Theoretical Study On Spontaneously Generated Coherence In A Coherently Driven Five-Level Atomic System

In this thesis, we investigate the coherent control of spontaneous emission in a coherently driven five-level atomic system, and simulate spontaneously generated coherence in the dressed state picture.Spontaneously Generated Coherence in a Five-Level Atomic System without a Microwave fieldWe first study the spontaneous emission in a five-level atomic scheme of rubidium atom. By theoretical calculation and numerical analysis, 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 three 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 five-level atomic system we considered is shown in Fig. 1(a). Coherent fieldsΩ1 ,Ω2,Ω3 drive the transitions between 1 , 2 , 3 and 0 . Here,Δi =ω0 i ?ωi (i = 1,2,3) are detunings of corresponding coherent fields. The decay rate from state 0 to j isΓ0 . And in the dressed state picture, state 0 is instead of three dressed states ~0 , 1 , 2 and 3 , as shown in Fig. 1(b). Thus, the conditions of spontaneously generated coherence can be met. So the typical character of SGC, such as extremely narrow peaks and spontaneous emission quenching are expected in such a system.1. Characters of spontaneous emission under CPT conditionIn the condition of CPT, when the system is initially prepared in dark state, the population cannot transfer between atomic states, so no spontaneous emission happens, and the spontaneous emission spectra is fully quenched, shown in Fig. 2(a). As the system is not initially prepared in dark state, there is no quenching point in the spectra, as Fig. 2(b) shows.Fig. 3(a) and Fig. 3(b) show the spontaneous emission spectra when the CPT condition is deviated. Compared with Fig. 2(a) and Fig. 2(b), a sharp and narrow peak occurs in the spectra. The peak become lower and wider as far away from the CPT condition. Under CPT condition, the quantum interferences between spontaneous transitions are maximum. When CPT condition is slightly deviated, the quantum interferences become a little weak, and lead to a sharp and narrow peak. For a strong deviation, the quantum interferences are weaker and weaker, so the peak gets lower and wider.2. Effect of coherent field intensity and detuning on the spontaneous emission spectraFor the symmetry of the system and for simplicity, we only study the effect of coherent field intensity and detuning on the spontaneous emission spectra under condition of initially population prepared in ground state.In such situation, as shown in Fig. 4(a), there are two quenching points and four peaks which correspond to the four dressed states in the spontaneous emission spectra. We contribute the quenching to the quantum interferences between spontaneous emission channels. Under particular condition, the two quenching points degenerate and one peak disappears, shown in Fig. 4(b). detuning of coherent field. By tuningΔ1 can lead to one of the four peaks narrow, or wider, or lower, or enhanced. By tuningΩ1 can lead to the two inboard peaks narrow, or wider, or lower, or enhanced, simultaneously, with the symmetry keeping on. The positions of the four peaks shift according with the energy variation of the four dressed states, and the variations of the spontaneous emission spectra are due to the different quantum interferences between spontaneous emission channels.Spontaneously Generated Coherence in a Five-Level Atomic System with a Microwave fieldWe utilize a microwave to couple the two excited states of previous proposed five-level atomic system and show some various spontaneous emission spectra of such system. By tuning the parameters of coherent fields, the quantum interferences between different spontaneous emission channels lead to some interesting characters, such as spectra narrow, spectra enhanced, and spectra quenching. We give theoretical analysis on such phenomenon in the dressed state picture.The scheme we considered is shown in Fig. 6(a). Coupling fields , , drive the transitions between state 2 and 1 , 3 , 4 . A microwave couples 3 and 4 by magnetical dipole interaction. Under dressed state picture, state 2 is instead of four dressed state 1 , 2 , 3 and 4 , as shown in Fig. 6(b) The quantum interferences between spontaneous transition channels in dressed state picture lead to special characters of spontaneous emission spectra. 1. Characters of spontaneous emission under CPT conditionUnder CPT condition,when the system is initially prepared in dark state, the population cannot transfer between atomic states, so there is no spontaneous emission happen, and the spontaneous emission spectra is full quenched, shown in Fig. 7(a). As the system is not initially prepared in dark state, there is no quenching point in the spectra, as Fig. 7(b) shows. 2. Spontaneous emission spectra when the CPT condition is deviatedGenerally, the quantum interferences between spontaneous transitions are maximum under CPT condition. Fig. 8(a) and Fig. 8(b) show the spontaneous emission spectra when the CPT condition is deviated. Compared with Fig. 7(a) and Fig. 7(b), a sharp and narrow peak occurs in the spectra. The peak become lower and wider as far away from the CPT condition. It is because that when CPT condition is slightly deviated, the quantum interferences become a little weak, and lead to a sharp and narrow peak. For a strong deviation, the quantum interferences are weaker and weaker, so the peak gets lower and wider.3. Amplitude and phase Control of spontaneous emission spectra by a microwaveAs the microwave and two control fields form a close loop, the spontaneous emission will depend on the relative phase of the three fields.Fig. 9(a) shows the spontaneous emission spectra with different values of . There are four symmetrical peaks and two quenching points in the spectra. The symmetry of the spectra is due to the symmetrical parameters of the system. Here, the positions of the peaks in the spectra are according with the energy shifts of the dressed states, and the quantum interferences between spontaneous emission channels lead to the inhibition of spontaneous emission. With the increase ofΩ_dΩ_d, the positions, intensities and widths for the peaks vary. As well as the positions of the quenching points. Those can be explained under dressed state picture: when is increased, the splits of the dressed states increase, which lead to spontaneous emission peaks shift to the large-detuning side. The quantum interferences between spontaneous emission channels lead to variation of intensities and widths of the peaks. As well As the position of maximum destructive interferences, which result to the quenching of spontaneous emission. Fig. 9(b) shows the variation of eigenvalues of the four dressed states as a function of . It meets the position of the four peaks very well. The microwave will lead to the phase dependence of spontaneous emission. We show the details of spontaneous emission as a function of phase from 0 to 2π, as shown in Fig. 10 (a)-10(e). The spontaneous emission spectra consist of four peaks, two of each side. And there are two quenching points between the two peaks on the same side. Whenθ=0/ 2, the spontaneous emission spectra is not symmetrical. As it evolves toθ=π, the spectra becomes symmetrical. Whenθ=π, it is opposite with the conditionθ= 0. Fig. 10(f) shows the variation of eigenvalues of the four dressed states as a function ofθ. It meets the position of the four peaks very well. In conclusion, we have studied in detail the spontaneous emission properties of a coherently driven five-level atomic system without close-lying levels and showed lots of interesting phenomena in the spectra, such as spontaneous emission narrow, enhanced and quenching. Then we investigate the amplitude and phase control of spontaneous emission when the previous atomic system is coupled by a microwave and form a closed loop. 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.