Molecular Response Theory in Terms of the Uncertainty Principle

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.