Dynamical Evolution And Nonclassical Properties Of Quantum Systems Interacting With Artificial Materials

It is known that owing to the vacuum fluctuation, an excited atom would spontaneously emit photons and decays to the ground state. After realizing that the spontaneous decay of atom can be modified by the appearance of material, people begin to study new kinds of arti-ficial materials, which aims at changing the environment around the atom. The improvement of experimental technology allows people to fabricate metamaterials, topological insulatros and grephene around year 2004. Metamaterials had been investigated in the early time among them since the designs are mostly focus on changing the electromagnetic response of natural materi-als, and they posses optical properties such as negative refraction, electromagnetic transparency and so on. In topological insulators, when the time reverse symmetry of gapless surface state is broken, its optical property would be changed by the appearance of topological parameter. In the monolayer of grphene, its optical properties can be changed by adjusting the gate voltage or doping concentration. Specially, at Terahertz region, graphene has metallic behavior and supports surface plasmon modes.According to the properties that mentioned above, in this thesis, we investigate the atomic decay in different structures made of different kinds of nanomaterials, and apply their optical properties to realize the entanglement, quantum interference and squeezing of resonance fluo-rescence of quantum systems.Firstly, we investigate the dynamics and entanglement of a pair of two-level atoms embed-ded into the zero-index material. The zero-index material is composed of two single-negative slabs that have the same thickness. We place the atom pair closed to the interface of two slabs in order to build a strong coupling between the quantum system and the plasma field. Assume that the system has only single excitation, then the motion equations of the possibility amplitudes can be derived according to Schrodinger equation, without making Markovian approximation. When the thickness of meta slabs is much larger than the localized strength of the plasma field, the Green function can be simplified and the analytical form can be achieved. After solving the motion equations it can be clearly seen that there exists a threshold which could separate the Markovian and NonMarkovian behavior of the system. More detailed, it depends on whether the coupling strength between the symmetric mode(antisymmetric mode) and the plasma field exceeds the critical value or not. The entanglement of the system, which is affected by the initial state, could be decrease with time till disappears, or gain with time and keep for long period. It is also found that when the interaction between atoms are strong enough, even if there is detuning between the atom and the plasma field, entanglement can be generated.Then, we have studied the quantum interference of three-level Zeeman atom in a cavity constructed by topological insulators. Owing to the topological electromagnetic effect, when the cavity length is smaller than half vacuum wave length, the radiation from dipole paralleled to the cavity mirror would be suppressed while the radiation from dipole perpendicular to the cavity mirror would be enhanced. Especially, when the axion field is strong enough, the decay of paralleled dipole component would be totally suppressed, thus strong quantum interference between transition channels of Zeeman atom could be generated. Then enlarge the cavity length, due to the superposition of electromagnetic wave inside the cavity, the strength of quantum interference would strongly depends on the location of the atom. However, real material posses some loss. Then we take it into account and find that the dissipation dominates in the atomic decay rate only in a short region around the cavity mirror. When atom locates in this region, the contributions of other electromagnetic modes on the decay rate are subtle and can be neglected, and the decay through dissipation will have a destructive effect on quantum interference. This effect would disappear when the distance between the atom and the cavity mirror becomes larger, and the circumstance would be similar to the lossless case.Lastly, we discuss the radiation property of a quantum dot closed to a graphene sheet. In Terahertz region, the Purcell factor of the quantum dot exhibits Lorentz-like shape. And with the increase of the environment temperature, the maximum of Purcell factor suffers a de-crease and its distribution tends to be average on the frequency. When the quantum dot couples stronger to the plasma field than other modes, by adjusting the pump intensity and the pump frequency, squeezing could be obtained if two transition channels of the dressed quantum dot decay at different rates. However, dephasing will bring destructive effect on squeezing. It has been found that by placing the quantum dot closer to the graphene, the enhancement of the cou-pling strength between quantum dot and surface modes could overcome this issue. Specially, when the population difference of the dressed quantum dot is prominent, then reasonably pick the experimental parameters squeezing at room temperature could be stronger than zero tem-perature case. Thus it indicates, by adjusting the Fermi energy of graphene and the intensity or central frequency of the pump laser, the squeezing of resonance fluorescence could be largely enhanced.