Study On Spontaneously Generated Coherence In Atomic System

In this thesis for doctorate that consists of three parts, we study the spontaneously generated coherence in a feasible atomic system, the Doppler effects on the spontaneous emission spectra, and control of the spontaneously generated coherence by phase and amplitude of a microwave.Spontaneously generated coherence in a four-level atomic systemIn this part we study the spontaneous emission property of a four-level atomic system driven by two coherent fields. By numerical calculations in the bare state picture, we show that such interesting phenomena as extremely narrow peaks and spontaneous emission quenching can be realized, which are well understood by qualitative explanations in the partially and fully dressed state pictures. Specially, this coherently driven atomic system has two close-lying levels in the partially dressed state picture so that spontaneously generated coherence arises. Our considered scheme is feasible to carry out experiments based on spontaneously generated coherence because all rigorous requirements have been avoided in the bare state picture.The four-level atomic system we considered is shown in Fig. 1. One Fig.1: Relevant energy levelscoherent pumping field with frequencyωp is used to pump atoms into level 2 from level 1 . Another coherent coupling field with frequencyωc is used to drive the auxiliary transition between level 2 and level 3 .Δp =ω21?ωp andΔc =ω32?ωc are detunings of the pumping and coupling field, respectively.First, we investigate the spontaneous emission spectra by modulating frequencies and Rabi-frequencies of the coherent fields. Enhanced narrow spectral lines and fluorescence quenching points are clearly shown in Fig. 2 and Fig. 3, which can be attributed to the quantum interference similar to SGC in the partially dressed state picture. Note that only when the CPT conditionΔp +Δc= 0 is slightly deviated, is the quantum interference so strong that we can observe an extremely narrow and greatly enhanced spectral line. In the case of strongly deviation of the CPT condition, we can see that this narrow spectral line becomes much wider and lower because the quantum interference similar to SGC becomes much weaker.Fig. 4 shows that the spontaneous emission spectrum is also sensitive to amplitudes of the applied driving fields. It is found that the central narrow spectral line becomes wider and higher with the increasing ofΩc, which implies that much more atoms have been transferred to dressed levels from the central one 0 .When the CPT conditionΔp +Δc= 0 is satisfied, the spontaneous emission spectra are clearly doubly peaked as shown in Fig. 5. This can be well understood in the fully dressed state picture, where the central dressed level 0 is not contributed by level 2 and thus cannot decay to level 4 whenΔp +Δc= 0. We also can see that the two spontaneous emission peaks are always symmetric and their heights depend on the frequencies of both driving fields. The reason is that, as long asΔp +Δc= 0, the two dressed levels will be equally contributed.At last, we plot time evolutions of different levels for different parameters that satisfy the CPT condition or not. From which we can see that Fig.4: Spontaneous emission spectra forΔp =0.5γ,Δc =0.0,Γ2 =3γ,Ωp =1.5γ, andΩc =0.3γ,0.9γ,1.3γ。 whenΔp +Δc=0, there are non-vanishing population distributions for a long time in upper levels, which means that some atoms are trapped in these levels. WhenΔp +Δc≠0, however, population distributions in upper levels are constantly zero for a long time, and the time for complete population transfer to level 4 depends on to what extent the CPT condition is destroyed. Comparing with Fig. 2 and Fig. 3, we can infer that a long population transfer time corresponds to a small deviation of the CPT condition and leads to a relative narrow and high spectral line, while a short population transfer time corresponds to a large deviation of the CPT condition and leads to a relative wide and low spectral line. Spontaneously generated coherence in a Doppler broadened atomic systemWe investigate the spontaneously generated coherence (SGC) in a Doppler broadened four-level atomic system driven by two coherent fields. We plot the spontaneous emission spectra with different parameters and discuss how the initial atomic conditions and parameters of both fields change the number of peaks and dark lines of spontaneous emission spectra. Further more, we also show how the spontaneous emission spectrum is modified by Doppler effects in the viewed direction. Our results have important references to the experimental observation of SGC in hot atomic vapors.The four-level atomic system is depicted in the Fig. 1, which is investigated in the Doppler-free