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Physical Review A

Electromagnetically induced grating with maximal atomic coherence

Silvânia A. Carvalho, Luı́s E. E. de Araujo

Published Oct 31, 2011• 12 citations
Publisher

Abstract

We describe theoretically an atomic diffraction grating that combines an electromagnetically induced grating with a coherence grating in a double-$\ensuremath{\Lambda}$ atomic system. With the atom in a condition of maximal coherence between its lower levels, the combined gratings simultaneously diffract both the incident probe beam as well as the signal beam generated through four-wave mixing. A special feature of the atomic grating is that it will diffract any beam resonantly tuned to any excited state of the atom accessible by a dipole transition from its ground state.

DOI
10.1103/physreva.84.043850

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We describe theoretically an atomic diffraction grating that combines an electromagnetically induced grating with a coherence grating in a double-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ atomic system. With the atom in a condition of maximal coherence between its lower levels, the combined gratings simultaneously diffract both the incident probe beam as well as the signal beam generated through four-wave mixing. A special feature of the atomic grating is that it will diffract any beam resonantly tuned to any excited state of the atom accessible by a dipole transition from its ground state.
We propose a scheme for effectively creating a type of all optical device called electromagnetically induced two-dimensional grating by utilizing a four-level coherent atomic medium, which is coherently driven by two orthogonal standing-wave fields. With a far-off resonant trigger field, a spatially modulated cross-phase modulation takes place accompanied by vanishing absorption. The resulting phase grating can diffract the probe beam into high-order directions. When a resonant trigger field is applied on the atoms, the probe obtains gain without inversion due to the atomic coherence effect. And then a gain-phase grating is formed. The diffraction efficiency can be significantly improved compared with that of phase grating. The results show that the diffraction efficiencies attainable by the gratings strongly depend on the interaction length, coherent field intensity, probe field detuning and coherent field detuning. Therefore, the proposed gratings can be used as two-dimensional multi-channel beam splitter which have potential application in optical networking and communication.
We have experimentally investigated laser diffraction on electromagnetically induced gratings in a degenerate open two-level system. The experiment employs the standard backward four-wave mixing configuration and the open ${6S}_{1/2}(F=4)\ensuremath{\rightarrow}{6P}_{3/2}{(F}^{\ensuremath{'}}=4)$ transition of cold cesium atoms. Population and coherence gratings are accessed for different relative polarizations of the incident laser beams. Natural and subnatural linewidths are observed depending on which frequency of the incident beams is scanned and reveal the effect of the atomic motion on the diffraction spectra. A simple theoretical model using a three-level $\ensuremath{\Lambda}$ system is in reasonable agreement with the observed results and allowed us to make a close connection with the phenomenon of electromagnetically induced transparency.
We demonstrate a scheme for coherently induced grating based on a mixture of two three-level atomic species interacting with two standing-wave fields. As a result of interaction between the absorptive and amplified Raman resonances, the refractive index of the medium can be enhanced and modulated periodically. Then a sinusoidal grating, which can diffract the probe field into high-order directions, is coherently formed in the medium. The proposed scheme is theoretically investigated in a mixture of atomic isotopes of rubidium. The results show that the diffraction efficiency depends strongly on the two two-photon detunings of the two Raman transitions and the intensities of the two driving standing-wave fields. The proposed electromagnetically induced grating scheme may be applied to the all-optical switching and beam splitting in optical networking and communication.
An electromagnetically induced grating in a four-level tripod-type atomic system is studied theoretically. By virtue of a weak standing-wave signal field, the phase modulation effectively diffracts a weak probe field into the first-order direction. By changing the weak signal field, the diffraction of the weak probe field can be modulated in real time, and a first-order diffraction efficiency of more than 32% can be obtained with proper parameters. Such a system has a potential application in an all-optical switch controlled by a weak optical signal.
Abstract A scheme for two-dimensional (2D) electromagnetically induced grating via spatial gain and phase modulation is presented in a two-level atomic system. Based on the interactions of two orthogonal standing-wave fields, the atom could diffract the weak probe beam into high-order directions and a 2D diffraction grating is generated. It is shown that the diffraction efficiency of the grating can be efficiently manipulated by controlling the Rabi frequencies of control fields, the detunings of the control and probe fields, and interaction length. Different from 2D cross-grating via electromagnetically induced transparency in a four-level atomic system, the present scheme results from the spatial modulation of gain and phase in a simple two-level system, which could lead to 2D gain-phase grating with larger diffraction intensities in the diffraction directions. The studies we present may have potential applications in developing photon devices for optical-switching, optical imaging and quantum information processing.
The electromagnetically induced grating is investigated in a four-level double V-type quantum system. It is shown that the electromagnetically induced transparency established by the cross-Kerr nonlinear effect can be canceled by the four-wave mixing in a closed-loop atomic system and that the diffraction of the probe beam depends on the relative phase of the applied fields and can be controlled by this parameter. We find that an additional nonlinear contribution is established in the medium response by applying a microwave field to the system and that the electromagnetically induced absorption grating turns to the electromagnetically induced phase grating. This contribution leads to 100% diffraction efficiency in the first-order direction, so we can say that the proposed grating could be considered as a special candidate for the optical networking and communication.