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Quantum Information and Measurement (QIM)

Peculiarities of Coherent Population Trapping During the Interaction of Three-level Atom with Non-classical Light

D. V. Popolitova, Olga V. Tikhonova

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Dynamics of three-level atom in non-classical fields is investigated analytically. Significant change of photon statistics and entanglement between the atom and quantum field are demonstrated. Peculiarities of coherent population trapping in quantum light are found.
DOI
10.1364/qim.2019.f5a.56

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Abstract The interactions of a three-level atomic system with a single mode of quantized field is investigated analytically. The effect of coherent population trapping is demonstrated for an arbitrary initial quantum field state and the peculiarities of this regime in squeezed vacuum light are found. Mutual influence between atomic and field subsystems and their entanglement arising during the interaction is demonstrated. A significant change of the field state during the interaction is shown. The possibility of photon bunching and anti-bunching and the formation of a quantum field with non-Gaussian properties is found.
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The interaction between a three-level atom and a polychromatic field with an equidistant spectrum (Λ-scheme of the atom--field interaction) has been studied theoretically. It is shown that the interaction of an atom with such a field can be reduced to its interaction with a bichromatic field with additional light shifts of transition frequencies and an additional coupling of the lower atomic levels, which is proportional to the field intensity. Owing to this coupling, the idea of the coherent population trapping can be considered only as an approximation, because the dark state is not an eigenstate of the effective Hamiltonian in the general case of arbitrary dipole moments. The analyzed model gives a simple theoretical interpretation for the formation of the atomic state, which is close to the coherent population trapping, in the radiation field of a femtosecond laser.
Coherent population trapping effect is widely studied for simple three-level systems of different types ((Xi) , (Lambda) , V). For real atoms situation is more complicated. Atomic levels are degenerated one and in the presence of external fields coupling of magnetic sublevels appears due to as radiation, so magnetic fields, leading to the systems of levels of the higher order. Our theory and model of calculation for interaction of multilevel atom with intense radiation field at the presence of external magnetic field have been applied for considering coherent population trapping effect for such systems.
The present study investigates the interaction of an equidistant three-level atom and a single-mode cavity field that has been initially prepared in a generalized coherent state. The atom–field interaction is considered to be, in general, intensity-dependent. We suppose that the nonlinearity of the initial generalized coherent state of the field and the intensity-dependent coupling between atom and field are distinctly chosen. Interestingly, an exact analytical solution for the time evolution of the state of atom–field system can be found in this general regime in terms of the nonlinearity functions. Finally, the presented formalism has been applied to a few known physical systems such as Gilmore–Perelomov and Barut–Girardello coherent states of SU(1,1) group, as well as a few special cases of interest. Mean photon number and atomic population inversion will be calculated, in addition to investigating particular non-classicality features such as revivals, sub-Poissonian statistics and quadratures squeezing of the obtained states of the entire system. Also, our results will be compared with some of the earlier works in this particular subject.