system in part one. In the following we will investigate the Doppler effects on the spontaneous emission spectra in Fig. 6-Fig. 9. Comparing the spectra with and without Doppler shifts, we find that the SGC phenomena in this hot atomic system are sensitive to Doppler effects. Large Doppler shifts will result in weaken quantum interference among the adjacent transition pathways, then the distinct SGC features, such as narrow peaks and dark lines, will be blurred with large Doppler widths. In the case of two dark lines in spontaneous emission spectra as shown in Fig. 6, we can see that the narrow central peak reduces rapidly and both side peaks also become wider and shorter with increasing Doppler widths. The narrow central peak and two dark lines result from SGC disappear and are replaced by one peak when the Doppler width increased to 10.14MHz. In one dark line case as shown in Fig. 7, the dark line weaken and the narrow central peak becomes wider and lower with increasing Doppler widths, which are more sensitive than two dark lines. And the spontaneous emission spectrum becomes a low Gaussian shape peak when the Doppler widths increase to 10.14 MHz. In Fig. 8, we can see that a small central peak appears between the two peaks with increasing Doppler shifts, the reason is that the increasing Doppler shifts make the parameters not satisfy the CPT condition anymore. The CPT condition is destroyed by the increasing Doppler widths and the spontaneous emission spectra show the same features as that in Fig. 6(b) with initial atoms populated in level 2 . In Fig. 9(a), we can see the fluorescence total quenching in the spontaneous emission spectra for free of Doppler effects. The fluorescence quenching disappears and is replaced by a peak as soon as there is any Doppler width as shown in Fig. 9 (b).All the discussion above is based on the co-propagation of both coherent and pump fields, the SGC features in spontaneous emission spectra are more sensitive to the Doppler widths in the case of counter-propagation of both fields. We compare the spontaneous emission spectra in those two cases, and find that under the same conditions, the central narrow peak in co-propagation of both fields even disappears in the case of counter-propagation. At last, we show the spontaneous emission spectra with Doppler width 0.507 MHz in different viewed angles, from which we can see that the height of the central peak becomes higher with increasing viewed angle from 0 toπin general. Fig.6: Spontaneous emission spectra forΔc = 0.5MHz,Δp = 0.2MHz,Ωp = 1.5MHz,Ωc = 0.9MHz, and a1 (0) = a3(0) = 0, a2 (0) = 1. (a) Spectra for free of Doppler shifts; (b) Spectra with Doppler widths D of 0.507 MHz (solid), 5.07 MHz (dashed) and 10.14 MHz (dotted)Δc = 0.5MHz,Δp = 0.2MHz,Ωp = 1.5MHz,Ωc = 0.9MHz, a1 (0) = a3(0) = 0, a2 (0) = 1. Fig.8: Spontaneous emission spectra in CPT conditions for a1 (0) = a3(0) = 0, a2 (0) = 1,Δc = ?0 .2MHz,Δp = 0.2MHz,Ωp =Ωc=0.9MHz. (a) Spectra for free of Doppler shifts; (b) Spectra with Doppler widths D of 0.507 MHz (solid), 5.07 MHz (dashed) and 10.14 MHz (dotted). Fig.9: Doppler effects on fluorescence quenching of the spectra ( )Sδk for a1 (0) = 0.707, a2 (0) = 0, a3 (0) =?0 .707,Δc = ?0 .2MHz,Δp = 0.2MHz,Ωp =Ωc=0.9MHz. (a) The spontaneous emission spectra for free Doppler broadening; (b) Spectra with Doppler widths D of 0.507 MHz (solid), and 5.07 MHz (dashed). Effects of spontaneously generated coherence in a microwave-driven four-level atomic systemWe studied the effect of spontaneously generated coherence (SGC) on spontaneous emission and dynamical evolution of a microwave-driven four-level atomic system. Interesting phenomena due to SGC, such as spectral-line narrowing, spectra-line enhancement, spectral-line suppression, and fluorescence quenching, are shown in the spontaneous emission spectra, which can be effectively modulated by amplitude and phase of the microwave field. Due to SGC, the total populations are partly, even completely trapped in upper levels in steady-state, the decay time of which is sensitive to phase of the microwave field. In the dressed state picture, multiple SGC arise during the process of three close-lying states decaying to the same state. The corresponding experiment to observe the expected phenomena related to SGC can be more conveniently realized in atoms, since no rigorous conditions are required and the amplitude and phase of the microwave field can be conveniently controlled.The four-level Y-type atomic system is shown in Fig. 10. The level 1 is coupled to the levels 2 and 3 by coherent laser fields with carrier frequencies ofω1 ,ω3 , and Rabi frequencies ofΩ1 ,Ω3, respectively. A resonant microwave field with frequencyω2 and Rabi frequencyΩ2 is used to couple the highest lying