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arXiv:1310.3318 · Physical Review A

Double-double electromagnetically induced transparency with amplification

Hessa M. M. Alotaibi, Barry C. Sanders

Published Feb 27, 2014• 54 citations
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Abstract

We show that an alkali-metal atom with a tripod electronic structure can yield rich electromagnetically-induced-transparency phenomena even at room temperature. In particular we introduce double-double electromagnetically induced transparency wherein signal and probe fields each have two transparency windows. Their group velocities can be matched in either the first or second pair of transparency windows. Moreover, signal and probe fields can each experience coherent gain in the second transparency windows. We explain using a semiclassical dressed picture to connect the tripod electronic structure to a double-$\ensuremath{\Lambda}$ scheme.

DOI
10.1103/physreva.89.021802

Related papers

Double Double Electromagnetically Induced Transparency

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This study demonstrates that tripod atom-field electronic structure can yield rich electromagnetically induced transparency phenomena, even at room temperature. In particular, we introduce double double electromagnetically induced transparency (DDEIT), wherein signal and probe fields each have two transparency windows. Their group velocities can be matched in either the first or second pair of transparency windows. Moreover, signal and probe fields can each experience coherent Raman gain in the second transparency window. Our investigation has demonstrated that the self-phase modulation (SPM) and cross-phase modulation (XPM) vanish at the center of two transparency windows for resonant coupling field. However, the values of the XPM and SPM in the region of the second EIT window are improved by a factor of $1000$ compared to their values in the region of the first EIT window under the same conditions, and have non-zero values at the center of the second EIT window for nonresonant coupling field. Additionally, we derive an analytical solution for the wave equation describing the propagation of the probe field whose amplitude-envelope function is described by the fundamental mode Laguerre-Gaussian function. Our solution exhibits that the group velocity of the probe field reduces as the field propagates through the medium. The group velocity reduction is a consequence of spatially-varying susceptibility. The variation of the susceptibility is established by employing signal field whose amplitude-envelope functions is also described by the fundamental mode Laguerre-Gaussian function. For Doppler-broadened media, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of electromagnetically induced transparency (EIT) windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-field strength regimes quantified by the Rabi frequency, for slowing the probe field. Our scheme exploits the fact that the second transparency window is sensitive to a temperature-controlled signal-field nonlinearity, whereas the first transparency window is insensitive to this nonlinearity.

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Journal of Atomic and Molecular Physics•Jan 1, 2008•0 citations
We show that an alkali-metal atom with a tripod electronic structure can yield rich electromagnetically-induced-transparency phenomena even at room temperature. In particular we introduce double-double electromagnetically induced transparency wherein signal and probe fields each have two transparency windows. Their group velocities can be matched in either the first or second pair of transparency windows. Moreover, signal and probe fields can each experience coherent gain in the second transparency windows. We explain using a semiclassical dressed picture to connect the tripod electronic structure to a double-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ scheme.
This study demonstrates that tripod atom-field electronic structure can yield rich electromagnetically induced transparency phenomena, even at room temperature. In particular, we introduce double double electromagnetically induced transparency (DDEIT), wherein signal and probe fields each have two transparency windows. Their group velocities can be matched in either the first or second pair of transparency windows. Moreover, signal and probe fields can each experience coherent Raman gain in the second transparency window. Our investigation has demonstrated that the self-phase modulation (SPM) and cross-phase modulation (XPM) vanish at the center of two transparency windows for resonant coupling field. However, the values of the XPM and SPM in the region of the second EIT window are improved by a factor of 100010001000 compared to their values in the region of the first EIT window under the same conditions, and have non-zero values at the center of the second EIT window for nonresonant coupling field. Additionally, we derive an analytical solution for the wave equation describing the propagation of the probe field whose amplitude-envelope function is described by the fundamental mode Laguerre-Gaussian function. Our solution exhibits that the group velocity of the probe field reduces as the field propagates through the medium. The group velocity reduction is a consequence of spatially-varying susceptibility. The variation of the susceptibility is established by employing signal field whose amplitude-envelope functions is also described by the fundamental mode Laguerre-Gaussian function. For Doppler-broadened media, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of electromagnetically induced transparency (EIT) windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-field strength regimes quantified by the Rabi frequency, for slowing the probe field. Our scheme exploits the fact that the second transparency window is sensitive to a temperature-controlled signal-field nonlinearity, whereas the first transparency window is insensitive to this nonlinearity.
We investigate the nonlinear optical susceptibility of an alkali-metal atom with tripod electronic configuration responsible for generating cross-phase modulation and self-phase modulation under the condition of double-double electromagnetically induced transparency. Our investigation demonstrates an enhancement in the nonlinear optical susceptibility of an alkali-metal atom by a factor of 1000 in the region of the second transparency window. This enhancement is in comparison with the atom's susceptibility in the first transparency window for the same parameters under the same conditions. Nonlinear-absorption enhancement arises by canceling Raman-gain generation, which arises when the probe and signal fields have equal intensities. At the center of the second transparency window, we obtain the condition required to attain a nonvanishing nonlinear optical susceptibility. In the bare-state picture, the coupling field must be off resonant from a bare-to-bare-state transition, while working in the semiclassical dressed picture required the signal field to be tuned off resonantly with a bare-to-dressed-state transition. The relation that governs the values of coupling- and signal-field detuning are also obtained. Our scheme exhibits the fact that the second transparency window has advantages over the first transparency window with respect to obtaining an enhanced Kerr effect, and our calculation includes simulation of both low-temperature and Doppler-broadened regimes.
We experimentally demonstrate coherent amplification of probe field in a tripod-type atoms driven by strong coupling, signal and weak probe fields. We suppress linear and nonlinear atomic absorptions for resonant and near resonant probe via double electromagnetically induced transparency (DEIT). Combining these advantages of suppressed absorption along with temperature- or atomic-density-controlled transfer of population(ToP) between hyperfine ground states, we can induce near-resonant amplification of probe through stimulated Raman scattering(SRS) pumped by low-intensity signal field. The increased population difference of initial and final states of SRS due to increased ToP rate, together with reduced absorption at the second EIT window in an optically thick Cesium vapor, gives rise to highly effective coherent amplification.
The electromagnetically induced transparency (EIT) phenomenon in a four level atomic system with tripod configuration is studied. The results show that this configuration is equivalent to the combination of two single three-level ΛΛΛ configurations, which, under certain conditions, results in the so-called double-EIT (DEIT) phenomenon. The properties of the double transparency windows for DEIT are discussed in detail and the possible experimental scheme is proposed.
We implement double electromagnetically induced transparency (DEIT) in rubidium vapor using a tripod-shaped energy-level scheme consisting of hyperfine magnetic sublevels of the 5S1/2-->5P1/2 transition. We show experimentally that through the use of DEIT one can control the contrast of transparency windows as well as group velocities of the two signal fields. In particular, the group velocities can be equalized, which holds promise to greatly enhance nonlinear optical interaction between these fields.
The absorption properties in an inverted-tripod scheme atomic system driven by the coherent fields are investigated by means of the semiclassical theory.The result obtained by means of numerical method indicates that by adjusting the Rabi frequencies of the coherent fields,there appear triple,double,single electromagnetically induced transparency(EIT).In the triple EIT,the location of transparent windows can be controlled by adjusting the detunings for the coherent fields,and changes continuously,i.e.there exist a series of continuous frequencies for the probe field propagating in an atomic medium without absorption in a certain range.Finally,the explanations of these phenomena are given by using the dressed states.