Abel-Plana公式在Jaynes-Cummings模型Rabi振荡崩溃和恢复中的应用
Application of Abel-Plana formula for collapse and revival of Rabi oscillations in Jaynes-Cummings model
摘要：
本文给出了Jaynes-Cummings模型（JCM）中Rabi振荡的坍缩和恢复的解析处理。JCM是一个精确可解的量子力学模型，它描述了二能级原子与电磁场的单腔模之间的相互作用。当原子处于基态，腔模处于相干态时，JCM在其时间演化过程中以复杂的模式多次引起Rabi振荡的坍缩和恢复。在这种现象中，原子布居数反转用一个难处理的无穷级数来描述。(When电磁场与原子共振，该无穷级数的第项$n$由$\sqrt{n}t$的三角函数给出，其中$t$是时间变量。）根据Klimov和Chumakov的方法，使用Abel-Plana公式，我们将这个无穷级数重写为两个积分的和。我们研究了这两个积分的物理意义，发现第一个积分表示初始坍缩（半经典极限），第二个积分表示JCM中的复兴（量子修正）。此外，我们还计算了低温下腔模初始热相干态的JCM随时间演化的一阶和二阶微扰，并利用Abel-Plana公式将其修正项记为积分之和。
英文摘要：
In this paper, we give an analytical treatment to study the behavior of the collapse and the revival of the Rabi oscillations in the Jaynes-Cummings model (JCM). The JCM is an exactly soluble quantum mechanical model, which describes the interaction between a two-level atom and a single cavity mode of the electromagnetic field. If we prepare the atom in the ground state and the cavity mode in a coherent state initially, the JCM causes the collapse and the revival of the Rabi oscillations many times in a complicated pattern in its time-evolution. In this phenomenon, the atomic population inversion is described with an intractable infinite series. (When the electromagnetic field is resonant with the atom, the $n$th term of this infinite series is given by a trigonometric function for $\sqrt{n}t$, where $t$ is a variable of the time.) According to Klimov and Chumakov's method, using the Abel-Plana formula, we rewrite this infinite series as a sum of two integrals. We examine the physical meanings of these two integrals and find that the first one represents the initial collapse (the semi-classical limit) and the second one represents the revival (the quantum correction) in the JCM. Furthermore, we evaluate the first and second-order perturbations for the time-evolution of the JCM with an initial thermal coherent state for the cavity mode at low temperature, and write down their correction terms as sums of integrals by making use of the Abel-Plana formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
