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Showing papers on "Electromagnetically induced transparency published in 2001"


Journal ArticleDOI
25 Jan 2001-Nature
TL;DR: A theoretical model is presented that reveals that the system is self-adjusting to minimize dissipative loss during the ‘read’ and ‘write’ operations, anticipating applications of this phenomenon for quantum information processing.
Abstract: Electromagnetically induced transparency1,2,3 is a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium; a ‘coupling’ laser is used to create the interference necessary to allow the transmission of resonant pulses from a ‘probe’ laser. This technique has been used4,5,6 to slow and spatially compress light pulses by seven orders of magnitude, resulting in their complete localization and containment within an atomic cloud4. Here we use electromagnetically induced transparency to bring laser pulses to a complete stop in a magnetically trapped, cold cloud of sodium atoms. Within the spatially localized pulse region, the atoms are in a superposition state determined by the amplitudes and phases of the coupling and probe laser fields. Upon sudden turn-off of the coupling laser, the compressed probe pulse is effectively stopped; coherent information initially contained in the laser fields is ‘frozen’ in the atomic medium for up to 1 ms. The coupling laser is turned back on at a later time and the probe pulse is regenerated: the stored coherence is read out and transferred back into the radiation field. We present a theoretical model that reveals that the system is self-adjusting to minimize dissipative loss during the ‘read’ and ‘write’ operations. We anticipate applications of this phenomenon for quantum information processing.

1,902 citations


Journal ArticleDOI
TL;DR: An experiment is reported in which a light pulse is effectively decelerated and trapped in a vapor of Rb atoms, stored for a controlled period of time, and then released on demand.
Abstract: We report an experiment in which a light pulse is effectively decelerated and trapped in a vapor of Rb atoms, stored for a controlled period of time, and then released on demand. We accomplish this ``storage of light'' by dynamically reducing the group velocity of the light pulse to zero, so that the coherent excitation of the light is reversibly mapped into a Zeeman (spin) coherence of the Rb vapor.

1,651 citations


Journal ArticleDOI
20 Sep 2001-Nature
TL;DR: Theoretical and experimental work has demonstrated that this phenomenon can be used to slow down light pulses dramatically, or even bring them to a complete halt.
Abstract: It is well known that a dielectric medium can be used to manipulate properties of light pulses. However, optical absorption limits the extent of possible control: this is especially important for weak light pulses. Absorption in an opaque medium can be eliminated via quantum mechanical interference, an effect known as electromagnetically induced transparency. Theoretical and experimental work has demonstrated that this phenomenon can be used to slow down light pulses dramatically, or even bring them to a complete halt. Interactions between photons in such an atomic medium can be many orders of magnitude stronger than in conventional optical materials.

691 citations


Journal ArticleDOI
TL;DR: It is proved that it is possible to freeze a light pulse or even to make its group velocity negative in a coherently driven Doppler broadened atomic medium via electromagnetically induced transparency (EIT).
Abstract: We prove that it is possible to freeze a light pulse (i.e., to bring it to a full stop) or even to make its group velocity negative in a coherently driven Doppler broadened atomic medium via electromagnetically induced transparency (EIT). This remarkable phenomenon of the ultraslow EIT polariton is based on the spatial dispersion of the refraction index n(omega,k), i.e., its wave number dependence, which is due to atomic motion and provides a negative contribution to the group velocity. This is related to, but qualitatively different from, the recently observed light slowing caused by large temporal (frequency) dispersion.

