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The Journal of Chemical Physics

Investigation of photoassociation with full-dimensional thermal-random-phase wavefunctions

Jinwei Hu, Yong‐Chang Han

Published Aug 12, 2021• 6 citations
Publisher

Abstract

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.

DOI
10.1063/5.0059543

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Physical Review A•Oct 15, 2018•11 citations
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.
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.
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.
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.
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.
The formation of ultracold Cs 2 molecules via photoassociation (PA) with a spectral π-jump laser pulse is theoretically investigated by solving the time-dependent Schrödinger equation using the mapped Fourier grid method. Numerical calculations show that the population distributions of associated molecules mainly result from the off-resonant excitation of the π-jump laser pulse. Compared with the transform-limited pulse, an efficient population accumulation in the PA process is achieved with the π-jump pulse. An oscillation pattern appears in the population on the vibrational levels of the state owing to the action of the post-half-pulse in the π-jump pulse. The PA efficiency is related to the Rabi angle of the laser pulse. A π-jump pulse can be used to enhance more effectively the PA efficiency than a transform-limited pulse with the same Rabi angle.
We investigate theoretically the photoassociation (PA) of two Cs\mathrm{Cs}Cs atoms using a slowly-turned-on and rapidly-turned-off (STRT) laser pulse at the temperature of $54\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ by taking the thermal average of the initial continuum states into account. For comparison, the PA probabilities under the action of the STRT and typical Gauss-type pulses are calculated, respectively. The rising and falling times of the STRT pulse are set to be ${\ensuremath{\tau}}_{r}=10$ ps and ${\ensuremath{\tau}}_{f}=0.2$ ps, and the two Gauss-type pulses are set to be ${\ensuremath{\tau}}_{r}={\ensuremath{\tau}}_{f}=10$ ps and ${\ensuremath{\tau}}_{r}={\ensuremath{\tau}}_{f}=5.1$ ps, respectively. Compared to the calculation considering a single initial continuum state (non-thermal-average calculations), the PA probabilities with the consideration of the thermal average are reduced to different extents according to different laser pulses. The PA process induced by the STRT pulse is more robust than that by the two Gauss-type pulses. For the STRT pulse, the PA probability is reduced by roughly 30%, while for the two Gauss-type pulses, it is reduced by roughly 97% and 64%, respectively. Because of the larger bandwidth and the asymmetric time profile of the STRT pulse, the PA probability induced by this pulse is related to both the off-resonant and the near-resonant transitions in a much broader phase space formed by the initial continuum states and the final vibrational states. Consequently, the thermal average of the initial continuum states has relatively smaller influence on the PA probability induced by the STRT pulse. By changing the pulse shape of the standard Gaussian to the sin2{\mathrm{sin}}^{2}sin2 and the Lorentz ones, the STRT pulse still results in the highest PA probability and is the most robust to the thermal average.