| SGC (Spontaneously Generated Coherence) is a kind of coherence generated by Spontaneous emission and can modify the process of the interaction between radiation fields and matter. There are a great number of interesting effects related to SGC, such as transparency of a short laser pulse, lasing without inversion, coherent population trap and transfer, photon correlation, control of group velocity, enhanced Kerr nonlinearity, phase control of gain and absorption, cancellation and quenching of spontaneous emission, narrowing and squeezing of fluorescence, phase sensitive spectra of spontaneous emission. The study of SGC not only gives insight of the basic quantum dynamics, but also has potential applications on applied technologies, such as optical switch, quantum information and computing, transparent material with high refraction, and high precise spectrometer and magnetometer. The effect of SGC has attracted much attention in the past decades, and there are more than a hundred related theoretical papers.However, the existence of SGC requires two stringent conditions: there exist two close-lying levels which are near degenerated, and corresponding dipole moments of the two transitions are not orthogonal. It is very difficult to find a suitable system in real atoms. As a result, most works on SGC discuss theoretical aspects of the problem without touching the practical side. In order to observe the phenomena based on SGC, a few methods have been proposed to simulate this intriguing effect, such as with a dc field, a microwave field, or a laser field. Nevertheless, most works of this type are theoretic and need experimental verification. This dissertation investigates the effects of SGC in a four-levelΛsystem and a four-level V system. By simulating SGC with coherence induced by laser fields, the effects of SGC are both theoretically discussed and experimentally observed. The main contents can be divided into two parts.1. SGC in a four-levelΛsystemWe investigate the effects of spontaneously generated coherence (SGC) in a four-levelΛ-type system [see Fig. 1], and find that the effect of SGC between the two excited close-lying levels |2> and |3> changes the absorption of the probe field dramatically.The calculated absorption spectrum of such a system is shown in Fig.2. With no coupling field, there is a SGC induced transparency; when a coupling fieldωc is added, we can make the spectrum show one transparency window [see Fig. 2 (a)] or two transparency windows [see Fig. 2 (c) and (d)] by adjust the detuning of the coupling field. In the latter case, when we increase the detuning of the coupling field , the transparency windows locate farther with each other, and the height and width of the absorption peak also increase [see Fig. 2 (c) and (d)]. We propose an experimental approachable energy scheme which consists of four levels interacting with two coupling fields [see Fig.3 (a)]. The two fields lead to several competitive pathways for the absorption ofωp. With the quantum interference between different competitive channels for absorption, we can realize the phenomena predicted above. In the dressed-state representaion ofω1 , the system turns out to be a four-level system with two upper levels |+> and |-> [see Fig.3 (b)]. Such a system is obviously equivalent to the system with SGC [Fig. 1]. We find the system proposed here in the hyper fine levels of 85Rb [see Fig. 4]. We carry out the corresponding experiment in a rubidium atomic beam to reduce the effect of Doppler broadening. To minimize the effect of the residual Doppler broadening, the three laser beams are nearly in a line, and the coupling fieldω1 propagates in the opposite direction of the other two beams. The experimental configuration is shown in Fig. 5.The experimental results are shown in Fig. 6 by solid lines. We also make theoretical simulations with the parameters of rubidium atoms. The effects of the residual Doppler broadening and laser linewidths are taken into account as well. The results are shown in Fig. 6 by dotted lines.When no coupling field is applied, we get a standard absorption line shape of 85Rb 5 S1 /2 , F = 3→5 P1 / 2, F= 3 [see Fig. 6(a)], and the FWHM is estimated to be 14MHz. When only the coupling fieldω1 is added, there is a transparency in the line shape [see Fig. 6 (b)]. This situation is equivalent to the transparency induced by SGC [see Fig. 2(a)] in the four-levelΛsystem. In the case of applying two coupling fields, the line shape varies with the detunings of the coupling fields ?1 +? 2. When ?1 +? 2=0, there is a deep and broad transparency window [see Fig. 6 (c)]. This situation corresponds to the case of ? c=0 in the system with SGC [see Fig. 2(b)]. When ? 1 +?2≠0, we get two transparency windows with a narrow absorption peak in the middle. This situation corresponds to the case of ?c≠0 in the system with SGC [see Fig. 2(c, d)]. By tuning the value of ?1 +? 