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Journal of Physics B Atomic Molecular and Optical Physics

The influence of higher-order anharmonic corrections to the energy spectrum on the evolution of quantum wavepackets

Petr A. Braun, В. И. Савичев

Published Apr 28, 1996• 14 citations
Publisher

Abstract

We consider the peculiarities of the long-time evolution of the quantum wavepackets prepared in the range of the weakly anharmonic spectrum. We establish the revival periods connected with the contribution of the higher-order anharmonic corrections to the energy spectrum.
DOI
10.1088/0953-4075/29/8/004

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In terms of the action-angle Wigner function, we analyse the effects of energy spectrum anharmonicity on the evolutions of wavepackets in long time scales. The formulation shows a close connection between classical periodic motions of phase space points and the quantum (full and partial) revivals of wavepackets. This enables us to find the conditions of (full and partial) revivals in an intuitive way. For one-dimensional cases, we obtain analytic solutions for times of equal partial revivals, i.e. an initial wavepacket splits equally into several small parts in long time scales. Numerical results for the JC model confirm the theoretical predictions.
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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.
In the present investigation we assess the relevance of both classically forbidden phenomena and higher-order asymptotic contributions for the semiclassical energy quantization of a particle in the anharmonic oscillator potential V(x)=x 2 /2+ lambda x 4 . We propose an iterative method (Iq) for obtaining higher-order semiclassical corrections, which is similar to the WKB and phase-integral methods in the lowest order, but in higher orders the approximation differs significantly. A 'primitive' Bohr-Sommerfeld energy quantization is compared with a more complete semiclassical quantization, taking into account both complex trajectory contributions and higher-order (quantal) corrections.