New mechanism for non-trivial intra-molecular vibrational dynamics

Abstract

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state, coupled to all other intra-molecular vibrational states of the same molecule, and also to its environment. Molecular states forming the first reservoir are characterised by a discrete dense spectrum, whereas the environment reservoir states form a continuous spectrum. Assuming the equidistant reservoir states we find the exact analytical solution of the quantum dynamic equations. System reservoirs couplings yield to spontaneous decay of the states, whereas system-reservoir exchange leads to recurrence cycles and Loschmidt echo and double resonances at the interlevel reservoir transitions. Due to these couplings the system $S$ time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are four possible dynamic regimes of the evolution: (i) - independent of the environment exponential decay suppressing backward transitions, (ii) Loschmidt echo regime, (iii) - incoherent dynamics with multicomponent Loschmidt echo, when the system state exchanges its energy with many states of the reservoir, (iv) - cycle mixing regime, when the long term system dynamics appear to be random. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.