levels 2 and 3 through an allowed magnetic transition. First of all, we analyze the SGC effects on the spontaneous emission spectra. When initial population distributed in level 1 , the spontaneous emission are quenched at two frequencies as shown in Fig. 11(a) and Fig. 11(b). We also can see that when two fluorescence quenching points are separated from a long to a short distance, two ultra-narrow lines at sidebands evolve into two peaks, while the central peak evolves into an ultra-narrow line simultaneously. Figs. 11(c)-11(f) show the spontaneous emission spectra when initial population distributed in level 2 . In general, as shown in Fig. 11(d), the spontaneous emission is quenched at one frequency as being expected. In this case, we can see that the central suppressed peak in Fig. 11(c) can be evolved into an extremely enhanced ultra-narrow line as shown in Fig. 11(d) and 11(e). Although the phase of microwave field is zero, there is no fluorescence quenching in the spectrum in Fig. 11(f), which can be easily Fig.10: Schematic representation of the relevant atomic energy levels. (a) The atomic energy levels in the bare state picture; (b) The atomic energy levels in the dressed-state picture. understood: the denominator of S (δk)tends to zero when the numerator equals In Fig. 12, we will investigate the spontaneous emission behaviors by the phase and amplitude of microwave field. We find that the spectra are effectively modulated by the amplitude of microwave. Increasing the amplitude of microwave, two dark lines are separated from each other further, a central ultra-narrow line evolves into one central peak, and a side peak evolves into a side ultra-narrow line simultaneously. Moreover, we can change the positions of dark lines and ultra-narrow line by choosing different values ofΩ2. Details about the variation of the spontaneous emission spectra with the relative phase of microwave field are shown in a periodicity 2πin Fig. 12(b). Whenθ=0, the spontaneous emission spectra is composed of two peaks. A third peak is submerged into the central peak whenθ=0 and will appear whenθis increased from zero,which is increased rapidly with increasing of the phase difference. After its maximum, it becomes lower quickly, meanwhile, the left peak becomes higher slowly, and both reach the same height atθ= 0.5π; at the same time, height of the suppressed central peak slowly reaches its maximum. Whenθis varied from 0. 5πtoπ, the right side peak continues to be lower, but with a slow variation, meanwhile, the left peak continues to be higher, but with a quick variation, and height of the left peak is decreased rapidly after its maximum. Whenθ=π, the left peak is submerged into the central peak and the spontaneous emission is composed of two peaks again. Then whenθis varied fromπto 2π, the spontaneous emission spectra show a contrary variation and we can get the conclusion that S (δk ,π-θ)= S(δk,π+θ). As shown in Fig. 12(b), the left peak and the right peak show a mirror inversion in the spontaneous emission spectra whenθis varied from 0 toπor fromπto 2π.Now we turn our attention to the time evolution of populations. As shown in Fig. 13 (a), populations can be trapped in upper levels in steady-state on CPT conditions. The total population in upper levels in steady-state is about 50% of the initial value. The decay time to the steady-state is sensitive to the phase of microwave field. It is enlarged more than 20 times when the phase is increased only from 0.0 to 0. 1πas shown in Fig. 13(b).Finally, we plot the time evolution of populations and corresponding spontaneous emission spectra on fluorescence quenching conditions in Fig. 14. We can see that total populations are trapped in upper levels and no spontaneous emission in this case. In conclusion, we have studied in detail the spontaneous emission properties of a coherently driven four-level atomic system without close-lying levels and showed lots of interesting phenomena in the spectra. Our considered scheme is feasible to carry out experiments based on spontaneously generated coherence because all rigorous requirements have been avoided in the bare state picture. Then a completed survey of Doppler effects on the spontaneous emission spectra is given with different parameters. Since few work is devoted to discussing Doppler effects on the spontaneous emission spectra before, our results provide valuable reference for carrying the experiments for observation of SGC in atomic vapors. We also studied the control of the spontaneously generated coherence by phase and amplitude of a microwave. In this configuration, the spectral behavior was sensitive to variables of the phase and amplitude of microwave field, so we can control the spontaneous emission more conveniently.