The quantum transitions probability as paths-integral in energy states space

By the use of the functional integration approach (paths integral approach) we present a non-perturbative method for dynamics of multi-levels quantum systems (such as atoms, molecules and nanosystems) interacting with high-intensity laser field describing. The probability of transitions between investigated quantum system states under electromagnetic field action is written as functional integral in energy representation (in investigated quantum system energy states space). In this approach we calculate probabilities of diatomic molecules transition between rotating quantum states under the ultrashort laser pulses train action by the use of numerical simulations. We investigate the dynamics of rotating quantum states population for $^{14}\mathrm N_2$ and $^{15}\mathrm N_2$ molecules interacting with a train of picoseconds laser pulses with different train period and intensity. We show for some train periods there are resonances of population transfer from low rotating quantum states of investigated molecules to high states. We study these resonances for various laser field intensities and pulses train periods. We note that in resonance case the parameters of laser field are different for $^{14}\mathrm N_2$ and $^{15}\mathrm N_2$ molecules. Obtained results indicate on the possibility of molecules rotating states selective exitation by ultrashort laser pulses train. Our numerical results are in agreement with results of experimental studies [Phys. Rev. Lett., 2012, vol. 109, 043003].