| Since the laser was invented, the diverse nonlinear optical effects, which can be generated by the interactions between light and matter, have been investigated extensively and profoundly. The study of nonlinear optics is not only important for practical applications, but also a significant branch in the field of optics and nonlinear physics. The conventional nonlinear optics focus on the investigation and application of nonlinear phenomena induced by the interaction between the optical media and a strong coherent laser light field. In recent years, due to the discovery of electromagnetically induced transparency (EIT), the fresh field of weak-light nonlinear optics was emerged, which is very intriguing and significant for many promising applications, such as precision spectroscopy, precision mea-surement, photon manipulation, quantum information processing, optical soliton communication, and so on.The phenomenon of EIT was firstly found, when researchers investigated the resonant interaction between the laser light field and the three-level atomic ensembles. The basic principle is that, the absorption spectrum of the probe laser field forms a transparent window near the resonant point via a quantum interference effect between the two excitation pathways induced by an applied control laser field. EIT can largely eliminate the absorption of probe laser field and steeply change the dispersion of the media, which can result in an ultraslow light. Furthermore, the nonlinear optical coefficients can also be dramatically enhanced, which can lead to the strong nonlinear effect under weak-light and even single-photon level, and so on.As we all know, there is no interaction between the light fields in the vacuum. Thus, it is impossible to realize the light manipulation via another light field in the vacuum. However, when a light passes through the optical media, the dielec-tric polarization occurs, changing the refractive index of the optical media and furthermore providing an effective interaction with another light field. Therefore, light manipulation via a light field (including light trapping, deflection, guiding, controlling, and so on) can be realized by means of optical medias (including active and passive optical medias). However, most researches have some inade-quacies, such as requiring an extremely strong laser field; existing dispersion and diffraction effect; hard to realize an active manipulation; and so on.In this dissertation, we have investigated magneto-optical manipulation of weak-light optical solitons in the coherent multi-level atomic ensembles. The main idea is that, the weak-light optical solitons can be formed by the balance between a giant Kerr nonlinearity induced by EIT and diffraction or dispersion effect; to stabilize and manipulate the optical solitons, we apply some extra mag-netic fileds or optical fields to the system as external magneto-optical potentials. Fourthermore, we can realize the Stern-Gerlach deflection of weak-light optical solitons, trapping of weak signal light field by a soliton and their trajectory control, and storage and retrieval of (3+1)-dimensional weak-light bullets and vortices. The main work contains the three following aspects:1. Study on Stern-Gerlach deflection of high-dimensional weak-light optical solitons in the multi-level atomic system. Based on the Maxwell-Bloch equations of quadric-pod (4-pod) atomic system, we firstly derive the (3+1)-dimensional coupled nonlinear Schrodinger equations of three probe fields by the method of multiple scales. To obtain the stable weak-light optical solitons, we introduce a far-detuned Stark optical lattice in the system, which can induce a trapping potential to localize the transverse diffractive dimension (i.e., x) of the probe fileds. We show that the group velocity of the three probe fields can be matched each other through detuning the system parameters, and the stabilized high-dimensional weak-light optical solitons can be also formed. We then apply a gradient magnetic field to the atomic system, which leads to Stern-Gerlach deflection of weak-light optical solitons. Furthermore, we obtain the deflection angles of weak-light optical solitons, which is the function of the magnitude of gradient magnetic field. We show that the order of deflection angles are as large as 10-2 rad. Finally, we study Stern-Gerlach deflection of several weak-light optical solitons for a general case, i.e., (N - 1) weak-light optical solitons in N-pod (N> 4) atomic system. The results obtained here have potential applications in precision spectroscopy, precision measurement (i.e., optical magnetometery), quantum information processing, etc.2. Study on the trapping of weak signal light field by a soliton and their trajectory control in the four-level tri-pod atomic system. Firstly, we consider that a probe field and a signal field are applied to the atomic ensem-bles coupling the corresponding energy levels. In addition, the light intensity of probe filed is larger than that of signal field. Through the multi-scale method and Maxwell-Bloch equations, we then derive nonlinear equations controlling the motion of the envelope of the probe and signal fields. We show that the probe field can induce an enough strong nonlinear effect to balance the diffraction effec-t; however, the signal field relies on the nonlinearity of the strong probe field via cross-phase modulation to form a spatially localized wave packet. By choosing the appropriate system parameters, the group velocity of the both fields can or-der the matching relation, which increases the interaction time between the two light fields effectively. Thus the cross Kerr nonlinearity induced by the probe field can be enhanced significantly, which leads to the trapping of weak signal light field by a soliton. To manipulate the trajectory of the two fields, we apply a gradient magnetic field to the system. The results we obtain may be useful for light information processing, such as the design of all-optical switching at very low light level, optical cloaking, etc.3. Study on storage and retrieval of (3+1)-dimensional weak-light bullets and vortices in the A-type three-level coherent atomic system. From the Maxwell-Bloch equations and the method of multiple scales, we first-ly obtain the (3+1)-dimensional nonlinear Schrodinger equations of the probe field. To form the stabilized high dimensional optical solitons and vortices, a far-detuned Stark field is applied to the system, which can produce a trapping well to localize the transverse dimensions. Through switching off and on a control field appropriately, we demonstrate that these high-dimensional light pulses can be s-tored and retrieved very stably. The basic progress of light storage and retrieval is that, when switching off the control field, the probe field is stopped in the atomic system, thus the light information change into atomic spin; when switching on the control field, the light stored in the atom can be re-accelerated, thus atomic spin turn into light information again. The results here maybe provide a new theoretical foundation and technology method in the effective memory, transmis-sion and prossing of optical information, and have important applications in the field of quantum information network and technology, etc.All results presented above not only have significant theoretical values for revealing nonlinear optical effect, developing the theory of weak-light nonlinear optics and high dimensional optical solitons in the multi-level atomic system, but also may have promising applications and theoretical guidance in precision spectroscopy, precision measurement, design of weak-light all-optical switching, quantum information processing, and so on. |
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