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

Coherent control of two-level system under bichromatic excitation

Valery Alexandrovich Astapenko

Published Jun 15, 2007• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.752096

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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.
A review of experimental and theoretical studies on radiative processes induced by a bichromatic (two-frequency) laser radiation in atoms, molecules, and solids is presented. The optical excitation of matter is considered at transitions of different types: bound—bound, bound—free, and free—free. A special attention is devoted to the possibility of the coherent control of the basic characteristics of radiative phenomena by varying the relative phase of monochromatic components of radiation. It is shown that this method opens up new possibilities for controlling photoinduced processes.
A new method for coherent phase control of excitation of atoms in a discrete spectrum under the action of bichromatic laser radiation with the frequency ratio 1 : 2 is analysed. An important feature of this control method is the presence of a electrostatic field, which removes the parity selection rule for one of the control channels. It is shown that for the phase difference between the monochromatic radiation components, corresponding to the destructive interference between channels, there exists the electrostatic field strength at which the excited atomic transition is `bleached'. It is proposed to use luminescence at the adjacent atomic transition for detecting the phase dependence of optical excitation.
The paper is devoted to the theoretical investigation of the phase control of atomic photo-excitation in discrete energy spectrum under the action of bichromatic laser field with the frequency ratio 1:2 in the presence of stationary electric field. The calculations are made for the case of alkali atoms. It is shown that the phase modulation of the photo-excitation strongly depends upon the electric field strength and the ratio between the intensities of the monochromatic components of the radiation. The optimal range of parameters for the effect observation is determined.
Abstract Mathematical modeling of the excitation dynamics of an isolated two-level particle under bichromatic irradiation is carried out on basis of solutions of the Schrödinger equation for the probability amplitudes of the states of the composite system of the particle and an interaction two-mode quantized radiation field, with the photons for each of which in a superposition state at the initial time. An analytical expression describing the change in the time of the population of the excited state of a particle in the adsorption of one of the irradiation photons in the simplest case when the irradiation is a sequence of identical pulses of a sinusoidal form is obtained. The obtained time dependence is compared with the time dependence of the diagonal matrix element of the statistical operator of the particle in the excited state found on the basis of the numerical solution of the system of the optical Bloch equations, with the corresponding irradiation described by the classical theory. Examples of significant differences in the type of these compared time dependences for a number of characteristic cases of irradiation are given.
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.