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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling

The description of two-photon Rabi oscillations in the path integral approach

Yana Vladimirovna Degtyareva, Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков

Published Apr 26, 2018• 0 citations
Publisher

Abstract

The probability of quantum transitions of a molecule between its states under the action of an electromagnetic field is represented as an integral over trajectories from a real alternating functional. A method is proposed for computing the integral using recurrence relations. The method is attached to describe the two-photon Rabi oscillations.

DOI
10.1117/12.2315595

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The probability of quantum transitions of a molecule between its states under the action of an electromagnetic field is represented as an integral over trajectories from a real alternating functional. A method is proposed for computing the integral using recurrence relations. The method is attached to describe the two-photon Rabi oscillations.
We study the dynamics of multi-level quantum systems under the influence of electromagnetic field.Basing on the path integral approach to the quantum density matrix and transitions probability we represent functional averaging electromagnetic field influence.We demonstrate that the transition probability can be written as a path integral of real functional (the product of exponent and cosine).The numerical integration algorithm of the transitions probability in energy representation was developed.The numerical simulations of the quantum system dynamics under electromagnetic field action describe the well-known Rabi oscillations, their fluctuations and multi-photon quantum transitions.
Rabi oscillations reflect the existence of a coherent superposition of two molecular eigenstates during the interaction of molecules with a strong, resonant electromagnetic field. This phenomenon is not restricted to two-level systems. We demonstrate its occurrence in a three-level system where the radiation induces a two-photon absorption. The intermediate level is (slightly) detuned from resonance. For a theoretical description the dressed-state picture is adopted. The two-photon excitation is performed either by using one laser, yielding a one-color two-photon process, or by using two counterpropagating, spatially overlapping laser beams, yielding a two-color two-photon process. Rabi oscillations are produced by varying the fluence, i.e., by changing either the laser power or the molecule-laser interaction time. For the one-color case the two-photon transition dipole moment for an SF6{\mathrm{SF}}_{6}SF6​ transition has been determined from the relation between laser fluence and number of Rabi oscillations. For the two-color cases the detuning with the intermediate level is varied by tuning the respective laser frequencies while keeping the sum frequency constant. A dramatic change in the degree of excitation as a function of the intermediate detuning has been observed. \textcopyright{} 1996 The American Physical Society.
Abstract The evolution of the system is described as a stochastic process in the space of random joint events, in which both a symmetric difference and a symmetric sum of events are introduced. The probability of a system transition between states is represented by a series of double, triple, etc., integrals of real functionals of joint event trajectories. The expression coincides with the transition probability in quantum theory if only pairwise joint random trajectories are taken into account in the model.
We describe multilevel quantum systems dynamics in electromagnetic fields using the influence functional approach in path integration formalism. We obtain equations for the statistical density matrix and the probability of transitions of quantum systems induced by the electromagnetic field. The explicit form of the quantized electromagnetic field influence functional is concretized. Spontaneous transition of the quantum systems, the Rabi oscillations and their fluctuations are obtained. The two#photon photoelectric effect is explained.