230 citations


Journal ArticleDOI
TL;DR: In this article, a low-cost, potentially compact and robust microwave frequency reference can be constructed by use of vertical-cavity surface-emitting lasers and coherent population-trapping resonances in Cs vapor cells.
Abstract: A low-cost, potentially compact and robust microwave frequency reference can be constructed by use of vertical-cavity surface-emitting lasers and coherent population-trapping resonances in Cs vapor cells Fractional frequency instabilities of 2×10-11/τ/s have been achieved with a minimum of 7×10-13 at τ=1000 s The performance of this device as a function of external parameters such as light intensity, optical detuning, and cell temperature is discussed The dependence of the dark-line resonance signal on these parameters can be understood largely by means of a simple, three-level model The short-term stability depends critically on the optical detuning, whereas the long-term stability is limited currently by line shifts due to drifts in cell temperature

127 citations


Journal ArticleDOI
TL;DR: Raman-excited spin coherences were experimentally observed in nitrogen-vacancy (N-V) diamond color centers by means of nondegenerate four-wave mixing and electromagnetically induced transparency, which represents efficient preparation of quantum bits, as well as the ability to perform arbitrary single-quantum-bit rotations.
Abstract: Raman-excited spin coherences were experimentally observed in nitrogen-vacancy (N-V) diamond color centers by means of nondegenerate four-wave mixing and electromagnetically induced transparency. The maximal absorption suppression was found to be 17%, which corresponds to 70% of what is possible given the random geometric orientation of the N-V center in diamond. In the context of quantum computing in solids, this level of transparency represents efficient preparation of quantum bits, as well as the ability to perform arbitrary single-quantum-bit rotations.

91 citations


Journal ArticleDOI
TL;DR: The study shows that radiation trapping must be taken into account to fully understand many electromagnetically induced transparency experiments with optically thick media.
Abstract: We show that the effective decay rate of Zeeman coherence, generated in a (87)Rb vapor by linearly polarized laser light, increases significantly with the atomic density. We explain this phenomenon as the result of radiation trapping. Our study shows that radiation trapping must be taken into account to fully understand many electromagnetically induced transparency experiments with optically thick media.

88 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that there is no need for adiabatic passage in the storage and retrieval of information in the optically thick vapor of Lambda-type atoms.
Abstract: We show that there is no need for adiabatic passage in the storage and retrieval of information in the optically thick vapor of Lambda-type atoms. This information can be mapped into and retrieved out of long-lived atomic coherence with nearly perfect efficiency by strong writing and reading pulses with steep rising and falling edges. We elucidate similarities and differences between the ``adiabatic'' and ``instant'' light storage techniques, and conclude that for any switching time, an almost perfect information storage is possible if the group velocity of the signal pulse is much less than the speed of light in the vacuum c and the bandwidth of the signal pulse is much less then the width of the two-photon resonance. The maximum loss of the information appears in the case of instantaneous switching of the writing and reading fields compared with adiabatic switching, and is determined by the ratio of the initial group velocity of the signal pulse in the medium and speed of light in the vacuum c, which can be very small. Quantum restrictions to the storage efficiency are also discussed.

87 citations


Journal ArticleDOI
TL;DR: In this article, the suppression of two-photon absorption in a four-level atomic system by destructive quantum interference among multiple excitation paths created by a coherent coupling field was investigated.
Abstract: Electromagnetically induced transparency may lead to suppression of two-photon absorption in a four-level atomic system. This phenomenon is manifested by destructive quantum interference among multiple excitation paths created by a coherent coupling field. We report an experimental observation of such suppression of two-photon absorption in cold ${}^{87}\mathrm{Rb}$ atoms.

80 citations


Journal ArticleDOI
TL;DR: In this article, the authors reported an experimental observation of narrow and high contrast spectra induced by interacting dark resonances and have been predicted in Phys. Rev. A 60, 3225 (1999).
Abstract: We report an experimental observation of narrow and high-contrast spectra, which are induced by interacting dark resonances and have been predicted in Phys. Rev. A 60, 3225 (1999). Spectra are measured with cold ${}^{87}\mathrm{Rb}$ atoms produced by a magneto-optical trap. In this experimental system, a coupling laser and a weak probe laser form a three-level \ensuremath{\Lambda}-type configuration of electromagnetically induced transparency (EIT); a microwave drives a magnetic-dipole transition between the fourth level and the ground state that is coupled with the excited state by the coupling laser. The observed spectral profile of probe absorption exhibits a very sharp peak emerging inside a narrow EIT dip. Such spectral feature provides more opportunities in manipulating atomic-optical response.

76 citations


Journal ArticleDOI
TL;DR: In this paper, the Hanle effect on a closed Fg→Fe = Fg + 1 transition was analyzed for linearly and circularly polarized laser radiation, with the applied magnetic field collinear to the laser light wavevector.
Abstract: We analyse the Hanle effect on a closed Fg→Fe = Fg + 1 transition. Two configurations are examined, for linearly and circularly polarized laser radiation, with the applied magnetic field collinear to the laser light wavevector. We describe the peculiarities of the Hanle signal for linearly polarized laser excitation, characterized by narrow bright resonances at low laser intensities. The mechanism behind this effect is identified, and numerical solutions for the optical Bloch equations are presented for different transitions.

Journal ArticleDOI
TL;DR: In this article, the authors present a theoretical analysis of EIT effects in the two-level atomic system and show that the presence of a strong control field can establish frequencies at which the atomic absorption vanishes or is negative, and that the third-order nonlinear optical response leading to self-action effects can be quite large at these particular frequencies.
Abstract: Electromagnetically induced transparency ~EIT! has been studied primarily within the context of multilevel atomic systems. We show that EIT can occur also in a two-level atomic system and can lead to strong self-action and slow-light effects that are not hampered by material absorption, with important potential implications for processes such as squeezed-light generation and the propagation of optical solitons. Electromagnetically induced transparency ~EIT! is a powerful technique that can be used to render a material system transparent to resonant laser radiation, while retaining the large and desirable nonlinear optical properties associated with the resonant response of a material system @1#. EIT has been observed in several different experimental configurations @2,3#, and its occurrence in still other configurations has been predicted theoretically @4#. Laboratory studies have confirmed that EIT can be used to enhance the efficiency of physical processes including nonlinear frequency conversion @3,5# and optical phase conjugation @6#. In addition, it has been predicted that EIT can enhance the properties of a much broader range of processes including squeezed-light generation @7# and low-light-level photonic switching @8#. EIT has been observed both in atomic vapors @2,3,5,6,9# and in solids @10#, and it plays a key role in the generation of slow light @11# and its concomitant production of extremely large nonlinear optical effects @12#. Intimately related to EIT is coherent population trapping @13#, and the establishment of high refractive indices @14#. Most previous work on EIT has dealt with multilevel atomic systems. In this article, we present a theoretical analysis of EIT effects in the two-level atomic system. The analysis of EIT within the context of a much simpler level scheme leads to additional insight into the origin of EIT. Our analysis confirms previous work showing that the presence of a strong control field can establish frequencies at which the atomic absorption vanishes or is negative, and, most importantly, that the third-order nonlinear optical response leading to self-action effects can be quite large at these particular frequencies @15#. Thus two-level-atom EIT effects hold considerable promise for applications such as spatial soliton propagation @16#, squeezed-light generation by selfphase modulation @19#, and many types of optical switching devices @20#. We also find that low group velocities ~slow light! can occur within the context of the strongly driven two-level atom, and that in some ways the large nonlinear optical response can be understood as a direct consequence of the slowness of the light propagation. The origin of EIT in the two-level atom can be understood in terms of the energy-level diagram shown in Fig. 1, which shows a strong control field of frequency v c and amplitude Ec interacting with the atomic system. Population is coherently cycled between the lower level a and the upper level b

Journal ArticleDOI
TL;DR: Electromagnetically induced transparency is observed in a mismatched-wavelength cascade system with a room-temperature rubidium vapor cell and the ratio of the observed Rabi frequencies for coupling to the 5P(3/2) ?
Abstract: Electromagnetically induced transparency is observed in a mismatched-wavelength cascade system with a room-temperature rubidium vapor cell. A cw probe laser beam monitors the 5S1/2 → 5P3/2 transition while another cw laser couples the 5P3/2 state to a higher excited state. The ratio of the observed Rabi frequencies for coupling to the 5P3/2 → 8D3/2,5/2 transitions agrees well with that predicted by use of the transition oscillator strengths. Optical switching is demonstrated with an 80-mW coupling laser beam modulated up to 1 MHz.

