Optical Properties Of Two Coupled Cooper-pair Boxes Interacting With Two Modes Field

Since the phenomenon of superconductivity has been found, superconductor's characteristics of low loss, low fever, attracting much attention, and been extensively studied. Josephson junction is one of most important applications of superconductivity. It has lots of advantages, such as show the nature of quantum coherence in a relatively large scale, easily made to integrated circuit which let complex system scale small. These features are just what quantum information and quantum computing required, so it has been widely study in quantum information and quantum computing field, and developed three types of quantum circuits------charge qubit quantum circuit(Cooper pair box circuit),the phase qubit circuit, the flux qubit circuit. In studies, found that these circuits are very similar with atomic systems, a numbers of quantum optics phenomena which appeared in atomic system before now appeared in these circuits, for examples, Rabi oscillation, vacuum Rabi splitting, artificial atom laser, and resonance fluorescence. Accordingly, the concept of an artificial atom is proposed for its similarity with the atom.Now the research of superconducting circuit is divided in tow aspects, one is to realize quantum information and quantum computing with quantum circuits. Quantum circuits are used to realize quantum logic operations and quantum algorithms. Making efforts to improve the operating time or coherence time is another important subject to this aspect, because it can achieve a more complex algorithm. Another is the on-chip quantum optics, which can achieve the entire quantum optics phenomena what atomic system has achieved.This article discusses the case of two coupled Cooper pair boxes interact with two mode field to achieve a number of quantum optics phenomena ----electromagnetically induced transparency (EIT) and controlled resonance fluorescence. The main work of this paper is divided into several sections, as follows:The first part is the introduction; in this section we introduce the background of our work and the development of on-chip quantum optics, also, we brief introduce the concept that we will involve later ---electromagnetically induced transparency and resonance fluorescence.The second section, introduce the theoretical basis of this article----the basic method to quantize a circuit, this is the starting point of our work, in the later section, we will use this method to quantize our model.The third section introduce how to quantize a single Cooper pair box, and discuss its energy levels and eigenstates characteristics, have a preliminary understanding of Cooper pair box.The fourth section introduce how to quantize the two coupled Cooper pair boxes and its energy level characteristics, interact with tow mode field ,resulting in electromagnetically induced transparency and controlled resonance fluorescence phenomenon .