T ) +AA2A(20A( 2 p A Re ' . A (T ) + A%&A!

T-0dt0 (t )2dt 1 A (t ) * )i ( H 0A ( /0 (t )) . A (t ) $"#0*t-T(1)ࠍ⠨߃ࠆ‫ޕ‬Jߪਃߟߩ㗄߆ࠄߥࠆ㧦(1) ᵄേ㑐ᢙ.A(t)ߩ࠲࡯ࠥ࠶࠻⁁ᘒ+A߳ߩㆫ⒖⏕₸ߩห૏૕A
ߦߟ޿ߡߩ๺‫ޔߢߎߎޕ‬pAߪห૏૕Aߩሽ࿷⏕₸‫ޔ‬Tߪࡄ࡞ࠬᤨ㑆ߢ޽ࠆ㧧(2)㔚႐0(t)ߩࡈ࡞ࠛࡦࠬ
ߦኻߔࠆࡍ࠽࡞࠹ࠖ࡯㗄‫ޕ‬20ߪᱜߩᢙߢ޽ࠆ㧧(3) .A(t)߇Schrögingerᣇ⒟ᑼࠍḩߚߔߣ޿߁᜔᧤᧦
ઙߦ⿠࿃ߔࠆ㗄‫ޔߢߎߎޕ‬1A(t)ߪ Lagrangeᧂቯਸ਼ᢙ‫ޔ‬H0Aߪfield-free Hamiltonian‫ޔߚ߹ޔ‬/ߪ෺ᭂሶࡕ࡯ࡔࡦ࠻ߢ޽ࠆ‫⎇ᧄޕ‬ⓥߩਥߥ⋡⊛ߩ৻ߟߪ‫ޔ‬Jࠍᦨᄢߦߔࠆ㔚႐0(t)ࠍᄌಽᴺߦࠃࠅ᳞߼ࠆߎߣߢ޽ࠆ‫ޕ‬ ౕ૕⊛ߦߪ133CsIߣ135CsIߩ 1:1 ᷙว᳇૕(p133CsI = p135CsI = 0.5)ࠍ⠨߃‫ޔ‬ੑߟߩห૏૕ಽሶ߇ߣ߽ߦၮᐩ⁁ᘒ(X0+)ߩࡐ࠹ࡦࠪࡖ࡞ᦛ✢(PEC)਄ߩᝄേၮᐩ⁁ᘒߦ޽ࠆ⁁ᘒ(133CsI (v = 0); 135CsI (v = 0))
ࠍᤨೞ t = 0 ߦ߅ߌࠆೋᦼ⁁ᘒߣߒ‫ޔ‬135CsIߩߺ߇╙৻ᝄേബ⿠⁁ᘒߦ਄߇ߞߚ⁁ᘒ(133CsI (v = 0);CsI (v = 1)) ࠍt = Tߦ߅ߌࠆ࠲࡯ࠥ࠶࠻⁁ᘒߣߒߚ‫ޕ‬.A(t)‫ޔ‬31A(t)‫ޔ‬30(t)ߦ㑐ߔࠆJߩᄌಽ߇ 0 (4J =1350)ߣ޿߁᧦ઙࠃࠅᓧࠄࠇࠆᑼࠍ‫ޔ‬ㆡᒰߥ0(t)ߩೋᦼ୯ߦኻߒߡJ߇෼᧤ߔࠆ߹ߢ➅ࠅ㄰ߒⓍಽߔࠆߎߣߢᦨㆡ㔚႐0(t)ࠍᓧߚ‫ޕ‬PECߣ෺ᭂሶࡕ࡯ࡔࡦ࠻ߪᚒ‫߇ޘ‬ㆊ෰ߦ⸘▚ߒߚ߽ߩࠍ೑↪ߒߚ[3]‫ߚޕ‬ߛߒ‫ߪߢ▚⸘ᧄޔ‬㔚႐ߩಽᭂࡌࠢ࠻࡞ߣಽሶゲߪᐔⴕߦ࿕ቯߒߚ‫ޕ‬ᵄേ㑐ᢙߩᤨ㑆⊒ዷߩ⸘▚ߦߪੑߟߩᣇᴺࠍ↪޿ߚ㧦ၮᐩ㑐ᢙࠍ↪޿ࠆኒᐲⴕ೉ᴺߣⓨ㑆⊛ࠣ࡝࠶࠼਄ߢᵄ᧤ࠍᤨ㑆⊒ዷߐߖࠆㅢᏱߩsplit-operatorᴺߢ޽ࠆ‫ޕ‬‫⚿ޣ‬ᨐߣ⠨ኤ‫⴫ޤ‬㧝ߦኒᐲⴕ೉ᴺߣsplit-operatorᴺߦ߅޿ߡታ㓙ߦ⸳ቯߒߚࡄ࡞ࠬᤨ㑆(T)ߣၮᐩ㑐ᢙߩᢙ(Nbasis)‫ߦ߮ࠄߥޔ‬ᓧࠄࠇߚㆫ⒖⏕₸(yield)ࠍ␜ߔ‫ᤨޕ‬㑆 230,000 au (~5.6 ps)ߪ‫ޔ‬CsIಽሶ߇ฎౖ⊛ߦ 20 ࿁ᝄേߔࠆߩߦⷐߔࠆ߅߅ࠃߘߩᤨ㑆ߢ޽ࠆ‫ޔߕ߹ޕ‬2 Ḱ૏♽(Nbasis = 2)ߦ߅޿ߡߪ‫ޔ‬caseA1 (T = 3,680,000 au) ߅ࠃ߮A2 (T = 1,840,000 au)ߢߪ 100%ߩㆫ⒖⏕₸߇㆐ᚑߐࠇߡ޿ࠆ߇‫߽ᦨޔ‬ࡄ࡞ࠬᤨ㑆ߩ⍴޿case A3 (T = 920,000 au)ߢߪ⚂⴫㧝. ⸳ቯߒߚࡄ࡞ࠬᤨ㑆(T)‫ޔ‬ၮᐩ㑐ᢙߩᢙ

