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Journal of Experimental and Theoretical Physics

Coherent repopulation of the components of a three-level quantum system in the field of a pulsed bichromatic radio frequency wave

Д.Ф. Зарецкий, S. B. Sazonov

Published Apr 1, 1998• 0 citations
Publisher

Abstract

The coherent repopulation of a quantum system consisting of three nonequidistant levels in the field of a resonant bichromatic rf wave is studied. The atoms are assumed to have an impulsive interaction with the rf wave in which the pulse duration is less than any of the relaxation times. The hyperfine structure of gas atoms and a system of atomic oscillator levels in a magnetic trap are considered as examples of such a quantum system. It is shown that in the second case, the coherent repopulation effect can be used to cool neutral atoms in magnetic traps.

DOI
10.1134/1.558520

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The coherent repopulation of a quantum system consisting of three nonequidistant levels in the field of a resonant bichromatic rf wave is studied. The atoms are assumed to have an impulsive interaction with the rf wave in which the pulse duration is less than any of the relaxation times. The hyperfine structure of gas atoms and a system of atomic oscillator levels in a magnetic trap are considered as examples of such a quantum system. It is shown that in the second case, the coherent repopulation effect can be used to cool neutral atoms in magnetic traps.
We consider the resonant interaction between atoms with hyperfine energy levels and a bichromatic radio-frequency field. Nuclear Zeeman levels of an impurity center in a magnetic host form a structure of this kind. Using the spin-density-matrix formalism, we solve the problem of coherent repopulation of a system of three of these levels under the action of a bichromatic resonant radio-frequency wave, taking into account transverse relaxation, and note the connection between this effect and the well-known phenomenon of coherent population capture when a laser bichromatic field interacts resonantly with a three-level system. We discuss various possibilities for observation of this effect experimentally.
We consider the case of interaction of a three-level atom with a high intensity pulse electromagnetic field. Rabi frequencies are assumed to be of the order of the transition frequency or greater. We demonstrate that coherent population trapping exists even in such a case when the usual rotating-wave approximation is no longer valid. However, a certain condition on the phases of electromagnetic wave components has to be satisfied in order to make coherent population trapping possible. This condition is specific for the strong field case in contrast to the case where the rotating-wave approximation is valid. Also we point out some elements for which a model of an atom with a finite number of levels may still be valid while the rotating-wave approximation breaks down.
Phase-dependent resonance transitions induced in two-level atoms by a bichromatic field are reported. Strong phase effects are observed in the interaction of a fast atomic beam with a standing-wave rf field. In the atomic rest frame, this field consists of two components with different frequencies and a controlled initial phase difference. Numerical calculations including well-defined phase factors are performed in the time-dependent density matrix formalism. The observed effects are in excellent agreement with this theory.
The theory of interaction of the elementary atomic systems with resonant laser fields is well known. At the same time multilevel systems are investigated in less details. We consider T1 atoms as multilevel system due to removal of degeneracy of levels with different magnetic quantum number in strong radiation and magnetic fields. It is known that recently investigated effect, connected with the quantum interference of states is coherent population trapping (CPT). We propose the method of numerical calculations of interaction of real atoms with strong radiation fields and magnetic field, valid in the case when the values of Rabi frequencies considerably exceed the line widths. This method can be applied to investigate the CPT effect and influence of the external magnetic field on it.
Nonlinear phenomena occurring during interaction between an atom and a strong rf field of resonant or nonresonant frequency are reviewed. The account is given in both semiclassical and consistently quantummechanical languages. The concept of an atom "dressed by the radiation field" in which not only the optical-frequency field but also the radio-frequency field is quantized is presented in detail. The results are summarized of theoretical and experimental studies of multiphoton transitions, radiative shifts of normal magnetic resonance lines, parametric resonance, and coherent resonances under the conditions of optical pumping. The influence of nonresonance rf fields on magnetic properties and the rate of magnetic relaxation of atoms is discussed.