| The conventional nonlinear optics mainly focus on the interaction between the electromagnetic medium and strong coherent laser fields and the produced nonlinear optics effect,while the discovery of electromagnetically induced trans-parency(EIT)in 1990s made a breakthrough on the investigation of strong non-linear optical effects with weak laser fields.EIT can effectively suppress the absorption of a propagating field and dramatically enhance the dispersion and the nonlinear optical susceptibility of the optical media.Under the EIT condi-tion,it is possible to realize not only the ultraslow propagation and the active manipulation of a light pulse with vanishing radiative loss,but also the nonlinear and quantum optical effects at single-photon level.In recent years,much attention has been paid to the investigation of ultra-cold Rydberg atoms,which possess many novel physical properties such as long lifetime,larger electric-dipole moment,and strong dipole-dipole interaction that is adjustable over 12 orders of magnitude.In addition to many other important research progress,the realization of EIT in Rydberg atoms(Rydberg-EIT)pro-vides a new platform for the exploration of nonlinear and quantum optics under weak light condition.Related research results have important applications the research areas such as precision spectroscopy,quantum computing and quantum information,quantum control and precision measurement,etc.EIT in atoms have become a key technique in quantum memory.In order to obtain high efficiency and fidelity of quantum memory,a large optical depth of atomic medium should be chosen,which may be accompanied,however,by the process of four-wave mixing(FWM)that results in the remarkable quantum noise in many traditional scheme of quantum memory based on EIT.Finding an effective approach to suppressing the quantum noise so as to improve the efficiency and fidelity of quantum memory has become one of the urgent issues of the research.In addition,current studies on Rydberg-EIT are not deep e-nough,and researches on some physical properties of Rydberg-EIT,including its transient optical response and the nonlocal Kerr effects induced by the strong dipole-dipole interaction between Rydberg atoms,are not comprehensive enough or even lacked.In this dissertation,we investigate the quantum effects of light propagation and nonlinear transient response via electromagnetically induced transparency,which includes:(i)Develop a theoretical method beyond mean-field approach to study the many-body dynamics of Rydberg atomic system,and calculate the linear and nonlinear transient optical response of Rydberg-EIT;(ii)Study the lin-ear propagations of photons under the conditions of EIT and FWM,and provide an effective approach to suppressing the quantum noise induced by FWM;(iii)Study the classical analogue of EIT and FWM in the metamaterial,and explore the linear and nonlinear propagation of high-dimensional plasmon polaritons.The main work contains the following aspects:1.Study on the propagation of photons under the conditions of EIT and FWM and the suppression of quantum noise.The set of Heisenberg-Langevin equations governing the three-level ?-type atomic system with FWM is derived in the Heisenberg picture,yielding the analytical results of the signal and the idler fields and their propagations are studied in detail.We show that the system possesses two normal modes,slow-light(quasi-EIT)mode and fast-light(gain)mode,constituting the propagations of the signal and the idler fields via linear superpositions.Due to the presence of the fast-light mode,both two fields undergo optical gain during the propagation,yielding the ampli-fications of the quantum noise and the Langevin noise.In order to suppress the dominant quantum noise,we propose a theoretical scheme of taking the correlat-ed squeezed-vacuum state as the input condition of the two fields,and calculate the propagation dynamics under this condition.We show that under the suit-able phase modulation of the input field,the fast-light mode of the system can be effectively suppressed,so that the fidelity of the two fields are improved.The scheme proposed here may provide new idea on improving the quantum memory based on EIT.and may have applications in quantum information process.2.Study on the transient optical response of EIT in ultracold Rydberg atomic system.Firstly,the two-atom model with dipole-dipole in-teraction is considered in the Schrodinger picture,and the time evolution of the optical susceptibility of the system based on the equation of density-matrix and Maxwell equation is studied.We show that the transient and steady-state re-sponses of EIT in strongly dependent on the dipole-dipole interaction between atoms,resulting in a fast response of EIT in the Rydberg atomic system(at least five times faster than the conventional atomic system with no dipole-dipole interaction).Secondly,the transient optical response of EIT is calculated in the ensemble of ultracold Rydberg atoms,which not only confirms the result-s obtained in the two-atom model,but also indicates that the response speed can be further increased with the increased amount of interacting atoms.Final-ly,by comparing the results obtained by two models,we find that the unique dipole blockade effect is the main physical reason of fast-responding properties of Rydberg-EIT.The results presented here not only help to thoroughly under-stand the physical properties of Rydberg-EIT,but are also meaningful to the realization and the optimization of the all-optical devices(including all-optical switches,transistors,etc.).3.Study on the classical analogue of FWM in the metamaterial and high-dimensional nonlinear vector plasmon polaritons.Recently,the classical analogue of EIT in the metamaterials,i.e.,plasmon-induced trans-parency(PIT),has attracted much attention.In order to realize the classical analogue of atomic FWM in the PIT metamaterial,a new kind of meta-atoms is proposed,which are arranged in periodic arrays in the present metamaterial,and each of the meta-atoms consists of two metallic cut-wires and a metallic split-ring resonator.The Maxwell-Lorentz equations governing the meta-atom is analyti-cally derived,and the spectral of the metamaterial is analyzed analytically and numerically.By comparing with results of the four-level double-A type atoms,we show that the present metamaterial can indeed mimic the analogue of the atom-ic FWM.In addition,the varactor diodes are mounted onto each meta-atom in order to acquire the nonlinearity.The nonlinear propagation of electromagnetic waves in the metamaterial are studied by using the singular perturbation the-ory.We show that under the condition of PIT,the metamaterial may possess enhanced second-order and third-order nonlinear susceptibility,which may be further enhanced when the resonant interaction between the longwave and short-wave occurs,resulting in the realization of nonlinear plasmon polaritons with extremely low power.We also study the collision interaction between the nonlin-ear plasmon polaritons and confirm their stability.The study presented here not only realize the classical analogue of atomic FWM,but also provide new research idea and method for the extensive study of nonlinear plasmon polaritons.The methods and the results presented in this dissertation not only help to thoroughly understand the properties of coherence,nonlinearity and quantum optics,but may also have practical applications in quantum information process and transmission. |
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