AI 中文总结
研究多模电磁腔中两个相互作用的偶极二能级系统，借助玻恩 - 马尔可夫近似，找到系统密度矩阵表达式，推导稳态并发度，计算并发度时间演化，观察到突然死亡和复苏现象，还推导了XXZ耦合的相关方程和并发度。
AI 中文摘要
相互作用的偶极二能级系统构成一类特殊的量子比特，它们以特定方式与腔相互作用。首先证明处于热平衡的多模腔中一个1/2自旋与量子化磁场相互作用的马尔可夫动力学等同于二能级原子在偶极近似下与腔电场相互作用。接着用玻恩 - 马尔可夫近似研究在同一环境中通过反铁磁海森堡耦合相互作用的两个自旋的动力学。找到系统密度矩阵的精确表达式及非对角相干衰减时间和自旋弛豫时间。明确推导了任意初始态下稳态的并发度并揭示单重态的作用。针对不同初始态数值计算并发度的时间演化，观察到即使在玻恩 - 马尔可夫近似下也存在突然死亡和复苏现象，并对维纳态的行为进行了分析。最后推导了XXZ耦合的方程和稳态并发度。
英文摘要
Interacting dipolar two-level systems form a special class of qubits that interact with a cavity in a particular way. We first prove that the Markovian dynamics of one 1/2-spin in interaction with a quantised magnetic field from a multi-mode cavity at thermal equilibrium is equivalent to a two-level atom interacting in the dipole approximation with the electric field of the cavity. We then use the Born-Markov approximation to study the dynamics of two spins interacting through the antiferromagnetic Heisenberg coupling in the same environment. By solving the GKSL equation, we find the exact expression of the density matrix of the system, with the off-diagonal coherence decay time and spin relaxation time. The concurrence for the stationary state is explicitly derived for any kind of initial state and the role of the singlet state is brought to light. The temporal evolution of the concurrence is numerically computed for different initial states, the phenomenon of sudden death and revival of the entanglement is observed for this dynamics. A detailed analysis of the sudden death and revival of the concurrence is conducted for Werner states, with new analytical results obtained thanks to the solution of the GKSL equation. We finally derive the equations and the stationary concurrence for the XXZ coupling.
Comments14 pages, 12 figures, reference added, typos corrected, title changed
