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International Science and Technology Journal

The Effect of Rabi Frequency on the Electric Susceptibility of the Six-levels Inverted-Y Atomic Systems

Suad A. Almjar, Eman O. Mafaa, Suad M. Abuzariba, Issra M. Bunhmada

Published Oct 5, 2024• 0 citations
Publisher

Abstract

The effect of changing the value of Rabi frequency has been studied in six level atomic system, Optical Bloch equations where used as the main tool to get the final shape of the model to treat the model. In this work we present a theoretical study of the non-linear optical properties of materials as a result of their interaction with laser radiation in resonance state. Density matrix was used in our formulation of Optical Bloch Equation. These equations were solved using Matlap program for Six-levels Inverted-Y Atomic Systems. A formula for calculation of electrical susceptibility was obtained. With increasing the real and imaginary parts of the electric susceptibility have also increased gradually which effects the index of refraction of the medium (real part), and the absorption window (described by the imaginary part). Moreover, when increasing the real and imaginary parts of the electric susceptibility decreased and we noticed that with increasing the value of the signal laser field related to transition |2⟩ ↔ |6⟩a distortion starts to appear on both real and imaginary parts. Key Words: Rabi frequency, Density matrix, electrical susceptibility, laser, Optical Bloch equations.

DOI
10.62341/ssei2035

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The effect of changing the value of Rabi frequency has been studied in six level atomic system, Optical Bloch equations where used as the main tool to get the final shape of the model to treat the model. In this work we present a theoretical study of the non-linear optical properties of materials as a result of their interaction with laser radiation in resonance state. Density matrix was used in our formulation of Optical Bloch Equation. These equations were solved using Matlap program for Six-levels Inverted-Y Atomic Systems. A formula for calculation of electrical susceptibility was obtained. With increasing the real and imaginary parts of the electric susceptibility have also increased gradually which effects the index of refraction of the medium (real part), and the absorption window (described by the imaginary part). Moreover, when increasing the real and imaginary parts of the electric susceptibility decreased and we noticed that with increasing the value of the signal laser field related to transition |2⟩ ↔ |6⟩a distortion starts to appear on both real and imaginary parts. Key Words: Rabi frequency, Density matrix, electrical susceptibility, laser, Optical Bloch equations.
Optical non-linearities and spectroscopy in fields that are strongly modulated and also intense are examined by obtaining the solution of the optical Bloch equations in modulated fields as a matrix continued fraction. Numerical results for emission and absorption in such fields are presented. The saturation optical susceptibilities and the different types of spectra show resonances at the Rabi frequency if the modulation index is small. With increase in this index, additional resonant features appear at submultiples of the Rabi frequency. These additional features become more and more prominent as the modulation index increases further. For modulated fields on resonance, a dressed-atom formulation is developed to explain the results obtained from the numerical evaluation of the continued fraction. The results are also applicable to non-linear spectroscopic measurements such as Raman gain when the probe field is modulated.
Abstract We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with 87Rb atoms. The density matrix equations are derived from the semi-classical Liouville’s equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n g values and the corresponding group velocities ν g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.
We investigate the interaction of a multilevel atom with a short femtosecond optical pulse beyond the scope of the rotating-wave approximation. We consider the behavior of a three-level atom under the action of two optical pulses resonant with two allowed transitions and a two-level atom under the action of a resonant optical pulse. It is shown that the imaginary part of the off-diagonal elements of the density matrix oscillates with high frequency due to the counter-rotating terms. It is shown also that an effective time-dependent addition to the Rabi frequency exists, which is of importance for ultrashort optical pulses.
In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.
In the present work, the possibility of observation of electromagnetically induced transparency in a two level system with the slow light propagation is investigated. The expression for the Rabi frequency is brought out within the rotating wave approximation and thereby it can be employed for the two level system in order to bring out the concepts of electromagnetically induced transparency in a two level system. The linear optical response of an atom with the resonant light in the medium is observed. The linear optical susceptibilities with the controlled field is found. The real part of the optical linearity leads to the refractive index of the medium.