Extremely Narrowed And Amplified Gain-spectrum Induced By The Doppler Effect With Enhanced Slow And Fast Light Based On Active Raman Gain

The thesis for masterate, consisting of two parts, is mainly about extremely narrowed and amplified gain-spectrum induced by the Doppler effect and the subsequent enhanced slow and fast light in an hot N-type atomic system. The two parts are shown as follows.Ⅰ. Extremely narrowed and amplified gain-spectrum in a hot N-type atomic systemIn this part, the gain-spectrum for the probe field in a cold four-level N-type atomic system based on active Raman gain(ARG) is investigated. The relevant atomic level scheme is shown in Fig. 1. Raman-resonance is induced by transitions and , which are driven by the Raman and probe fields with respective Rabi frenq- uencies and , while the transition is driven by a controlled field of Rabi frequency . The frequency detunings of the Raman, the probe and the controlled fields are defined as respectively.In the interaction picture and under the dipole and rotating wave approximations, the Hamiltonian is: By including the spontaneous emission and decoherence rate, the density-matrix equation can be given:Assuming all populations are in 1 at the very beginning, some populations will be transferred to 2 by the two-photon Raman resonance transition. However, the atoms in 2 will be pumped to 4 by the controlled field, then spontaneously radiating back to 1 . That is to say that populations in 2 , 3 and 4 can be neglected, and. The assumption above is also verified by the numerical simulation. So we consider that active Raman gain(ARG) can be satisfied and the density-matrix equation can be solved under steady-state condition.The first-order susceptibility can be obtained: the real and imaginary parts of varied with the porbe detuning can be plotted in Fig. 2. The calculations show that in the vicinity of it is always negative for the absorption of the probe laser, which means the probe pulse is amplified at all time. For fixed , the gain peak at the two-photon Raman resonance point in the spectrum will be splitted into two peaks with a concave in the middle of the two ones FIG. 2 the gain-spectrum and corresponding dispersive curve for the probe based on ARG in a cold four-level N-type atomic system. The data in a, c related to have been divided by 40, and related to being divided by 2; the data in b, d related to have been divided by 20, and related to 32being divided by 2。The relevant parameters are : as increases, the gain peak is reduced and broadened, at the same time the corresponding normal dispersion profile is shifted to anomalous dispersion with a negative slope near the point of . When increases to a certain value, the intensity and the width of the peak will never change, only leading to a widened and deepened concave. For fixed, increased results in rising peaks and a deepening dip in the two ones, with a steeper normal or anomalous dispersion. But can't be too strong, since intense means that the excitated rate from 1 to 2 by the two-photon Raman resonance will exceed that from 2 to 4 by the pump effect of the controlled field and then radiating to 1 . will be greater than when the two processes are in equilibrium, so the ARG condition will be destroyed and the probe field will be absorbed instead of gain. We should choose ? r and c properly to get the optimized normal and anomalous dispersion.The results described above can be clearly explained in the dressed state representation. The related dressed states have been shown in Figure 3. Fig. 3 The dressed states diagram for the N-type level scheme.Since the controlled field is resonant with the relevant levels, the dressed states can be quickly obtained in a simple expression: It can been seen that the controlled field acts in two aspects: on the one hand, ? c drives the atoms in 2 to 4 , and then back to 1 , maintaining all populations in 1 ; on the other hand , it creates two dressed states for the double two-photon Raman resonance processes: (actually driven to the component 2 in the two dressed states), resulting in two peaks in the spectrum. The two peaks will be same in width and intensity because of the equal component 2 in the two dressed states. For little , the two peaks are too close to be separated because of small energy space , the superposition of which leads to only one gain peak, corresponding to normal dispersion at the Raman resonance point. As ? c increases, the spectrum exhibits double attenuated peaks located at and a broadened and deepened dip. The corresponding dispersion becomes anomalous and exhibits a negative slope near .Then we calculated the spectrum and relevant dispersion for the probe in a hot atomic system at room temperature (T=300K). When the three fields are co-propagating in the sample, the Doppler effect can be taken into account for replacing , and N by After integrating different (the ARG condition is satisfied in the numerical simulation) at room temperature, the spectrum and the corresponding response are shown in Figure 4 by the solid curve. It can be soon found from Figure (4a) and (4c) that the gain peak in the spectrum by the solid curve is divided into two asymmetry peaks in the vicinity of the resonance point Fig. 4 the gain spectrum and corresponding dispersion in hot and cold atoms condition when the three fields are co-propagating(solid curve for T=300K and dashed curve for T=0K). The data for the solid curve in c, d have been divided by 100. The integrating range are , other parameters are the same as in Fig. 2. with a dip between the two ones when cincreases, and the correspondingdispersion changes from normal to anomalous at the point. As compared with that in cold atoms condition by the dashed curve, the gain peaks are extremely narrowed and amplified due to