Researching | Laser control strategies in full-dimensional funneling dynamics: the case of pyrazine [Invited]

Chinese Optics Letters, Volume. 20, Issue 10, 100007(2022)

Laser control strategies in full-dimensional funneling dynamics: the case of pyrazine [Invited]

Samrit Mainali, Fabien Gatti^*, and Osman Atabek

Author Affiliations

Institut des Sciences Moléculaires d’Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France

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Equations(30)

H_{S} (Q) = \sum_{n} | n 〉 H_{n n} (Q) 〈 n | + \sum_{n \neq m} | n 〉 H_{n m} (Q) 〈 m |,

(1)

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H_{n n} (Q) = {\tilde{ϵ}}^{(n)} + \sum_{α}^{N_{α}} [P_{α}^{2} + {ω_{α}^{(n)}}^{2} {(Q_{α} - d_{α}^{(n)})}^{2}],

(2)

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H_{n m} (Q) = \sum_{α}^{N_{α}} λ_{α}^{(n m)} Q_{α},

(3)

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H_{n n} (Q) = ϵ^{(n)} + \sum_{α}^{N_{α}} (P_{α}^{2} + {ω_{α}^{(n)}}^{2} Q_{α}^{2}) + \sum_{α}^{N_{α}} κ_{α}^{(n)} Q_{α},

(4)

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| Ψ^{Tot} (Q, t) 〉 = \sum_{n = 1}^{3} Ψ_{n} (Q, t) | n 〉 .

(5)

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- i ℏ \frac{\partial}{\partial t} Ψ_{n} (Q, t) = H_{n n} Ψ_{n} (Q, t) + \sum_{m \neq n} H_{n m} Ψ_{m} (Q, t) .

(6)

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Ψ_{n} (Q, t) = \sum_{J}^{N_{J}} A_{J, n} (t) Φ_{J, n} (Q) .

(7)

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Ψ_{n} (Q, t) = \sum_{j_{1} = 1}^{n_{1}} \dots \sum_{j_{f} = 1}^{n_{f}} A_{j_{1},\dots j_{f}} (t) \prod_{α = 1}^{f} φ_{j_{α}}^{(α)} (Q_{α}, t),

(8)

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φ_{j_{α}}^{(α)} (Q_{α}, t) = \sum_{i_{α}}^{M_{α}} c_{i_{α}}^{(α, j_{α})} (t) χ_{i_{α}}^{(α)} (Q_{α}) .

(9)

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{\tilde{Q}}_{κ} \equiv (Q_{κ,1}, Q_{κ,2}, \dots, Q_{κ, d}),

(10)

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φ_{j}^{(κ)} ({\tilde{Q}}_{κ}, t) = φ_{j}^{(κ)} (Q_{κ,1}, Q_{κ,2}, \dots, Q_{κ, d}, t),

(11)

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Ψ ({\tilde{Q}}_{1}, \dots, {\tilde{Q}}_{p}, t) = \sum_{j_{1} \dots j_{p}}^{n_{1} \dots n_{p}} A_{j_{1} \dots j_{p}} (t) \prod_{κ = 1}^{p} φ_{j}^{(κ)} ({\tilde{Q}}_{κ}, t),

(12)

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φ_{j}^{(κ)} ({\tilde{Q}}_{κ}, t) = \sum_{i_{1} \dots i_{d}}^{M_{κ 1} \dots M_{κ d}} C_{i_{1} \dots i_{d}}^{(κ, j)} (t) χ^{(κ,1)} (Q_{κ,1}) \dots χ^{(κ, d)} (Q_{κ, d}) .

(13)

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P_{n} (t) = \int {| Ψ_{n} (Q, t) |}^{2} d Q .

(14)

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H (Q; t) = H_{S} (Q) + V (Q; t),

(15)

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V (Q; t) = - μ (Q) E (t) .

(16)

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μ_{01} (Q) = ξ_{10 a}^{(01)} Q_{10 a},

(17)

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μ_{02} (Q) = μ_{02} (0) + \sum_{α \neq 10 a} ξ_{α}^{(02)} Q_{α} + \frac{1}{2} ρ_{10 a}^{(02)} Q_{10 a}^{2} .

(18)

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\tilde{p} (t) = \frac{P_{1} (t) - P_{2} (t)}{P_{0} (t)} .

(19)

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\tilde{p} (t) = \frac{r (t) - 1}{1 / P_{2} (t) - [r (t) + 1]} .

(20)

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p = \frac{1}{t_{\max} - t_{\min}} \int_{t_{\min}}^{t_{\max}} \tilde{p} (t) d t .

(21)

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E (t) = \sum_{i = 1}^{N} \sqrt{I} E_{i} (t) \sin (ω t),

(22)

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E_{i} (t) = \sin^{2} [\frac{π}{T} (t - t_{i})] H (t - t_{i}) H (t_{i} + T - τ),

(23)

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A = \int_{0}^{\infty} E^{2} (t) d t .

(24)

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A = a \int_{0}^{\infty} ϵ^{2} (t) d t .

(25)

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T_{1} = V + V G_{0} V,

(26)

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T_{1} = 〈 S_{1} | W_{12} \frac{1}{E_{S_{0}} - E_{S_{2}} + ℏ ω} μ_{20} E_{1} | S_{0} 〉,

(27)

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T_{2} = 〈 S_{1} | μ_{01} E_{2} | S_{0} 〉,

(28)

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P_{1} = {| T_{1} + T_{2} e^{- i E τ / ℏ} |}^{2},

(29)

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P_{1} = {| T_{1} + T_{1} e^{- i E τ / ℏ} |}^{2} .

(30)

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Samrit Mainali, Fabien Gatti, Osman Atabek. Laser control strategies in full-dimensional funneling dynamics: the case of pyrazine [Invited][J]. Chinese Optics Letters, 2022, 20(10): 100007

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Paper Information

Special Issue: ULTRAFAST OPTICS: FUNDAMENTALS AND APPLICATIONS

Received: Jul. 30, 2022

Accepted: Sep. 2, 2022

Published Online: Sep. 26, 2022

The Author Email: Fabien Gatti (fabien.gatti@universite-paris-saclay.fr)

DOI:10.3788/COL202220.100007

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology