We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the solutions is: first, we use the system symmetries to describe the evolution in an operator space whose dimension grows polynomially with the number of atoms. Second, we expand the solutions in a basis composed of eigenvectors of the dissipative part of the master equation that models the independent dissipation of the atoms. This atomic damping basis is an atomic analog to the damping basis used for bosonic fields Briegel and Englert (1993 Phys. Rev. A 47 3311–29). The solutions show that the system decays as a sum of sub- and super-radiant exponential terms.

中文翻译：

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原子阻尼的基础和相互作用的两能级原子的集体衰减

当主方程在原子标记的排列下对称时，我们找到了相互作用的两级原子演化的解析解。主方程包括与原子无关的耗散。获得解的方法是：首先，我们使用系统对称性描述一个维数随原子数成倍增长的算子空间中的演化。其次，我们在由主方程耗散部分的特征向量组成的基础上扩展解，该方程对原子的独立耗散进行建模。该原子阻尼基础与原子能场Briegel和Englert（1993 Phys。Rev. A 47 3311-29）所使用的阻尼基础类似。解表明，该系统以次辐射指数和超辐射指数项之和衰减。