Multi-Mode Electromagnetically Induced Transparency And Applications

In the last ten years, much attention has been paid to understandings and applications of systems exhibiting electromagnetically induced transparency (EIT). The EIT method is a powerful technique with significance and practicability that can make the dispersive and absorptive properties of optical medium modified dramatically, i.e., make the medium having large dispersion without the resonant absorption by means of destructive interference. Recently, EIT has been applied extensively in slow light, quantum memory, four-wave mixing, electromagnetically induced grating, atom laser, optical bistability, optical switching, ultraslow optical solitons, Faraday rotation, optical frequency conversion, stationary pulses, quantum phase gate, atom-molecule dark state, high-accuracy optical clock, quantum imaging, and even astronomy. In this thesis, we study the theory of multi-mode EIT and its applications, including the propagation of slow light pulses, cross-phase modulation of photons, the photon-photon nonlinear interaction and its applications in quantum computation and quantum information. This thesis is divided into five parts:The first part includes chapter 1 and chapter 2. In chapter 1, the background and the main research results of EIT are introduced. In the chapter2, we introduce the basic theory of EIT, including the characters of the dark state and the theoretical methods given to deal with the EIT system based on single-atom and collective atomic excitation of atomic ensemble.The second part includes chapter 3. Here we study the generalized Stern-Gerlach effect of the quantized linear-polarized light in a magneto-optically manipulated atomic ensemble. We derive an effective Shr(o|¨)dinger equation for the spatial motion of two dark-state polaritions (DSPs), which behave as a quasi-particle with an effective magnetic moment. We investigate the Stern- Gerlach effect of light in an nonuniform magnetic field and an inhomogeneous coupling field, respectively, via the methods based on the particle feature of the DSPs and the wave feature of light pulses.The third part includes chapter 4 and chapter 5. In chapter 4, we propose a scheme to generate triple EIT (TEIT) where EIT is induced imultaneously for three weak slow light pulses. We calculate the complex polarizibilities and group velocities of the three slow light pulses in the weak field limit by means of the full Hamiltonian approach. It is shown that strong cross-phase modulation can be realized and large cross-phase shifts on the order ofπcan be generated for three slow weak pulses in very short interaction distance. It is indicated that the three slow weak pulses can reach matching of group velocities through adjusting the Rabi frequency of the control fields. In chapter 5, we study the photon-photon interaction in the TEIT system and its applications in quantum computation. We find that we can obtain a three-mode cross-Kerr-like interation of photons in the TEIT system and we can implement an all-optical Toffoli gate directly via the three-mode cross-Kerr-like interaction.The fourth part includes chapter 6. We propose optical schemes to generate W-type entangled coherent states in free travelling optical fields, including the generation of four-mode W-type entangled coherent states based on two-mode cross-Kerr media and the generation of three-mode hybrid W-type entangled coherent states based on three-mode cross-Kerr media. In the ideal conditions, the success probabilities of our schemes are unity.A summary of the work and an outlook of this thesis are given in the last part.