90%ᱛ߹ࠅߢ޽ߞߚ‫ޕ‬Ḱ૏ߩᢙࠍ 12 ߦჇ߿ߔߣ‫( ޔ‬Nbasis)‫ޔ‬ᓧࠄࠇߚㆫ⒖⏕₸(yield)
2 Ḱ૏♽ߩcase A3 ࠃࠅ߽⍴ᤨ㑆ߢ޽ࠆߦ߽߆߆ࠊ

T / aucaseNbasis

yield / %aኒᐲⴕ೉ᴺࠄߕ‫ޔ‬case A4 (T = 460,000 au)ߢߪ 100%ߩㆫ⒖⏕₸߇㆐ᚑߐࠇ‫ޔ‬case A5 (T = 230,000 au)ߢ߽ 100%ㄭ޿
ߘࠇ߇㆐ᚑߐࠇߡ޿ࠆ‫ߦࠄߐޕ‬Ḱ૏ߩᢙࠍ 20 ߹ߢ

A13,680,000 (~ 89 ps)

2100.0, 100.0

A21,840,000 (~ 45 ps)

2100.0, 100.0

A3920,000 (~ 22.2 ps)

289.6, 89.7

Ⴧ߿ߒߡ߽(case A6, T = 460,000 au)‫⚿ޔ‬ᨐߪ case

A4460,000 (~ 11.1 ps)

12100.0, 100.0

A4 ߣ߶߷หߓߢ޽ߞߚ‫ޔߦ߁ࠃߩߎޕ‬Ḱ૏ߩᢙࠍ

A5230,000 (~ 5.6 ps)

1298.6, 98.5

A6

460,000 (~ 11.1 ps)

20

99.2, 99.1

B1

920,000 (~ 22.2 ps)

99.9, 99.9

B2460,000 (~ 11.1 ps)

97.7, 97.3

2 Ḱ૏♽߆ࠄჇ߿ߔߎߣߦࠃߞߡ‫ࠅࠃޔ‬⍴ᤨ㑆ౝߢ

split-operatorᴺ㜞ല₸ߩห૏૕ㆬᛯ⊛ᝄേബ⿠߇㆐ᚑน⢻ߢ޽ࠆߎߣ߇␜ໂߐࠇߚ[4]‫“ߩߎޕ‬ᄙḰ૏ലᨐ”ߪ‫ޔ‬ੑߟaߩห૏૕ಽሶߩᝄേ࡟ࡌ࡞ߩห૏૕ࠪࡈ࠻㧔หߓᏀߣฝߪߘࠇߙࠇ 133CsI, 135CsI ߦኻߔࠆ୯ᝄേ࡟ࡌ࡞ߩࠛࡀ࡞ࠡ࡯Ꮕ㧕߇㜞ᝄേബ⿠⁁ᘒߢ