Journal ArticleDOI
TL;DR: This experiment demonstrates the EIT system proposed by Harris and Yamamoto, which absorbs two photons but not one photon in the dressed-state picture, in a multilevel Rb system in which the third-order nonlinear absorption is enhanced by constructive quantum interference while the linear absorption is inhibited by destructive interference.
Abstract: We report an experimental observation of third-order nonlinear absorption by quantum interference in 87Rb atoms cooled and confined in a magneto-optic trap. A coupling laser creates electromagnetically induced transparency (EIT) in a multilevel Rb system in which the third-order nonlinear absorption is enhanced by constructive quantum interference while the linear absorption is inhibited by destructive interference. Our experiment demonstrates the EIT system proposed by Harris Yamamoto [Phys. Rev. Lett. 81, 3611 (1998)], which absorbs two photons but not one photon in the dressed-state picture.

Journal ArticleDOI
TL;DR: In this paper, the authors report experimental studies of electromagnetically induced transparency in Λ-type and ladder-type atomic systems realized in ǫ-87Rb atoms cooled and confined in a magneto-optical trap.
Abstract: We report experimental studies of electromagnetically induced transparency in Λ-type and ladder-type atomic systems realized in 87Rb atoms cooled and confined in a magneto-optical trap. Complete transparency is observed in the Λ-type system with a moderate coupling field. Comparison between the two systems reveals that at the line center of a weak probe transition, destructive interference occurs for the Λ-type system, whereas constructive interference occurs for the ladder-type system. We discuss conditions of complete transparency in the Λ-type system that contains hyperfine magnetic sublevels. Our experimental measurements for the two systems agree with theoretical calculations based on simple three-level Λ-type and ladder-type models.

Journal ArticleDOI
TL;DR: In this article, the role of hyperfine structure in electromagnetically induced transparency (EIT) was investigated by studying the 5S1/2-5P3/2/5D3/ 2,5/2 cascade system in 85Rb and 87Rb.
Abstract: The role of hyperfine structure in electromagnetically induced transparency (EIT) is investigated by studying the 5S1/2-5P3/2-5D3/2,5/2 cascade system in 85Rb and 87Rb. We show that if the hyperfine splitting Δhfs is larger than the Rabi frequency of the coupling beam, Ωc, then the observed EIT spectra can be modelled by adding terms corresponding to each hyperfine state. However, in the strong-coupling limit, Ωc>>Δhfs, a complete multilevel description is required.

Journal ArticleDOI
TL;DR: In this article, a novel ground-state laser cooling of trapped atoms utilizes the absorption profile of a three-or multi-level system tailored by a quantum interference, with cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved.
Abstract: A novel method of ground-state laser cooling of trapped atoms utilizes the absorption profile of a three- (or multi-) level system that is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca+ ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground-state cooling of neutral atoms trapped by a far-detuned standing wave laser field.

Journal ArticleDOI
TL;DR: In this paper, the authors examined electromagnetically induced transparency (EIT) in cascade schemes with N levels and N −1 fields and showed that transparency effects are present when N is odd and that destruction of EIT is present on line centre when N was even.

Journal ArticleDOI
TL;DR: In this article, an optical double-cavity resonator whose response to a signal is similar to that of an electromagnetically induced transparency (EIT) medium was proposed.
Abstract: We propose an optical double-cavity resonator whose response to a signal is similar to that of an electromagnetically induced transparency (EIT) medium. A combination of such a device with a four-level EIT medium can serve for achieving large cross-Kerr modulation of a probe field by a signal field. This would offer the possibility of building a quantum logic gate based on photonic qubits. We discuss the technical requirements that are necessary for realizing a probe-photon phase shift of $\ensuremath{\pi}$ caused by a single-photon signal. The main difficulty is the requirement of an ultralow reflectivity beam splitter, and we must be able to operate a sufficiently dense cool EIT medium in a cavity.