the Doppler effect at room temperature. The data in Figure (4c) present that the higher peak in the double peaks in the spectrum at room temperature have been narrowed down to 32 and amplified by 157 times, resulting in a steep anomalous slope near . For fixed c, the narrowing and amplification for the gain-spectrum becomes more and more evident when ? r increases, following a steeper normal and anomalous dispersion slope near the point . However, r cannot be increased too strong, since the ARG condition will be destroyed.We can also explain the results above in the dressed state representation. The eigenvalues and relevant dressed states for the atom with are: where . The absorption or gain for the probe is determined by the two-photon Raman resonance processes and , the Raman-resonance transition strength for is dominated by and the strength for is dominated by . For moving-forward atoms), as increases from 0 with fixed related to the gain peak located at is reduced from to 0 and will approach to the Raman resonance point from the left hand, is increased from . That is to say that the contribution to the gain spectrum caused by transition gets more and more significant and closer to the point ? r ? ? p as ? increases. At the same time, ?? related to the gain peak located at ? p ? ? r ? ?? is increased from ?? c to ?? , and ? 3? is reduced from ? 32 2 to 0. It seems that the spectrum are squeezed up to the right in the left side by the atoms with . However, the atoms with are reduced by according to the Maxwell velocity distribution. The contribution to the spectrum by the atoms with , which are proportional to , will be increased at first and then reduced at last, leading to the extremely narrowed and amplified gain peak in the left component of the spectrum. For moving-backward atoms, the situation is reversed. It can be concluded that the gain spectrum is squeezed up in the left component of the profile contributed by atoms with and in the right component by atoms with Then the gain spectrum at room temperature is extremely narrowed and amplified by the Doppler effect. We plot the gain profile for different in Figure 4, where it can be found the gain peak contributed by certain v > 0 is lower than that by the same but with negative value. Consequently, the integral of leads to the asymmetry of the two peaks in the gain spectrum. According to the theoretical analysis above, the gain spectrum for the probe will be the mirror-symmetry of Fig. 5 when the Raman and the probe fields are co-propagating and the controlled field is counter-propagating. The two-photon Raman resonance condition will be destroyed if the Raman and the probe fields are incident in opposite direction, resulting in the normal Doppler-broadening gain spectrum.Ⅱ. The enhanced slow and fast light induced in hot atomic systemIn order to confirm the results discussed above, we numerically simulate the propagation of the probe pulse when the three fields are co-propagating in the sample. The Raman and controlled fields are choosed to be continuous wave and the probe field is pulse-shape with a Gaussian profile. The simulations in cold atoms condition and in hot atoms condition are presented in the same picture for comparison. The subluminal light propagation for the probe pulse is shown in Fig. 6.It can be easily found that the subluminal effect for the probe at room temperature is more evident than that at T=0K. That is to say the subluminal effect has been enhanced by the Doppler effect. Furthermore, the amplification for the probe pulse at room temperature is stronger than that at T=0K. The data in Fig. 6 present that the probe pulse has been delayed by 50.4ns at T=0K, the corresponding group velocity of the slow light is , compared with the delayed time 118ns and at room temperature.The superluminal light propagation for the probe pulse is shown in Fig. 7. Obviously the superluminal effect at room temperature is much more evident than that at T=0K. The superluminal light in Fig. 7 at T=0K is too weak to be observed. It means that the superluminal effect has been severely enhanced by the Doppler effect. The amplification for the probe pulse at room temperature is also stronger than that at T=0K. The data in Fig. 7 present that the probe pulse has been advanced by 14.4ns at T=0K, the corresponding group velocity of the fast light is c864, compared with the advanced time 117ns and c7020 at room temperature.The same result will be obtained when the Raman and probe fields are co-propagating and the controlled field is incident in the opposite direction. The subluminal and superluminal effect for the probe pulse will be attenuated when the Raman and probe fields are counter- propagating.In conclusion, the significance and innovations of the thesis can be summarized as follows:(1) The spectrum will be broadened and attenuated by the Doppler effect in the traditional conception, leading to a reduced resolution. Although the Doppler effect can be eliminated by the nonlinear saturated spectrum technique, the spectrum resolution will still be theoretically limited by the natural width. However, we find that the gain-spectrum can be extremely narrowed and amplified by the Doppler effect in the thesis. The best result in our calculation is that the gain peak in the spectrum can be narrowed down to 10-3 of the natural width (0.005? ) and be amplified by 157 times. That means the spectrum resolution will be sharply improved.(2) The switch between slow and fast light is realized by simply changing the intensity of the controlled field in an N-type atomic system. The subluminal and superluminal effect for the probe pulse can be drastically enhanced by the Doppler effect, further verifying the conclusion that the gain-spectrum can be extremely narrowed and amplified by the Doppler effect.