Molecular Response Theory in Terms of the Uncertainty Principle

Abstract

We investigate the time response of molecular transitions by observing the pulse reshaping of femtosecond THz-pulses propagating through polar vapors. By precisely modeling the pulse interaction with the molecular vapors, we derive detailed insight into this time response after an excitation. The measurements, which were performed by applying the powerful technique of THz time domain spectroscopy, are analyzed directly in the time domain or parallel in the frequency domain by Fourier transforming the pulses and comparing them with the molecular response theory. New analyses of the molecular response allow a generalized unification of the basic collision and line-shape theories of Lorentz, van Vleck-Weisskopf, and Debye described by molecular response theory. In addition, they show that the applied THz experimental setup allows the direct observation of the ultimate time response of molecules to an external applied electric field in the presence of molecular collisions. This response is limited by the uncertainty principle and is determined by the inverse spitting frequency between adjacent levels. At the same time, this response reflects the transition time of a rotational transition to switch from one molecular state to another or to form a coherent superposition of states oscillating with the splitting frequency. The presented investigations are also of fundamental importance for the description of the far-wing absorption of greenhouse gases like water vapor, carbon dioxide, or methane, which have a dominant influence on the radiative exchange in the far-infrared.

Radiation Transfer Calculations and Assessment of Global Warming by CO2

“…While the preceding calculations are based on the standard molecular collision theory, considering collisional broadening of spectral transitions, which are characterized by a Lorentzian lineshape or at higher altitudes also by a Voigt profile, we have also performed extensive calculations using a more sophisticated lineshape as given by the molecular response theory (MRT) (Harde et al [40][41][42][43][44]). This theory represents a generalization and unification of the classical collision theories of Lorentz and on the other hand of van Vleck and Weisskopf, considering thermalization of molecules during a collision, which in its limit is determined by the reciprocal of the molecular transition frequency and controlled by Heisenberg's uncertainty principle (Harde & Grischkowsky [44]). The specialty applying MRT is that it not only describes the near resonance absorption and emission behavior as already adequately characterized by a Lorentzian, but also reflects the far wing response, which is mainly caused by the ultrafast time response of molecules to an external electric field during collisions.…”

Terahertz spectroscopy of nitric oxide for emissions monitoring in bioenergy systems

“…For higher frequencies of optical and infrared transitions, the simple Lorentzian line-shape [40] provides excellent agreement with experiment, particularly for the central region of absorption lines [41]. Lower frequencies (in the range of microwave or far-infrared, and under conditions when a linewidth becomes comparable to the transition frequency), the absorption profile of a collisionally broadened line is better represented by the van Vleck−Weisskopf lineshape [41].…”

“…Lower frequencies (in the range of microwave or far-infrared, and under conditions when a linewidth becomes comparable to the transition frequency), the absorption profile of a collisionally broadened line is better represented by the van Vleck−Weisskopf lineshape [41].…”

“…Vleck−Weisskopf theory is that the response of a molecule to an external field is considered in its two limiting cases [41]. The Lorentz line-shape assumes that after a collision, molecules are oriented randomly with respect to the driving field, and therefore no macroscopic polarization in the sample will be found.…”

“…The Lorentz line-shape assumes that after a collision, molecules are oriented randomly with respect to the driving field, and therefore no macroscopic polarization in the sample will be found. van Vleck-Weisskopf line-shapes take into account Boltzmann statistics, assuming instantaneous realignment during a collision such that the molecules are oriented as to have a low energy in the field [41].…”