Journal ArticleDOI
TL;DR: In this paper, the authors observed electromagnetically induced absorption (EIA) spectra depending on intensities and detunings of the coupling field in the cycling transition (6S1/2, F = 4↔6P3/2 and F' = 5) of the Doppler-broadened Cs atomic system.
Abstract: We have observed electromagnetically induced absorption (EIA) spectra depending on intensities and detunings of the coupling field in the cycling transition (6S1/2, F = 4↔6P3/2, F' = 5) of the Doppler-broadened Cs atomic system. With a weak coupling field, we were able to see an EIA spectrum with a subnatural linewidth. On increasing the intensity of the coupling laser, we found that a transmission dip produced by an electromagnetically induced transparency appeared at the centre of the EIA structure, which is the first time that this has been observed. By detuning the frequency of the coupling laser, we were able to obtain a clear dispersion-like spectrum for blue-side detuning, but we obtained a complicated shape for red-side detuning because of the influences of other hyperfine levels. These results were compared qualitatively with theoretical curves obtained from a simple model.

Journal ArticleDOI
TL;DR: In this paper, a Raman scheme is described where the group velocity of an optical pulse can be altered dramatically, and it is shown that a light pulse can propagate with extremely slow group velocity when on a two-photon resonance.
Abstract: We describe a Raman scheme where the group velocity of an optical pulse can be altered dramatically. With this none electromagnetically-induced-transparency scheme, we show that when on a two-photon resonance, a light pulse can propagate with extremely slow group velocity. Both pulse narrowing and broadening can occur depending upon the choice of two-photon detuning. When using a tuned far-off two-photon resonance, we show that the pulse propagates ``superluminally'' in the medium with pulse narrowing.

Journal ArticleDOI
TL;DR: In this article, a combination of two-level electromagnetically induced transparency and dark states was studied, and it was shown that desirable features of both phenomena can be obtained in a single system.
Abstract: We study a combination of two-level electromagnetically induced transparency and dark states, and show that desirable features of both phenomena can be obtained in a single system. In particular, large self-phase modulation can be produced without pump or probe absorption, and without spontaneous-emission noise. We point out possible application of our system as a source for squeezed light.

Journal ArticleDOI
TL;DR: In this article, a collinear Raman generator was used to generate subfemtosecond pulses with a frequency equal to the fundamental vibrational frequency of molecular deuterium.
Abstract: It is well known that a carrier and two sidebands, depending on their relative phases, correspond to a frequency ~FM! or amplitude modulated ~AM! signal. Light is most often modulated by driving the dielectric constant of a material so as to produce phased sidebands with a frequency spacing of, at most, 150 GHz. In this Rapid Communication, we describe AM and FM light with a sideband spacing, and therefore modulation frequency, equal to the fundamental vibrational frequency of molecular deuterium (2994 cm '90 THz). We believe that this is a first step toward the synthesis of subfemtosecond pulses with prescribed temporal shape. As a light source for this experiment, we use a recently developed collinear Raman generator @1,2#. This light source produces a comb of ~at present! 17 sidebands spaced by about 2994 cm and extending from 2.94 mm in the infrared to 195 nm in the vacuum ultraviolet. The light source is based on the off-resonance adiabatic excitation of a Raman mode with a coherence that is sufficiently large that the importance of phase matching is negated and generation occurs collinearly. Although it was expected that sidebands obtained from such a source are mutually coherent, until now it was not clear if the relative phase among the sidebands remained the same across their temporal and spatial profiles. It is this uniform mutual coherence among the sidebands that allows the synthesis of AM and FM light, and in the future may lead to the generation of subfemtosecond pulses. In this work we separate out and use only three sidebands ~1.06 mm, 807 nm, and 650 nm! from the Raman comb. Frequencyor amplitude-modulated light is obtained by manually adjusting the relative phases of these sidebands. To detect this modulation, we make use of the fact that a Raman transition is driven by the near resonance component of the temporal envelope of the applied light intensity. These sidebands may be phased so that this component is either zero ~FM!, or maximized ~AM!. We note that it is essential that three sidebands be used in an experiment of this type. If two sidebands are used, as in coherent anti-Stokes Raman spectroscopy @3#, then the magnitude of the envelope is independent of phase. Our experimental setup is shown in Fig. 1. To construct the Raman generator, we use two transform-limited laser pulses at wavelengths of 1.0645 mm and 807.22 nm, such that the ~tunable! laser-frequency difference is approximately equal to the fundamental vibrational frequency in D2. The first laser is a Quanta-Ray GCR-290 Q-switched injectionseeded neodymium-doped yttrium aluminum garnet

