Molecular spectroscopy with light pulses of arbitrary pulse shape and field strength: A nonperturbative approach

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Abstract
We present a novel approach to molecular spectroscopy with light pulses of arbitrary strength and duration. The key quantity is the frequency‐resolved net energy transferdE/dω which reveals at which frequencies energy is transferred from the field to the molecule (absorption) or from the molecule to the field (stimulated emission). It is shown that dE/dω can be expressed as the Fourier transform of the cross‐correlation function of the molecular polarizationP(t) and the time derivative of the applied field, dE/dt. In this sense, it is formally equivalent to the absorption cross section under weak‐field conditions which, as commonly known, can be represented as the Fourier transform of the autocorrelation function S(t). The time‐dependent polarizationP(t) is determined by exact integration of the time‐dependent Schrödinger equation including the light‐matter interaction to all orders. It is shown that under weak‐field conditions the expression for dE/dω reduces to the well‐known cross section formula in the time‐dependent picture of spectroscopy, multiplied by the spectral intensity of the light pulse. Therefore, we consider the expression for the frequency‐resolved energy transfer, which is valid for arbitrary electric fields, as the natural extension of the absorption cross section in the weak‐field limit. Furthermore, dE/dω is shown to be formally equivalent to the change of the spectral intensity, ΔI(ω), of an optical pulse after transmission through a sample, the latter being derived by solving Maxwell’sequations under well‐known approximations. The theory is applied to a simple one‐dimensional model with two electronic states and the frequency‐resolved energy transfer is investigated as a function of the field strength. For sufficiently strong fields, dE/dω exhibits transitions between essentially all vibrational levels in the ground and all states in the excited electronic manifold. The new expression distinguishes between absorption and emission and that is clearly seen in the spectra.