2, we can increase the width and height of the absorption peak. In the meanwhile, the separation of the two transparency windows increases together [see Fig.6(d,e)]. The observed spectrum are in good accordance with the theoretical simulations.In this way, we demonstrate the effects of SGC to the four-levelΛsystem.2. SGC in a four-levelΛsystemWe consider the effects of SGC in a four level V- type system [see Fig. 7 (b)], and find that SGC induces interference effects of the absorption. In a three-level V system [see Fig. 7 (a)], when one of the two excited states |e> is replaced by a pair of close-lying levels |3> and |4>, the absorption of the probe fieldωp becomes much different, and depends on the relationship between the Rabi frequency of the coupling field ? c and the space between the two close-lying levels.The calculated spectra of absorption under different Rabi frequency of the coupling field are shown in Fig. 2. Comparing to the line shape of a standard EIT (Electromagnetic Induced Transparency) [see Fig. 2 (a)], the absorption spectrum of the four-level V system shows more transparency windows [see Fig. 2 (b), (c), and (d)]. When the Rabi frequency of the coupling field is relatively small, ? c <ω34 / 2,the transparencies are weaker, but there are three windows [see Fig. 2 (b), ? c = 0.6γ]; when the Rabi frequency is comparable to half of the distance between the levels |3> and |4>, there are two transparency windows and four absorption peaks, and the peak in the middle is higher than the other two peaks [see Fig. 8 (c), ? c =γ]; when the Rabi frequency is increased larger, ? c >ω34 / 2, there are three transparency windows and four absorption peaks again [see Fig. 8 (d), ? c = 2γ].The origin of the line shapes can be easily seen in the dressed states representation of the coupling fieldωc [see Fig. 7(c)]. There are four absorption peaks which can be attributed to the transitions from |1-> and |1+> to |3> and |4>. In the case that the splitting between |1-> and |1+> is equal to that of |3> and |4>, the transitions |1->→|3> and |1+>→|4> are degenerate. As a result, the number of absorption peaks becomes three, and the middle absorption peak is higher than the other two peaks. The effects of the coupling field and SGC induce destructive interferences between the transitions, so we see transparency windows between the absorption peaks.We propose an experimental approachable scheme which consists of four levels interacting with two coupling fields [see Fig.9 (a)].In the dressed-state representation ofω2, the scheme is shown in Fig. 9 (b). There are effects of interference between the states |+> and |->. This system is obviously equivalent to the system with SGC [see Fig. 7(b)].In the dressed-state representation of both of the coupling fieldsω1 andω2, the system turns to be a four-level case [see Fig. 9 (c)] similar to that in Fig. 7(c). There are four transitions from the levels |1+> and |1-> to the levels |+> and |->. By tuning the Rabi frequencies of the two coupling fields, we can modify the spaces between the upper levels and between the lower levels, so that we can control the degeneracy of the transition |1+>→|+> and the transition |1->→|->. In this way, we can switch the absorption spectrum ofωp to be a three-peak structure and a four-peak structure.We find the system proposed above in the hyper fine levels of 85Rb [see Fig. 10].Using the rule of transition, we can prevent the population of 5S1/2,F=3 being pumped to 5S1/2,F=2 by the coupling fieldω1 . As a result we find proper three-level and four-level V systems.The experimental setup is shown in Fig. 11. The three laser beams are nearly collinear, and the coupling fieldω2 propagates in the opposite direction of the other two beams. The experimental results are shown in Fig. 12 by solid lines. The dotted lines are corresponding theoretical simulations. When no coupling fields are applied, we get a standard absorption line shape of 85Rb 5 S1 /2 , F = 3→5 P1 / 2, F= 3 [see Fig. 12 (a)]. When only the coupling fieldω1 is added, the line shape turns to be the case of V type EIT [see Fig. 12(b)]. In the case of applying two coupling fields, the line shape varies with the Rabi frequencies of the coupling fields ?1 and ? 2. When ?1 < ? 2, we see that the transparency becomes much weaker, but the transparency window spits into three sub windows [see Fig. 12(c)]. This situation is in accordance with the case of ? c <ω34 / 2 in the system with SGC [see Fig. 8(b)]. Under the condition of ?1 = ? 2, we get two transparency windows and three absorption peaks. We see that the middle peak is much higher then the other two peaks on the sides [see Fig. 12(d)]. This situation corresponds to the case of ? c =ω34 / 2 in the system with SGC [see Fig. 8(c)]. When ?1 > ? 2, we get three transparency windows again [see Fig. 12(e)]. This situation corresponds to the case of ? c >ω34 / 2 in the system with SGC [see Fig. 8(c)]. The observed results correspond to the theoretical simulation well.In this way, we demonstrate the effects of SGC on the four level V system.In one word, this dissertation use the coherence induced by laser fields to simulate SGC, and experimentally investigate the effects of SGC which are intensively concerned but lack of experimental verifications. This work will facilitate the research on the effects of SGC and related technologies.
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