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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multilevel systems and resonant interaction with bichromatic fields

Alexander F. Bukatin, Mikhail Borisovich Mysenko, Sergey K. Potapov

Published Jul 1, 1992• 0 citations
Publisher

Abstract

The problem of a two-level system perturbed by a strong resonant bichromatic field was examined theoretically and later experimentally in the microwave region. The two-level model can be inadequate in the optical region, for example in sodium vapors due to the fine structure of the upper state. The two-level model fails for barium vapor when the linear polarizations of bichromatic fields are different. Consequently, the theoretical investigation of the multilevel case can be a problem of great interest.

DOI
10.1117/12.131174

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The problem of a two-level system perturbed by a strong resonant bichromatic field was examined theoretically and later experimentally in the microwave region. The two-level model can be inadequate in the optical region, for example in sodium vapors due to the fine structure of the upper state. The two-level model fails for barium vapor when the linear polarizations of bichromatic fields are different. Consequently, the theoretical investigation of the multilevel case can be a problem of great interest.
Coherent phase control under the interaction between bichromatic radiation with multiple frequencies and quantum systems is the topic of the last time investigations both experimental and theoretical. This type of nonlinear optical control enables one to manipulate the characteristics of radiation processes by the change of the relative phase of bichromatic field. The present study is devoted to the theoretical analysis of the coherent control of two-level system behavior under bichromatic excitation in the frame of perturbation approach. The general expressions have been derived which are valid for any integer ratio n between the frequencies of monochromatic components of radiation. Obtained formulas describe the system characteristics as functions of relative phase of bichromatic field and other radiation parameters. Bichromatic excitation of Rubidium atom is considered as numerical example.
In recent years interest has significantly quickened in investigation of nonlinear optical and spectroscopic phenomena in such unique objects as Rydberg atoms (the atoms in the energy states near the ionization limit) and van der Waals complexes (dimers). These objects are characterized, in particular, by that their energy states are strongly degenerate due to a large value of angular (rotational) momentum. Here, the problem arises of adequate theoretical description of experimental results, especially when polarization peculiarities of nonlinear radiation processes are considered. The problem is caused by the existence of a huge number of quantum magnetic sublevels of energy states, which are, in the general case, coherently coupled to each other and take part in the radiation processes. Figure 1 gives a vivid presentation of the problem arising even in such a seemingly simple case when one need describe the radiation transitions caused by a strong monochromatic field between two energy levels with large values of the angular momentum J. If the field polarization is arbitrary, the whole set of the magnetic sublevels turn out to be coupled by radiative transitions. Formally, the problem becomes essentially multilevel. In this case not only the hope fades of solving it analytically using the traditional quantum-mechanical approach, but the problems of numerical solution grow abruptly with increasing quantum number J as well. On the other hand, as is often the case, every cloud has a silver lining. With large J we approach the situation when the rotational motion of particles can be described classically. It turns out that the transition from the quantum description of orientation states of the angular momentum to the classical one simplifies the problem radically: it reduces to the problem of radiation processes in the simplest model of nondegenerate states. In this case the rotational motion manifests itself in a dependence of the density matrix elements on orientation angles of the angular momentum as on a parameter.
The behavior of a two-level system interacting with a bichromatic classical field is studied. Analytic expressions are found for the Green's-function operator for the system if the field is weak and near resonance, and a systematic procedure is developed to obtain the Green's-function operator in a more general case. The results are used to calculate the probability of a transition from the lower to the upper state; resonance conditions occur when the level spacing of the system, ${\ensuremath{\omega}}_{ba}$, is near $n{\ensuremath{\omega}}_{\ensuremath{\lambda}}\ensuremath{-}(n\ensuremath{-}1){\ensuremath{\omega}}_{\ensuremath{\mu}}$, where nnn is a positive or negative integer, and ${\ensuremath{\omega}}_{\ensuremath{\lambda}}$ and ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ are the frequencies of the components of the field. The resonance frequency depends on the intensity of the field components. In addition, the cross section for scattering photons out of the field has been calculated. It is found that the spectrum of the scattered radiation consists of lines at frequency ${\ensuremath{\omega}}_{k}={\ensuremath{\omega}}_{\ensuremath{\mu}},{\ensuremath{\omega}}_{\ensuremath{\lambda}}$, and odd harmonics of these, combinations of the fundamental and the harmonics with $\ensuremath{\Delta}={\ensuremath{\omega}}_{\ensuremath{\lambda}}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\mu}}$, and satellites shifted from all of these features by an amount which depends on the intensity of the field and ${\ensuremath{\omega}}_{ba}$. The cross section is intensity dependent particularly insofar as the location of resonance peaks is concerned. It is suggested that this effect may be exploited in transferring intensity modulation of one component of the field to phase modulation in the other component.
We have theoretically and experimentally investigated the V-type three-level system in hot sodium atomic vapor interacting with two optical waves: probe, resonant to the D1 line, and coupling, the D2 line. Theoretically, probe transmission spectra are simulated by using a perturbative treatment including eight hyperfine levels (multilevel system) in the 3S1/2, 3P1/2, and 3P3/2 states. The spectra are composed of linear absorption, saturated absorption, and electromagnetically induced transparency (EIT) signals. By comparing this simulation with the experimental results, we concluded that we have indeed observed EIT signals when the coupling beam is resonant to the D2-line closed transition.
We have investigated the dynamic Stark effect in a J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0 three-level ladder system in an atomic beam of natural barium. An intense, actively stabilized cw dye laser was tuned to resonance between the upper two levels, and a similar laser was scanned through resonance with the transition connecting the lower two levels. Fluorescence arising from transitions out of the middle and upper levels was separately recorded as a function of probe laser frequency. This is the third and final paper in a series, of which the first two papers investigated theoretically and experimentally the ``weak-probe'' case, where the intensity of the probe laser was sufficiently low for the interaction between the atoms and the probe laser to be linear. In this paper we present an experimental investigation of the ``strong-probe'' case, where both lasers interact nonlinearly with the atoms, and we compare the results with the predictions of a theoretical model based on the optical Bloch equations.