论文标题
平均场激光器方程的基本属性
Basic properties of a mean field laser equation
论文作者
论文摘要
我们研究了在平均场近似下描述激光的非线性量子主方程。量子系统由单个模式光腔和两个与储层相互作用的原子形成。也就是说，我们确定了正在考虑的非线性操作员方程的常规解决方案的存在和唯一性，并且根据平均场随机schröndiger方程，我们获得了该解决方案的概率表示。为此，我们为Gorini-Kossakowski-Sudarshan-Lindblad形式的非自主线性量子主方程进行了常规解决方案，并且我们证明了Gorini-Kossakokowski-Sudarshan-lindblad形式的非自主线性邻接量子量子的解决方案的独特性。此外，我们从平均场激光器方程中严格地获得Maxwell-Bloch方程。
We study the non-linear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the non-linear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schröndiger equation. To this end, we find a regular solution for the non-autonomous linear quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form, and we prove the uniqueness of the solution to the non-autonomous linear adjoint quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form. Moreover, we obtain rigorously the Maxwell-Bloch equations from the mean field laser equation.