Proceedings ArticleDOI
11 May 2001
TL;DR: In this paper, the analysis of the dispersion of coupled Bloch waves propagating in a moire fiber grating is presented. But the analysis is limited, since the number of coupled bloch waves is infinite.
Abstract: Summary form only given. While the reflection and transmission properties of moire fiber grating (MFG) are well known, the analysis of their dispersion is more involved, since the number of coupled Bloch waves propagating in MFG is actually infinite. Here we report, for the first time to the best of our knowledge, the detailed analysis of the dispersion in MFG, show the analogy between the MFG and electromagnetically induced transparency (EIT) media, and its practical applications to linear and nonlinear processes.

Journal ArticleDOI
TL;DR: It is found that the dynamics of the SIT process are profoundly modified by the control field, in a manner reminiscent of the modification of other nonlinear optical interactions through the process of electromagnetically induced transparency.
Abstract: We consider self-induced transparency (SIT) in a two-level atomic system in the presence of an additional control laser field. We find that the dynamics of the SIT process are profoundly modified by the control field, in a manner reminiscent of the modification of other nonlinear optical interactions through the process of electromagnetically induced transparency. The presence of the control field allows SIT to occur under a much broader range of conditions and leads to dramatically reduced values of the group velocity of the SIT soliton.

Journal ArticleDOI
TL;DR: This work theoretically study how the phase of a light plane wave propagating in a resonant medium under electromagnetically induced transparency (EIT) is affected by the uniform motion of the medium.
Abstract: We theoretically study how the phase of a light plane wave propagating in a resonant medium under electromagnetically induced transparency (EIT) is affected by the uniform motion of the medium. For cuprous oxide (Cu2O), where EIT can be implemented through a typical pump-probe configuration, the resonant probe beam experiences a phase shift (Fresnel-Fizeau effect) that may vary over a wide range of values, positive or negative, and even vanishing, due to the combined effects of the strong frequency dispersion and anisotropy both induced by the pump. The use of such a coherently driven dragging medium may improve by at least 1 order of magnitude the sensitivity at low velocity in optical drag experiments.


Journal ArticleDOI
TL;DR: In this paper, the spatial and temporal evolution of two short laser pulses having different wavelengths and interacting with a dense three-level Lambda-type optical medium under coherent population trapping is studied.
Abstract: The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level \ensuremath{\Lambda}-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse ${T}_{1,2} {(T}_{2}g{T}_{1})$ are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"odinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].


Journal ArticleDOI
TL;DR: Efficient four-wave mixing in low-pressure molecular deuterium without the need for phase matching is demonstrated and results in highly efficient single-sideband conversion.
Abstract: We demonstrate efficient four-wave mixing in low-pressure molecular deuterium without the need for phase matching. We use two laser fields with opposite circular polarizations to produce a strong excitation of a rovibrational transition at a frequency of 3167 cm 21 . The coherent molecular motion, in turn, modulates a third laser field (also circularly polarized) and results in highly efficient single-sideband conversion. © 2001 Optical Society of America OCIS codes: 190.2620, 190.5650, 270.1670, 300.6270. Four-wave mixing in atomic and molecular gases has served, for more than 30 years, as an eff icient tool for producing coherent radiation at desired wavelengths. 1 An important development in this area was the invention of nonlinear optics at maximal coherence, 2,3 which allowed 100% frequency conversion without the need for phase matching, under conditions in which the nonlinear susceptibility is of the order of the linear susceptibility. This technique relied on all-resonant laser-pulse propagation in an atomic medium (L scheme) and utilized electromagnetically induced transparency. 4