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Communications in Physics

Influence of third-order susceptibility on electromagnetically induced grating in a three-level V-type atomic system

Bang Nguyen Huy, Khoa Dinh Xuan, Nga Luong Thi Yen, Ho Hai Quang, Van Ai Nguyen, Le Van Doai

Published Dec 15, 2024• 0 citations
Publisher

Abstract

In addition to the suppressed absorption in the atomic resonance region, an electromagnetically induced transparency (EIT) medium also possess giant nonlinear dispersion which significantly affects the optical properties of the medium. In this work, we study the influence of third-order nonlinear susceptibility on electromagnetically induced grating (EIG) in a three-level V-type atomic medium. By applying stationary perturbation theory to the density matrix equations describing the time evolution of the quantum states of the system, we have found density matrix solutions to the third-order perturbation corresponding to the third-order susceptibility, and found the transmission function for the probe light. Using the Fourier transform of the transmission function, we can obtain the intensity distribution function of the EIG diffraction spectrum as a function of laser parameters and the atomic medium. To see the influence of third-order susceptibility on EIG diffraction spectrum, we have simulated EIG spectra in two cases with and without third-order susceptibility. We found that the first-order diffraction efficiency was significantly enhanced when third-order susceptibility was introduced.

DOI
10.15625/0868-3166/21530

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In addition to the suppressed absorption in the atomic resonance region, an electromagnetically induced transparency (EIT) medium also possess giant nonlinear dispersion which significantly affects the optical properties of the medium. In this work, we study the influence of third-order nonlinear susceptibility on electromagnetically induced grating (EIG) in a three-level V-type atomic medium. By applying stationary perturbation theory to the density matrix equations describing the time evolution of the quantum states of the system, we have found density matrix solutions to the third-order perturbation corresponding to the third-order susceptibility, and found the transmission function for the probe light. Using the Fourier transform of the transmission function, we can obtain the intensity distribution function of the EIG diffraction spectrum as a function of laser parameters and the atomic medium. To see the influence of third-order susceptibility on EIG diffraction spectrum, we have simulated EIG spectra in two cases with and without third-order susceptibility. We found that the first-order diffraction efficiency was significantly enhanced when third-order susceptibility was introduced.
Abstract A probe laser beam can be completely absorbed in an atomic resonance frequency region, however, if a coupling laser beam is further applied to the atom, the atomic medium can exhibit electromagnetically induced transparency, i.e the probe beam can be completely transmitted through the atomic medium. Thus, if the coupling beam is a standing wave field with nodes and antinodes, it will cause in space a periodic modulation of the transmitted spectrum of the probe field. This means that the probe field propagates through the atomic medium just as it passes through a diffraction grating which is called electromagnetically induced grating. Based on amplitude or phase modulation of transmission function, the absorption grating or the phase grating can be formed, respectively. In this work, based on controllable absorption and dispersion properties of a three-level V-type atomic system, we study the control of the absorption grating and the phase grating with respect to the intensity and the frequency of the laser fields. The absorption diffraction pattern at the two-photon resonance is obtained, while the phase diffraction pattern appears when there is a frequency shift of either the coupling frequency or the probe frequency compared to the corresponding atomic resonance frequency. By adjusting the coupling or/and probe laser frequency, the absorption grating can be converted into the phase grating and the high-order diffraction efficiency can also be improved.
A strong coupling standing wave, interacting with three-level \ensuremath{\Lambda}-type (or ladder-type) atoms, can diffract a weak probe field (propagating along a direction normal to the standing wave) into high-order diffractions, a phenomenon which we name electromagnetically induced grating (EIG). We develop in this work a theory for studying EIG in a homogeneously broadened medium consisting of three-level \ensuremath{\Lambda}-type atoms. We show that by taking advantage of the absorption and dispersion properties of electromagnetically induced transparency one can create an atomic grating that can effectively diffract light into the first-order direction.
Abstract We have theoretically studied the electromagnetically induced grating (EIG) in a three-level closed Λ-type atomic system. The upper level is coupled to the two lower levels via a strong control and a weak probe field. In addition to these two optical fields a weak microwave field is also applied to couple the lower two levels. Our results show that the relative phase of the three fields in the presence of microwave field enhances the dispersion in the medium and consequently provides control over magnitude of the diffraction intensities. We have optimized the system parameters such as strength of the fields and interaction length to attain increased first order diffraction. Furthermore, we have also studied the effects of probe detuning on diffraction intensities. Interestingly, the probe detuning results in suppression of the zeroth order intensity while increasing the higher order intensities.
We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.
We propose a scheme for inducing a blazed transmission grating in a four-level, NNN-type atomic medium under electromagnetically induced transparency (EIT). The blazed grating relies on the giant Kerr nonlinearity that the atomic medium exhibits under EIT. The grating is created using an intensity mask in one of the driving optical fields and only weak fields with intensities below saturation level are involved. Diffraction efficiencies of a resonant probe beam close to 100100%100 are predicted.
Electromagnetically induced grating (EIG) is extensively investigated as an artificial periodic structure in recent years owed to its simple reconfiguration and flexible adjustability. We report the experimental observation of EIG in cold rubidium atoms. The coupling and probe lasers are corresponding to the 5S1/2−5P1/2 and 5S1/2−5P3/2 transitions of a V-type electromagnetically induced transparency (EIT) configuration, respectively. A clear spatial intensity distribution of the probe laser with distinguished third-order diffraction pattern is recorded to character the EIG. The influence of the pertinent experimental parameters, such as coupling laser intensity and two-photon detuning on the diffraction pattern is investigated in detail. This is the first observation in visual form of the EIG in cold rubidium atoms. These results may potentially provide a nondestructive method to image cold atoms and pave the way for investigating non-Hermitian physics and the control of light dynamics.