Electromagnetically Induced Grating And Control Of Group Velocity Of Light Pulses Based On Atomic Coherence Effects

This thesis for doctorate is mainly about the electromagnetically induced grating (EIG) and control of group velocity of light pulses based on atomic coherence effects and it relates to the refractive index and dispersion of probe wave modulated by the quantum interference of coherent laser fields. And the thesis contains four parts as followed.Electromagnetically induced grating in a homogeneous atomic mediumWe supply a theoretical method to solve the problems of EIG in ultracold or thermal atomic medium with the semi-classical theory of atom-field interaction, and the atomic energy levels are shown in Fig. 1 which can be described as a three-levelΛ-type configuration. In the system of EIG, we use a coherent standing-wave to replace the traveling wave in the technique of electromagnetically induced transparency (EIT). Due to the spatially periodic intensity of the standing wave, the absorption and refractive index of the probe wave is modulated spatially with a same period. As a result, the atomic medium driven by the standing-wave becomes a grating for the probe wave, and there can be some reflection signals when the probe wave traveling along the direction of the standing-wave.There have been some researches of EIG in ultracold and thermal atomic gas. In the ultracold atoms, due to the strong spatial coherence effects, the reflectivity is very high and one can obtain a photonic band gap which is the character of photonic crystal. While in the thermal atomic vapor, the reflectivity of the probe field is small. We realize that the results of EIG in ultracold atomic gas are different with that in hot atomic vapor and so far the existing theoretical calculations which have been performed for related standing wave can not be directly applied to explain the experimental results of EIG in the thermal atomic gas.Here we give a theoretical method of EIG using the semi-classical theory of atom-field interaction and the transfer matrix of the medium with a spatially periodic refractive index. In the limited case that the velocity of atoms is zero, our numerical results are agree with that of Artoni et al in ultracold atomic gas as shown in Fig. 2. Considering atomic velocities with a Maxwellian distribution, we study the transmission and reflection of the probe wave of EIG in the thermal atomic vapor. One can obtain a transparency window at the resonance point in the presence of only the co-propagation coupling wave, and this is the character of EIT. As the standing wave is formed, the transparency window of EIT changes to an enhanced absorption and two transparency windows emerge around the resonance point as shown in Fig. 3. Because the Bragg condition can not be satisfied, there are nearly no reflection signals.When there is a cross-angleθ= arccos (λpλc) between the probe wave and the standing wave, the reflection signal is enhanced due to the Bragg condition is satisfied, and the results are shown in Fig. 4(b). The EIG induced reflection signal has two peaks which correspond to the two dips as shown in Fig. 4(a) when the standing wave is resonance. If the detuning of the standing waveΔc > 20γ, we can obtain the reflection signal with one peak. The spectral characters of Fig. 4 have a good agreement with the experimental results reported by Brown et al. We theoretically present a numerical method to solve the transmission and reflection of the probe wave in the condition of EIG. For Doppler-broadened atomic system, our results are agree with the experimental results of Brown et al; for the ultracold atoms, the results of our method are consistent with the reports of Artoni et al. Our method is a way to understand the influences of the Doppler effects on atomic coherence and interference.Double tunable photonic band gaps in a homogeneous atomic mediumWe theoretically report that double tunable photonic band gaps appear induced by a strong coherent standing-wave and a traveling wave, and the atomic energy levels are shown in Fig. 5. Using the semi-classical theory of atom-field interaction and the transfer matrix of the medium with a spatially periodic refractive index, we calculate the transmission and reflection of the probe wave, and analyze the results in the dressed states. In the configuration of perfect standing-wave, we at first consider the Bloch vectorκand demonstrate it in Fig. 6(a). An investigation of Fig. 6(a) shows that two forbidden gaps open up in the frequency ranges for whichκ′=πa andκ′′≠0, and the two band gaps are symmetrical around resonance point.As followed, we present the reflectivity and transmissivity of probe wave propagating through a sample of a length L=2mm in Fig. 6(b). We further demonstrate that two photonic band gaps can grow in two different ranges of probe frequency. We