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Journal of Modern Optics

On the Population Loss Dynamics of a Strongly Excited Four-level System

Ludmila S. Kancheva, E. Popov, Georgi Georgiev

Published Feb 1, 1995• 0 citations
Publisher

Abstract

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.

DOI
10.1080/09500349514550361

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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.
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
We study the effects of statistical broadening and population loss on the dynamics of strongly excited three-level quantum systems. The results of both analytic and numerical treatments of the three-level Schr\"odinger equation are displayed. In order to allow for statistical broadening, solutions are required for arbitrary detuning of the two very intense monochromatic lasers. The most efficient statistically averaged population depletion occurs when the Rabi frequency of the second transition is greater than that of the first.
A great deal of effort has been applied to understanding population dynamics within a variety of coherent excitation schemes. The goal in such studies has been to understand the conditions necessary for efficient transfer of population from one state to another. While many theoretical treatments include the effects of natural lifetimes that are present in any given system, some neglect this important aspect when considering specific cases. Adiabatic approximations are also widely made. Additionally, it is often difficult to envision how the different parameters controlling efficient population transfer are interrelated or even which parameters are the most critical, especially when the decay lifetimes are taken into account. This work describes a numerical study of coherent excitation applied to a 87Rb^{87}\mathrm{Rb}87Rb ladder system where spontaneous decay rates are included, and adiabaticity is not assumed. A useful method is introduced to explore the interdependence of various excitation parameters. The efficiency of population transfer as a function of several experimentally controllable parameters is explored, and other general trends are summarized.
The paper presents an analytic study of a two-state system which interacts with an external pulsed field. The excited state is supposed to decay out of the system with a decay rate \ensuremath{\Gamma}. We present two exact analytic solutions, viz., the finite Landau-Zener model and the Demkov-Kunike model. We also derive an approximate formula for arbitrary pulse shapes and detunings in the limit of a large decay rate. It gives the exact result for the original Landau-Zener model and the correct asymptotics for large \ensuremath{\Gamma} in the general case. We conclude that the independence of the final ground-state population on the decay rate, recently established for the original Landau-Zener model [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)], is only valid for the latter and not for any other model. The results show that the population loss ultimately decreases at large decay rates which can be viewed as a quantum analog of the overdamped oscillator.
A five-level quantum system including two low-lying states and three excited states of the ladder type coupled with four laser fields is investigated as it relates to dressed-atom models, and a dressed state is found to be independent of the ionization decaying from the highest level. Under general conditions, half of the initial population of the two low-lying states is trapped in the dressed state, leading to a low probability of ionization. Based on the analytical results, two schemes are proposed for removing population trapping. For a five-level system with hyperfine structures, such as the system for ionizing 235U atoms, population trapping takes place when the laser fields are weak and can be gotten rid of by an increase in laser intensity.