含有复杂耦合的介观LC电路能级跃迁的选择定则

Selection Rules of Energy Level Transition for Mesoscopic LC Circuits with Complex Couplings

包含小型固态器件的介观电路因其易于集成、可大规模化的特点,在众多可能实现量子计算的方案中备受关注。本文利用正则量子化方法,给出了含有复杂耦合的介观LC电路的量子化方案,得到了该系统的能量算符;通过与一维量子谐振子相类比,并借助于幺正变换,导出了系统的能级公式及其态矢量表达式。在此基础上,讨论了介观电路两支路中电容器某一极板上的电荷量及穿过两线圈的等效磁通量在基态下的均方量子涨落。另外,考虑到一旦受到外电磁场的辐照,介观电路的状态将会改变,并可在相应能级之间发生跃迁,利用“不变本征算符”方法,得到了该系统能级跃迁的选择定则。

Due to the rapid development of quantum computing and quantum information,the physical study of solid-state quantum systems has revived significant interest.Among the possible schemes for the experimental realization of quantum computing,mesoscopic circuits containing small solid-state devices have attracted much attention,because of their advantages of easy integration and large-scale characteristics.Since the actual mesoscopic circuit is always in a certain environment,it is inevitably affected by the environment.For example,a mesoscopic circuit is radiated by an external electromagnetic field.The transitions will occur between different energy levels of the system.It is valuable to find the rules of energy level transition.In this paper,a more general mesoscopic LC circuit with complex coupling is chosen as the research object.By virtue of the canonical quantization method,the mesoscopic circuit is quantized and the Hamiltonian operator of the system is obtained.With the help of unitary transformation and analogy with a one-dimensional quantum harmonic oscillator,it is found that the mesoscopic LC circuits with complex couplings can be considered as two independent quantum mechanical harmonic oscillators.Then,the energy level formula and state vector expression of the system are deduced easily.In addition,the mean square quantum fluctuations,in the ground state,of the charges on one plate of the capacitor in the two branches of the mesoscopic circuit,and the equivalent magnetic flux passing through the two loops,are discussed.Considering that,once the mesoscopic circuit is irradiated by the external electromagnetic field,its state will change and a transition between the corresponding energy levels will occur.By using the “invariant Eigen-operator” method,the selection rules of energy-level transition for the mesoscopic LC circuit with complex couplings are obtained conveniently.It is believed that the application of this method will enrich the theoretical research on mesoscopic circuit from a fresh point of view.