Study On The Influence Of Decoherence Effect On The Evolution Of J-C Model

Quantum theory is one of the most important physical theories in the development of science in the twentieth century,and its role in advancing modern science and technology is self-evident.The use of quantum theory to study and design quantum components,and thus to manufacture quantum devices,has become an important research direction today.The ease of preparation and the excellent quality of the atom-light field interaction system make it one of the most important platforms for the realisation of quantum computing,quantum communication and quantum metrology.In these studies,the use of coherence,a fundamental property of quantum mechanics,is indispensable for achieving precise quantum measurements,preparing high-precision quantum bits,etc.Experiments have shown that in practice there is no quantum system that is absolutely isolated from its environment,and in the process of preparation,evolution and processing,quantum systems will always inevitably interact with their environment,leading to decoherence effects.Therefore,the study of the decoherence time evolution and its effect on the system is of great importance for the research and application of quantum technology.In this paper,we start from the Jaynes-Cummings model,a model of two-energy atoms interacting with a single-mode optical field in quantum optics,and consider various types of error flips in the subsystem during its evolution assuming different initial states,mainly using the Kraus summation method and the master equation method to derive its decoherence evolution.We find that the density matrix of the final states decays non-diagonally for subsystems interacting with the environment,while the density matrix of the final states does not change for closed systems evolving in a fixed state,confirming the existence of quantum decoherence effects on quantum states in open systems.On this basis,we also try to compare the changes in the properties of some quantum states after the fixed-state evolution of the closed system and the decoherence of the open system,and analyse the differences in the changes of the von Neumann entropy of the quantum system and the fidelity of the quantum states under the two evolutions.We find that,when the probability distributions of the initial state basis vectors are different,even if there is the same error flip,the von Neumann entropy and the fidelity of the values of change also differ.However,both decay to zero as the probability of error flip increases.The analysis of fidelity and von Neumann entropy with and without decoherent evolution for the chosen fixed initial state leads to similar conclusions,with the non-decoherent fixed state evolution maintaining regular oscillations as time evolves,while the fidelity undergoes periodic oscillations with changing amplitude for the evolution with decoherence effects,and the von Neumann entropy undergoes oscillations with decreasing amplitude until it stabilises.