Molecular orientation induced by H+ collision and modulated with combined fields

Zhiwei Ge; Xuequn Hou; Yu Zhao; Qingtian Meng

doi:10.3788/COL202119.110201

Journals >Chinese Optics Letters >Volume 19 >Issue 11 >Page 110201 > Article

Chinese Optics Letters
Vol. 19, Issue 11, 110201 (2021)

Molecular orientation induced by H⁺ collision and modulated with combined fields

Zhiwei Ge¹, Xuequn Hou², Yu Zhao¹, and Qingtian Meng^1、*

Author Affiliations

¹School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

²Shandong Labor Vocational and Technical College, Jinan 250022, China

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DOI: 10.3788/COL202119.110201 Cite this Article Set citation alerts

Zhiwei Ge, Xuequn Hou, Yu Zhao, Qingtian Meng. Molecular orientation induced by H⁺ collision and modulated with combined fields[J]. Chinese Optics Letters, 2021, 19(11): 110201 Copy Citation Text

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Abstract

We take

H^{+} + CO

as a prototype to analyze the effect of ion or proton collision on molecular orientation modulated by a two-color shaped pulse combined with the time-delayed terahertz (THz) pulse. Through examining the effect of ion collision on the molecular orientation, we found that when the impact parameter and collisional velocity have weak inverse influences on the maximal orientation degree, the appropriate two-color and THz field intensity employed can improve the molecular orientation degree. The carrier envelope phase and frequency of the THz laser pulse as well as the temperature also have certain influence on the collision-induced molecular orientation.

Keywords

combined fields ion collision orientation

E_{STRT} (t) = E_{1} (t) [\cos ω_{1} t + (\cos 2 ω_{1} t)],

(1)

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E_{1} (t) = E_{01} \exp (- t^{2} / 2 σ^{2}),

(2)

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E_{THz} (t) = E_{2} (t) \cos [ω_{THz} (t - t_{d} + φ)],

(3)

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E_{2} (t) = E_{02} \exp [- 2 \ln 2 {(t - t_{d})}^{2} / τ^{2}],

(4)

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V_{c} (r, R, γ) = - \frac{μ (r) \cdot R}{R^{3}} = - \frac{μ (r)}{R^{2}} \cos γ,

(5)

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\cos γ = \frac{v t}{R} \cos θ - {(1 - \cos^{2} θ)}^{\frac{1}{2}} \cdot \frac{b}{R},

(6)

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R (t) = b + v t,

(7)

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\hat{H} (t) = B_{e} {\hat{J}}^{2} - μ E_{THz} (t) \cos θ - \frac{1}{4} [(α_{∥} - α_{⊥}) \cos^{2} θ + α_{⊥}] E_{1}^{2} (t) - \frac{1}{8} [(β_{∥} - 3 β_{⊥}) \cos^{3} θ + 3 β_{⊥} \cos θ] E_{1}^{3} (t) + V_{c} (r, R, γ),

(8)

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〈 \cos θ 〉 = Tr {\cos θ \hat{ρ} (t)},

(9)

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\frac{d \hat{ρ} (t)}{d t} = - \frac{i}{ℏ} [\hat{H}, \hat{ρ} (t)] .

(10)

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\hat{ρ} (t) = \sum_{J, M, J^{'}, M^{'}} ρ_{J M J^{'} M^{'}} (t) | J M 〉 〈 J^{'} M^{'} |,

(11)

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\frac{d ρ_{J M J^{'} M^{'}} (t)}{d t} = - \frac{i}{ℏ} {(ε_{J} - ε_{J^{'}}) ρ_{J M J^{'} M^{'}} - \frac{μ v t}{{(b^{2} + v^{2} t^{2})}^{\frac{3}{2}}} \sum_{J_{1} M_{1}} [V_{J M J_{1} M_{1}}^{(1)} ρ_{J_{1} M_{1} J^{'} M^{'}} (t) - V_{J_{1} M_{1} J^{'} M^{'}}^{(1)} ρ_{J M J_{1} M_{1}} (t)] - \frac{μ b}{2 {(b^{2} + v^{2} t^{2})}^{\frac{3}{2}}} \sum_{J_{1} M_{1}} [V_{J M J_{1} M_{1}}^{(2)} ρ_{J_{1} M_{1} J^{'} M^{'}} (t) - V_{J_{1} M_{1} J^{'} M^{'}}^{(2)} ρ_{J M J_{1} M_{1}} (t)] - μ E_{THz} (t) \sum_{J_{1} M_{1}} [V_{J M J_{1} M_{1}}^{(1)} ρ_{J_{1} M_{1} J^{'} M^{'}} (t) - V_{J_{1} M_{1} J^{'} M^{'}}^{(1)} ρ_{J M J_{1} M_{1}} (t)] - \frac{1}{4} Δ α E^{2} (t) \sum_{J_{1} M_{1}} [V_{J M J_{1} M_{1}}^{(2)} ρ_{J_{1} M_{1} J^{'} M^{'}} (t) - V_{J_{1} M_{1} J^{'} M^{'}}^{(2)} ρ_{J M J_{1} M_{1}} (t)] - \frac{1}{8} E^{3} (t) \sum_{J_{1} M_{1}} {(β_{∥} - 3 β_{⊥}) V_{J M J_{1} M_{1}}^{(3)} ρ_{J_{1} M_{1} J^{'} M^{'}} (t) - V_{J_{1} M_{1} J^{'} M^{'}}^{(3)} ρ_{J M J_{1} M_{1}} (t) + 3 β_{⊥} [V_{J M J_{1} M_{1}}^{(1)} ρ_{J_{1} M_{1} J^{'} M^{'}} (t) - V_{J_{1} M_{1} J^{'} M^{'}}^{(1)} ρ_{J M J_{1} M_{1}} (t)]}},

(12)

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ρ_{0} (T) = \frac{1}{Z} \sum_{J = 0}^{\infty} \sum_{M = - J}^{M = J} | J M 〉 〈 J M | \exp [\frac{- B_{e} J (J + 1)}{K_{B} T}],

(13)

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Z = \sum_{J = 0}^{\infty} \sum_{M = - J}^{M = J} \exp [\frac{- B_{e} J (J + 1)}{K_{B} T}]

(14)

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Zhiwei Ge, Xuequn Hou, Yu Zhao, Qingtian Meng. Molecular orientation induced by H⁺ collision and modulated with combined fields[J]. Chinese Optics Letters, 2021, 19(11): 110201

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