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Frontiers in Physics

Steering thermal photoassociation of magnesium atoms by two time-delayed femtosecond laser pulses

Rong Zhang, Jinwei Hu, Yong‐Chang Han, Bina Fu, Maksim B. Shundalau

Published Jan 12, 2023• 1 citation
Publisher

Abstract

By solving the full-dimensional time-dependent Schrödinger equation with the thermal-random-phase wavepacket method, we investigate the photoassociation (PA) process of hot (1000 K) magnesium atoms induced by two time-delayed femtosecond laser pulses. Driven by the 840 nm fs laser pulses, the Mg2 molecules can be formed on the four excited states, (1)1Πg, (1)1Πu, (2)1Πu, and (2)1Σu+ , from the initial electronic ground state X1Σg+ . It is found that the three-photon couplings between X1Σg+ and the three ungerade states [(1)1Πu (2)1Πu, and (2)1Σu+ ], play dominant roles in the population transfer process. By scanning the pulse duration τ from 50 to 200 fs, and varying the delay time δt0 from 0 to 2τ fs, we find that the final PA population is strongly dependent on the two parameters. For a given δt0, the parameter τ can induce a significant variation (2 ∼ 6.8 times) for the final PA population transfer, and for a given τ, one can also obtain a significant variation (2.7 ∼ 3.5 times) of the final PA population by varying δt0. Additionally, the dynamics of the coherently vibrational wavepackets of the four excited states are also influenced by the two parameters.

DOI
10.3389/fphy.2023.1114719

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By solving the full-dimensional time-dependent Schrödinger equation with the thermal-random-phase wavepacket method, we investigate the photoassociation (PA) process of hot (1000 K) magnesium atoms induced by two time-delayed femtosecond laser pulses. Driven by the 840 nm fs laser pulses, the Mg2 molecules can be formed on the four excited states, (1)1Πg, (1)1Πu, (2)1Πu, and (2)1Σu+ , from the initial electronic ground state X1Σg+ . It is found that the three-photon couplings between X1Σg+ and the three ungerade states [(1)1Πu (2)1Πu, and (2)1Σu+ ], play dominant roles in the population transfer process. By scanning the pulse duration τ from 50 to 200 fs, and varying the delay time δt0 from 0 to 2τ fs, we find that the final PA population is strongly dependent on the two parameters. For a given δt0, the parameter τ can induce a significant variation (2 ∼ 6.8 times) for the final PA population transfer, and for a given τ, one can also obtain a significant variation (2.7 ∼ 3.5 times) of the final PA population by varying δt0. Additionally, the dynamics of the coherently vibrational wavepackets of the four excited states are also influenced by the two parameters.
By taking the femtosecond two-photon photoassociation (PA) of magnesium atoms as an example, we propose a method to calculate the thermally averaged population, which is transferred from the ground X1Σg+ state to the target (1)1Πg state, based on the solution of full-dimensional time-dependent Schrödinger equation. In this method, named as method A, we use thermal-random-phase wavefunctions with the random phases expanded in both the vibrational and rotational degrees of freedom to model the thermal ensemble of the initial eigenstates. This method is compared with the other two methods (B and C) at different temperatures. Method B is also based on thermal-random-phase wavefunctions, except that the random-phase expansion is merely used for the vibrational degree of freedom. Method C is based on the independent propagation of every initial eigenstate, instead of the thermal-random-phase wavefunctions. Taking the (1)1Πg state as the target state, it is found that although these three methods can present the same population on the (1)1Πg state, the computation efficiency of method A increases dramatically with the increase in temperature. With this efficient method A, we find that the PA process at 1000 K can also induce rotational coherence, i.e., the molecular field-free alignment in the excited electronic states.
We investigate femtosecond photoassociation of thermally hot atoms in the gas phase and its coherent control. In the photoassociation process, formation of a chemical bond is facilitated by light in a free-to-bound optical transition. Here, we study free-to-bound photoassociation of a diatomic molecule induced by femtosecond pulses exciting a pair of scattering atoms interacting via the van-der-Waals-type electronic ground state potential into bound levels of an electronically excited state. The thermal gas of reactants is at temperatures in the range of hundreds of degrees. Despite this incoherent initial state, rotational and vibrational coherences are observed in the probing of the created Mg2 molecules.
Quantum coherent control of ultrafast bond making and the subsequent molecular dynamics is crucial for the realization of a new photochemistry, where a shaped laser field is actively driving the chemical system in a coherent way from the thermal initial state of the reactants to the final state of the desired products. We demonstrate here coherent control over the relative yields of Mg2 molecules that are generated via photoassociation and subsequently photodriven into different groups of final states. The strong-field process involves non-resonant multiphoton femtosecond photoassociation of a pair of thermally hot magnesium atoms into a bound Mg2 molecule and subsequent molecular dynamics on electronically excited states. The branching-ratio control is achieved with linearly chirped laser pulses, utilizing the different chirp dependence that various groups of final molecular states display for their post-pulse population. Our joint experimental and theoretical study establishes the feasibility of high degree coherent control over quantum molecular dynamics that is initiated by femtosecond photoassociation of thermal atoms.
Two-photon photoassociation of hot magnesium atoms by femtosecond laser pulses, creating electronically excited magnesium dimer molecules, is studied from first principles, combining ab initio quantum chemistry and molecular quantum dynamics. This theoretical framework allows for rationalizing the generation of molecular rovibrational coherence from thermally hot atoms [L. Rybak, S. Amaran, L. Levin, M. Tomza, R. Moszynski, R. Kosloff, C. P. Koch, and Z. Amitay, Phys. Rev. Lett. 107, 273001 (2011)]. Random phase thermal wavefunctions are employed to model the thermal ensemble of hot colliding atoms. Comparing two different choices of basis functions, random phase wavefunctions built from eigenstates are found to have the fastest convergence for the photoassociation yield. The interaction of the colliding atoms with a femtosecond laser pulse is modeled non-perturbatively to account for strong-field effects.
Abstract By utilizing the time-dependent wavepacket method, we studied the population transfer between the electronic states of the Na 2 molecule driven by femtosecond laser pulses. Three electronic states, X 1 Σ g + , A 1 Σ u + and 2 1 Π g , are taken to be the initial, the intermediate and the target states, respectively. Two classes of calculations are performed for comparison: one is to invoke the rotating wave approximation (RWA), and the other is more accurate calculations without consideration of RWA (non-RWA). It is found that for this three-state-model, the RWA fails to describe the accurate population transfer process in femtosecond-pulse fields and that the adiabatic passage is hard to be constructed in the non-RWA calculations. Based on the non-RWA calculations, we determined a set of laser parameters, including the peak intensity, detuning, pulse duration and time delay, for efficient population transfer.
Abstract Quantum coherent control of ultrafast bond making and the subsequent molecular dynamics is crucial for the realization of a new photochemistry, where a shaped laser field is actively driving the chemical system in a coherent way from the thermal initial state of the reactants to the final state of the desired products. We demonstrate here coherent control over the relative yields of Mg 2 molecules that are generated via photoassociation and subsequently photodriven into different groups of final states. The strong-field process involves non-resonant multiphoton femtosecond photoassociation of a pair of thermally hot magnesium atoms into a bound Mg 2 molecule and subsequent molecular dynamics on electronically excited states. The branching-ratio control is achieved with linearly chirped laser pulses, utilizing the different chirp dependence that various groups of final molecular states display for their post-pulse population. Our joint experimental and theoretical study establishes the feasibility of high degree coherent control over quantum molecular dynamics that is initiated by femtosecond photoassociation of thermal atoms.