1.0ᄢ߈ߊߥࠆߎߣࠍᏁߺߦ೑↪ߒߚ⚿ᨐ⃻ࠇࠆߣ⸃

133CsI0.8ห૏૕ࠪࡈ࠻߇න⺞ߦჇടߔࠆߎߣ߇␜ߐࠇߡ޿ࠆ[3]‫৻ޕ‬ᣇ‫ޔ‬split-operatorᴺߢߪࠣ࡝࠶࠼ᢙࠍචಽ
ᄢ߈ߊߣࠇ߫ߔߴߡߩᝄേ⁁ᘒࠍ⠨ᘦߢ߈ࠆߩߢ‫ޔ‬

Population㉼ߢ߈ࠆ‫ޕ‬ታ㓙‫ޔ‬ᝄേḰ૏߇Ყセ⊛ૐ޿㗔ၞߢ‫ޔ‬

ߎߩᣇᴺߢኒᐲⴕ೉ᴺߩNbasis = 12 ߅ࠃ߮ 20 ߩ႐

0.6

v=012
34
56
78
910
110.40.2

วߣห᭽ߩ⚿ᨐ߇ᓧࠄࠇࠇ߫‫ޔ‬਄⸥ߩᄙḰ૏ലᨐ
0.0߇ౣ⏕⹺ߢ߈ߚߎߣߦߥࠆ‫ ⴫ޕ‬1 ߦ␜ߔࠃ߁ߦ‫ޔ‬ߘࠇ߇㆐ᚑߐࠇߡ߅ࠅ‫ޔ‬ኒᐲⴕ೉ᴺߦࠃࠆ⚿ᨐߣ߶߷৻⥌ߒߡ޿ࠆ‫ޔߡߒ߁ߎޕ‬v = 0 ߆ࠄv = 1 ߳ߩ
ㆫ⒖ߢ޽ߞߡ߽‫ࠅࠃޔ‬㜞࡟ࡌ࡞ߩᝄേ⁁ᘒࠍ೑↪

Population߇㆐ᚑߐࠇ‫ޔ‬case B2 (T = 460,000 au)ߢ߽ 100%ㄭ޿

135CsI

0.8

case B1 (T = 920,000 au)ߢߪ߶߷ 100%ߩㆫ⒖⏕₸

0.6
0.40.2ߔࠆߎߣߢࠃࠅ⍴ᤨ㑆ߢߩ㜞ല₸ㆫ⒖ࠍ㆐ᚑߢ߈
ࠆߣ޿߁ᄙḰ૏ലᨐ߇⏕⹺ߢ߈ߚ‫ޕ‬࿑㧝ߦߪ‫ޔ‬caseB1 ߦߟ޿ߡߩᦨㆡࡄ࡞ࠬߦࠃࠆ133CsIߣ135CsIߩᝄ

0.00

200000400000600000800000Time / auേ࡟ࡌ࡞ߩࡐࡇࡘ࡟࡯࡚ࠪࡦᄌൻࠍ␜ߔ‫ࡘࡇࡐޕ‬࿑ 1. ᦨㆡࡄ࡞ࠬߦࠃࠆ 133CsI ߣ 135CsI ߩᝄേ࡟ࡌ࡟࡯࡚ࠪࡦᄌൻߩ᭽ሶߪ‫ߩࠬ࡞ࡄޔ‬೨ඨߢߪ133CsI࡞ߩࡐࡇࡘ࡟࡯࡚ࠪࡦᄌൻ

ߣ135CsIߢ߶ߣࠎߤห᭽ߢ޽ࠆ߇‫ޔ‬ᓟඨߦ᣿⏕ߥᏅ⇣߇⃻ࠇ‫ߦ⊛⚳ᦨޔ‬133CsIߩv = 0 ߣ135CsIߩv = 1⁁ᘒߩࡐࡇࡘ࡟࡯࡚ࠪࡦ߇ 100%ߣߥߞߡ޿ࠆ‫ޕ‬࿑߆ࠄ‫ޔ‬ਥߦv = 5 ઃㄭ߹ߢߩ⁁ᘒ߇ᵄ᧤ߩ↢ᚑߦ૶ࠊࠇߡ޿ࠆߎߣ߇ࠊ߆ࠆ‫ޕ‬‫ޣ‬ෳ⠨ᢥ₂‫ޤ‬[1] B. Li, G. Turinici, V. Ramakrishna, and H. Rabitz, J. Phys. Chem. B 106, 8125 (2002).
[2] S. Shi and H. Rabitz, J. Chem. Phys. 92, 364 (1990).
[3] Y. Kurosaki, L. Matsuoka, K. Yokoyama, and A. Yokoyama, J. Chem. Phys. 128, 024301 (2008).
[4] Y. Kurosaki, K. Yokoyama, and A. Yokoyama, J. Mol. Struct. THEOCHEM in press (2009).