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arXiv:1201.1750 · The Journal of Chemical Physics

Femtosecond two-photon photoassociation of hot magnesium atoms: A quantum dynamical study using thermal random phase wavefunctions

Saieswari Amaran, Ronnie Kosloff, Michał Tomza, Wojciech Skomorowski, Filip Pawłowski, Robert Moszyński, Leonid Rybak, Liat Levin, Zohar Amitay, Jeff. Berglund, Daniel M. Reich, Christiane P. Koch

Published Oct 28, 2013• 37 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.4826350

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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.
The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalizes the generation of coherence by Franck-Condon filtering of collision energies and partial waves, quantifying it in terms of an increase in quantum purity of the thermal ensemble. Our results open the way to coherent control of a binary reaction.
Abstract The first step in the coherent control of a photoinduced binary reaction is bond making or photoassociation. We have recently demonstrated coherent control of bond making in multi-photon femtosecond photoassociation of hot magnesium atoms, using linearly chirped pulses (Levin et al 2015 Phys. Rev. Lett. 114 233003 ). The detected yield of photoassociated magnesium dimers was enhanced by positively chirped pulses which is explained theoretically by a combination of purification and chirp-dependent Raman transitions. The yield could be further enhanced by pulse optimization resulting in pulses with an effective linear chirp and a sub-pulse structure, where the latter allows for exploiting vibrational coherences. Here, we systematically explore the efficiency of phase-shaped pulses for the coherent control of bond making, employing a parametrization of the spectral phases in the form of cosine functions. We find up to an order of magnitude enhancement of the yield compared to the unshaped transform-limited pulse. The highly performing pulses all display an overall temporally increasing instantaneous frequency and are composed of several overlapping sub-pulses. The time delay between the first two sub-pulses fits very well the vibrational frequency of the generated intermediate wavepacket. These findings are in agreement with chirp-dependent Raman transitions and exploitation of vibrational dynamics as underlying control mechanisms.
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.
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.
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.