analyze the double photonic band gaps in the dressed states, and understand that two dark states emerge induced by the coupling fields, and a pair of transparency windows appear correspondingly; when the standing wave is formed, due the intensity pattern of the standing wave, the absorption and refractive index have the same spatial period. And then, the medium becomes a grating and leads to double photonic band gaps, which is the character of photonic crystal.We further present in Fig. 7 how to adjust the positions and widths of the gaps by changing intensities of the coupling and standing waves. With a stronger coupling wave, the frequency range of the band-gap becomes larger and the position of it becomes far away from the resonance point, and this trend is the same for the standing-wave. It also demonstrates that for larger intensities of the coupling and standing waves, one can obtain a larger reflectivity of the probe wave and a better gap structure. This result can be understood that when the intensities of the waves become stronger, the transparency window of dark state has a large frequency range and becomes far away from the resonance point, and the stronger fields also induce more highly effective quantum coherence and interference effects. In the three-levelΛ-type atomic system, one only can obtain single photonic band gap whose frequency region is at one side of the resonance point; while we can simultaneously have double band gaps in a four-level N -type atomic system, and the gaps locate at opposite frequency regions. We anticipate that this scheme can be used as an all-optical two-port signal router having double channels, and it has a potential application to control the propagation of two light pulses with different central frequencies.Slow light based on coherent hole-burning in a Doppler broadened three-levelΛ-type atomic systemIn the hot atomic system with a three-levelΛ-type configuration as shown in Fig. 8(a), we study the slow light based on the technique of coherent hole burning (CHB). Using the semi-classical theory of atom-field interaction, we consider the slow light in the configurations of laser beams as shown in Fig. 8(b) and Fig. 8(c).At first, we supply the imaginary and real parts of susceptibility in Fig. 9 which correspond the absorption and refractive index of the probe wave. With only the present of the saturating wave which co-propagates with the probe wave, the imaginary part of the susceptibility shows a typical Lamb dip at resonance which is the result of saturation absorption spectroscopy (SAS). Due to the quantum coherence effects of the coupling wave, one can obtain narrower dip of CHB than that of SAS at resonance no matter for what configurations of laser beams. As a result, the dispersion of CHB is much pronounced around resonance than the slope of Lamb dip.Secondly, we supply the calculated group index n gat resonance of the probe wave for two cases of CHB in Fig. 10. Without the effect of the coupling wave, the group index is the same with the result of SAS in a two-level atomic system. In the case of Fig. 8(b), we can get a large group index when the wavelengths of two transitions become matched, and under the case ofω3 2 = 0.9ω31, we can obtain a nearly ten times larger group index than that of Lamb dip. As a contrary result, in Fig. 10(b), it is found when the frequencies ofω3 1andω3 2 become much mismatched, the larger group index we can obtain, and in the case ofω3 2 = 0.01ω31, we can obtain a nearly two times larger group index than that of Lamb dip.Here the results of Fig. 10(a) and Fig. 10(b) are consistent, and they can be understood that the group index of CHB depends on the quantum interference effect induced by the coupling wave, and this effect is destroyed by the Doppler shifts due to the motions of atoms k pυ?α2kcυ. In the case of Fig. 8(b), when the two wavelengths of the two transitions become matched, the Doppler shifts of k pυ? kcυbecome small, and the effect of quantum interference is enhanced, and then the group index becomes larger. The Doppler shifts of case of Fig. 8(c) is k pυ+ kcυ, and this value can only be smaller as the value of k cbecome smaller. It is worthwhile to note that we can obtain a larger group index using the technique of CHB than that of SAS, no matter in what cases of Fig. 8(b) and Fig. 8(c). In the following, we consider the propagation of a Gaussian pulse through the sample having a length L=1cm and demonstrate the results in Fig. 11. Because the spectral widths of the Gaussian pulses are well contained within the regions of the burning-hole at resonance of CHB in the medium, there are no distortions for the propagation of the pulse. From the relative delay between the reference pulse and the output pulse, we calculate the group velocity of the pulse, and find it is consistent with the results as shown in Fig. 