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Study of the crossing of quasi-energy levels in a four-level system

S Arushanyan, A. Melikyan, S. G. Saakyan

Published May 31, 2011• 1 citation

Abstract

It was shown previously that in taking into account only dipole transitions, the crossing of quasi-energy levels is possible in the system if any of the transitions forms a closed loop [1]. It followed herefrom that for the analysis of the crossing conditions, it is necessary to consider a system which has at least four levels. In this paper we show that we can uniquely specify which quasi-energy levels cross at the given values of the parameters of the atomic system and radiation field, without solving an algebraic quartic equation. It was found that the most suitable system for the implementation of the crossing is the group of energy levels 5 S 1/2 , 5 P 1/2 , 5 P 3/2 and 5 D 3/2 of a rubidium atom. The performed calculations of the laser field intensity and frequency values at which crossing takes place in this system show that they are easily attainable. It turned out that in this system there occur crossing of quasi-energy levels corresponding to the excited atomic levels.

DOI: 10.1070/qe2011v041n05abeh014300

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It was shown previously that in taking into account only dipole transitions, the crossing of quasi-energy levels is possible in the system if any of the transitions forms a closed loop [1]. It followed herefrom that for the analysis of the crossing conditions, it is necessary to consider a system which has at least four levels. In this paper we show that we can uniquely specify which quasi-energy levels cross at the given values of the parameters of the atomic system and radiation field, without solving an algebraic quartic equation. It was found that the most suitable system for the implementation of the crossing is the group of energy levels 5 S 1/2 , 5 P 1/2 , 5 P 3/2 and 5 D 3/2 of a rubidium atom. The performed calculations of the laser field intensity and frequency values at which crossing takes place in this system show that they are easily attainable. It turned out that in this system there occur crossing of quasi-energy levels corresponding to the excited atomic levels.

We have studied the case of optical multistability in a four-level system interacting with two coherent fields. The system, shown in fig. 1, consists of two pairs of energy levels, 1, 2, and 3, 4, absorption occurs between levels 1- 4 and emission takes place from 3-2. The 'intra-band' transitions, 4-3 and 2- 1 are assumed non-radiative and extremely fast. The system is irradiated by two beams, one tuned to the absorption spectrum, the other to the emission spectrum, in a Fabry-Perot cavity. Solution of the optical Bloch equations following [1] enables us to write the input-output equations, la and lb, in the form where Yi, Xi, are the appropriately scaled input and output fields, Ci the 'bistability' parameter, and Δi, ϕi, the atomic and cavity detuning respectively, of field i.

We consider a gas of two-level atoms of two species (for example, natural Rb vapor consisting of two isotopes) in the field of laser radiation tuned close to resonance with the certain transition of a specific iostope. This radiation may turn to be rather close to a near lying transition of other isotope (within the linewidth of laser radiation), so it is necessary to take into account the possibility of excitation of other isotope in order to evaluate the enrichment degree if it is aimed at the isotope separation by means of selective excitation with subsequent chemcial reaction (in our example the rubidium hydride formation) of the excited isotope which is believed to take place at a rate much higher than that in the ground state of the atom.

Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly inhomogeneous line broadening due to such causes as doppler shift arising from translational velocity. The ratio of the number of molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width ∆, where E0 is the amplitude of the electric field in the incident radiation and is the dipole moment matrix element for the transition. Excitation functions obtained in a previous paper (I) for various values of the ratio γ/β, where γ is the half line-width in the absence of inhomogeneous broadening, are used to obtain the variation of N2/N with time under conditions of mixed broadening for various values of the ratio γ/∆ and γ/β, when the exciting radiation is in exact resonance with the central frequency of the transition.

Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly homogeneous line-broadening. The ratio of the number of atoms or molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width γ. E0 is the amplitude of the electric field in the incident radiation and the dipole moment matrix element for the transition. Exact expressions for N2/N as a function of time are given for the situation when the frequency ω/2π of the radiation is exactly equal to that of the transition ω0/2π. Numerical calculations are made for the situation when the ‘detuning’ δ ═ ω — ω0 is not equal to zero. Approximate expressions are also derived in terms of δ for use in a later paper which deals with mixed homogeneous and inhomogeneous line-broadening.