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Journal of Physics B Atomic and Molecular Physics

Population distribution in a strongly excited four-level system

Ludmila S. Kancheva, S. Rashev

Published Aug 28, 1985• 2 citations
Publisher

Abstract

The steady-state population distribution of a four-level system resonantly excited by three laser fields of arbitrary strength was studied using density matrix formalism. The conditions for obtaining maximum population in the highest level as well as for population inversion between the highest and the lowest levels of the system are discussed.

DOI
10.1088/0022-3700/18/16/024

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The steady-state population distribution of a four-level system resonantly excited by three laser fields of arbitrary strength was studied using density matrix formalism. The conditions for obtaining maximum population in the highest level as well as for population inversion between the highest and the lowest levels of the system are discussed.
A general method is given to determine the steady-state level populations for NNN-level systems interacting with $N\ensuremath{-}1$ strong resonant laser beams. For a three-level system it reproduces recent results of Whitley and Stroud. For a four-level system it leads to simple conditions for the population inversion between the highest and the lowest level. However, the population of the highest level can never exceed 0.5.
General expressions for the steady-state population distribution and complex susceptibilities of a three-level system interacting with two strong near-resonant electromagnetic fields are obtained using a density-matrix formalism. A complete treatment of the steady-state population distribution established in the three-level system, under the action of two strong fields with arbitrary resonance detunings is presented. The criterion for maximal populations of the exciting levels, as well as conditions in which the population of the exciting levels exceeds the population of the ground state are found. The modification of the absorption and emission lines with increasing intensity of the second (probe) field is considered. The emphasis in the present treatment, as distinct from Panock and Temkin (see IEEE J. Quantum Electron., vol.QE-13, p.476 (1977)) is on the consideration of the arbitrary distribution of the equilibrium populations of the system which exhibits a number of interesting features which have not been previously discussed.
The population dynamics of a four-level atom, with decay from the highest level, interacting with three arbitrarily intense laser fields is studied. In a previous paper [4], this four-level system was investigated with no decay included. For a specific set of input fields, it was found that substantial population could be transferred from the ground state to the highest excited state. In that study, the detunings required to obtain this maximum population transfer were not explained. In this present work, we have introduced a two-level atom model that explains this choice of detunings. They are such as to make the three fields resonant with the Stark-shifted
Interaction of multilevel atoms with intense radiation fields is treated in a simplified model using a semiclassical theory. Steady-state level-populations in four-level and five-level systems are calculated. It is found that population inversion appears between the highest level and an intermediate level under intense fields. The absorption lineshape of the transition between the highest two levels in a five-level or a six-level system is calculated in a weak probe-field approximation. The lineshape for the five-level (six-level) system splits into four (five) peaks at high excitation intensities.
In the case of incoherent pumping, laser without population inversion in a resonant three-level Δ -configuration system is investigated. By taking the strong coupling field limit, we obtain the approximate steady-state analytical solution of populations and imaginary part of coherences within the dressed-state regime, and discuss the condition of the generating of laser without inversion and the dependences of population distribution and system gain on Rabi frequency of the probe and coherence fields. The results show that the resonant three-level Δ-configuration system is always in the state of no population inversion, and laser without inversion occurs if one of the two fields is strong. When one of the two fields is much stronger than the other one, the gain without inversion is independent of the two Rabi frequencies.
The population dynamics of a strongly excited four-level quantum system with allowed loss out of the system from the highest state are analysed. This work has been stimulated by the paper of Cardimona et al. and represents a more general treatment of the problem studied by them. In particular, we show that the reduction in the ground-state population decay rate for large losses is not a consequence of the two-level behaviour but is a more general phenomenon. On the basis of numerical and analytical solutions we demonstrate that for an arbitrary excitation regime, at sufficiently large decay rate, the population loss dynamics of the four-level system is reduced to that of a slowly damped three-level system. We demonstrate also that the detailed knowledge of the coherent population dynamics enables us to predict the effect of decay rate on the population's time evolution for arbitrary choice of dynamic parameters.