10. And the transmission of Gaussian pulse in the condition of CHB is the same as that of SAS.Due to the quantum coherence effect of the strong coupling wave, we can have a better results of slow light of CHB than that of SAS in thermal atomic gas, and our scheme which is not a Doppler-free configuration does not need special requirements of the structure of the atomic energy levels. Our calculated results should be helpful for the experiments of slow light in hot atomic vapor.Switching from subluminal to superluminal light propagation via a coherent pump field in a four-level atomic systemIn the four-level atomic system, we theoretically investigate the effect of the coherent pump wave on the group velocity of probe pulse, and the energy levels are shown in Fig. 12(a).Using the semi-classical theory of atom-field interaction, we at first give the absorption and refractive index of the probe wave in the thermal atomic gas in Fig. 13. And the configuration of laser beams is shown in Fig. 12(b). An investigation of Fig. 13 shows that we can obtain a sub-Doppler spectral resolution of probe wave in the Doppler broadened system although the configuration of the laser waves is not a three-photon Doppler-free geometry. It is found that the dispersion of probe wave can be switched from positive to negative by increasing the pump wave intensity. In the dressed states, we give an explanation of result of Fig. 13, and it shows that due to the partial cancellation of the atomic motion, we obtain the sub-Doppler spectral resolution Secondly, we consider the group index of the probe wave at resonance in cold and hot atoms, and give the results in Fig. 14. It shows that the group index can be modulated from positive to negative by the pump wave, no matter in cold or hot atoms. It is noted that there is a largest negative group index in cold atoms, which is smaller than that one can achieve in hot atoms. Due to contributions of the atoms with a velocity on the absorption of the probe wave, the width of the probe absorption with anomalous dispersion in hot atoms is narrower than that of cold atoms. As a result, one can get a larger negative group index in the thermal atomic gas due to the Kramer-Kronig relation between the absorption and the refractive index of the probe wave.In order to confirm above results, we consider the propagation of a Gaussian pulse through the sample having a length L=1cm, and show the results in Fig. 15. An investigation of Fig. 15 shows that we can modulate the group index of probe pulse between slow light and fast light no matter in cold or hot atoms. Here we confirm that the spectral width of the Gaussian pulse is well contained within the region which is between two closely space gainliness, so there are no distortions for the propagation of the pulses. Calculating the relative delays between the reference pulse and the output pulses, we obtain the group velocities of the pulses, and find that there are very good agreement with the results in Fig. 14.Using our scheme, one can enlarge the delay between light pulses with a small depletion, and it can be used as an optical buffering in the field of optical information. In conclusion, we have got the following view points:(1) We supply a theoretical method of EIG, and it is not only suitable for the ultracold atomic gas, but also useful for the medium of thermal atomic vapor. Our calculations give a reasonable understanding of the experiment of Brown et al which can not be solved by other theories of standing wave system, and our results can be useful to optimize the experiments.(2) We obtain a double tunable photonic band gaps based on the theory of double dark states induced by a coupling wave and a standing wave. There are some advantages of double photonic band gap than the single photonic band gap in experiments, and one can realize quantum information with double light channels and control double light pulses with different central frequencies. Our proposal can be helpful in increasing the capacity of information in the field of information traffic of light.(3) We theoretically calculate the slow light based on coherent hole burning without a Doppler-free configuration in a hot atomic system. Our scheme does not require a special structure of the atomic energy levels, so it is helpful to realize the slow light in general atomic systems. And our calculations should be helpful for the experiments.(4) We theoretically supply a scheme to control the group velocity of light pulse from subluminal to superluminal induced by a coherent pump wave. Our proposal can be realized in cold or hot atomic systems, and it is easy to observe the fast light owing to the small absorption. The control of the coherent pump field can be used to enlarge the delay between light pulses with a small depletion, and the scheme has a potential to be used as an optical buffering.