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arXiv:2005.02956 · Journal of Physics B Atomic Molecular and Optical Physics

On the preservation of coherence in the electronic wavepacket of a neutral and rigid polyatomic molecule

András Csehi, Péter Badankó, Gábor J Halász, Ágnes Vibók, Benjamin Lasorne

Published Jun 29, 2020• 11 citations
arXivHTMLPDF

Abstract

Abstract We present various types of reduced models including five vibrational modes and three electronic states for the pyrazine molecule in order to investigate the lifetime of electronic coherence in a rigid and neutral system. Using ultrafast optical pumping in the ground state (1 1 A g ), we prepare a coherent superposition of two bright excited states, 1 1 B 2u and 1 1 B 1u , and reveal the effect of the nuclear motion on the preservation of the electronic coherence induced by the laser pulse. More specifically, two aspects are considered: the anharmonicity of the potential energy surfaces and the dependence of the transition dipole moments (TDMs) with respect to the nuclear coordinates. To this end, we define an ‘ideal model’ by making three approximations: (i) only the five totally symmetric modes move, (ii) which correspond to uncoupled harmonic oscillators, and (iii) the TDMs from the ground electronic state to the two bright states are constant (Franck–Condon approximation). We then lift the second and third approximations by considering, first, the effect of anharmonicity, second, the effect of coordinate-dependence of the TDMs (first-order Herzberg–Teller contribution), third, both. Our detailed numerical study with quantum dynamics is meant to be realistic for pyrazine over about 20 femtoseconds, and was further extended so as to probe the effect of such approximations on a model system. We show that long-term revivals of the electronic coherence persist up to the picosecond time range even for the most realistic model.

DOI
10.1088/1361-6455/aba10e

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Abstract We present various types of reduced models including five vibrational modes and three electronic states for the pyrazine molecule in order to investigate the lifetime of electronic coherence in a rigid and neutral system. Using ultrafast optical pumping in the ground state (1 1 A g ), we prepare a coherent superposition of two bright excited states, 1 1 B 2u and 1 1 B 1u , and reveal the effect of the nuclear motion on the preservation of the electronic coherence induced by the laser pulse. More specifically, two aspects are considered: the anharmonicity of the potential energy surfaces and the dependence of the transition dipole moments (TDMs) with respect to the nuclear coordinates. To this end, we define an ‘ideal model’ by making three approximations: (i) only the five totally symmetric modes move, (ii) which correspond to uncoupled harmonic oscillators, and (iii) the TDMs from the ground electronic state to the two bright states are constant (Franck–Condon approximation). We then lift the second and third approximations by considering, first, the effect of anharmonicity, second, the effect of coordinate-dependence of the TDMs (first-order Herzberg–Teller contribution), third, both. Our detailed numerical study with quantum dynamics is meant to be realistic for pyrazine over about 20 femtoseconds, and was further extended so as to probe the effect of such approximations on a model system. We show that long-term revivals of the electronic coherence persist up to the picosecond time range even for the most realistic model.
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In molecules, electronic coherence typically decays within a few hundred femtoseconds, a timescale usually attributed to the environment. We show that it is set to a large extent by which coherences are excited: the molecule can host coherences that the bath barely sees, and optimal control can find and exploit them. Using gradient-based optimal control (GRAPE) with Redfield dynamics, we maximize the total vibronic coherence between the electronic ground and an optically bright electronic excited state in a three-state model with nonadiabatic features, in two regimes of low and high nonadiabatic mixing and for different system-bath coupling strengths. The Liouvillian spectrum reveals, in both regimes, a well-separated coherence mode with substantial ground-bright character that decays on a picosecond timescale. This mode is protected by mixing with the dark state, which brings the geometry of the optically accessible excited state close to that of the ground state and thus weakens its coupling to the bath. Without prior information, GRAPE finds this mode and keeps the photoexcited wave packet near the Franck-Condon region. At equal fluence, it increases the coherence at 800 fs by more than two orders of magnitude over a Gaussian pulse at the weakest coupling, and by many more at stronger coupling. The Liouvillian predicts the bath dependence of the long-lived coherence to within 1\%, and a Gaussian pulse tuned to the mode frequency comes within 10\% of the best pulse found. Beyond two-level and spin systems, our study puts forward the vibronic structure of molecules as a route to protected coherence subspaces, identifying a dark-state protection mechanism and a design criterion based on molecular parameters. These results lay the groundwork for our goal of using vibronic molecular systems as a resource for long-lived, controllable coherences in molecular quantum information science.
The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.
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.
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