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Acta Physica Sinica

POPULATION TRAPPING PHENOMENA IN A TWO-LEVEL SYSTEM

LONG DE-SHUN, Ning Xi-Jing, 复旦大学现代物理研究所,上海200433

Published Jan 1, 2001• 1 citation
Publisher

Abstract

The critical criterion for realizing population trapping is deduced for a two-level system driven by a frequency-modulated laser field in terms of dressed atom model, followed by demonstrating the various population trapping behaviours under different conditions. Detailed numerical solutions of time-dependent Schr?idinger equation are found to be in good agreement with the analytical results.

DOI
10.7498/aps.50.2335

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Journal of the Optical Society of America B•Nov 1, 2003•2 citations
The critical criterion for realizing population trapping is deduced for a two-level system driven by a frequency-modulated laser field in terms of dressed atom model, followed by demonstrating the various population trapping behaviours under different conditions. Detailed numerical solutions of time-dependent Schr?idinger equation are found to be in good agreement with the analytical results.
The trapping states of a quantum system occupy a very special place in quantum optics. Here, we propose a method to realize the population trapping (PT) in a two-level atom driven by a carrier envelope phase (CEP) locked laser pulse. We present detailed numerical results on the influence of CEP in different detuned atoms beyond the rotating wave approximation and find the population is strongly dependent on CEP, the detuning and the Rabi frequency. This allows us to choose proper parameters to realize three specific trapping states: upper trapping state, half trapping state and lower trapping state. To explain the fantastic influence of CEP, we present an analytical solution under weak-field approximation, which is consistent with the numerical solution. We further define the action quantity of the pulse acting on the atom as the integral for the interaction Hamiltonian and find the population varies approximatively linearly with the action quantity. This investigation provides directive significance for achieving PT at arbitrary quantum states and insightful schemes to regulate and control the quantum dynamics of atoms via accurately controlled optical field, and the results could be beneficial for applications to laser cooling, isotope separation and so on.
We develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.
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.