少原子激光器的精确阻尼基连分数：超越二阶累积量闭合的集体关联
Exact damping-basis continued fractions for few-atom lasers: collective correlations beyond second-order cumulant closure
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中文总结 AI 辅助
本文结合阻尼基与置换不变Liouville基，提出少原子激光器的精确块三对角连分数解法，验证二阶累积量闭合的局限，并揭示双原子相干性与光谱窄化。
中文摘要 AI 辅助
我们将有损腔模的Briegel-Englert阻尼基与N个相同、非相干泵浦的二能级发射体的置换不变Liouville基相结合。由此得到的Liouvillian在单一径向场指标下精确地呈块三对角形式，原子块维度为\(\inom{N+3}{3}\)。稳态由矩阵连分数给出，其渐近闭合是一个线性矩阵方程，我们证明该方程在整个耗散区域\(A>0\)内具有唯一解；在相干性为一的扇区中，相同的构造可得到发射光谱。该方法通过与直接对角化、弱泵浦微扰理论和闭系统光谱的对比得到验证，在少量子区域可在数十秒内达到\(N=16\)，并在大光子数下具有量化的精度极限。我们利用该方法推导出一个精确的双原子光子平衡恒等式，该恒等式分离出腔诱导的成对相干性，并将其与单重态-三重态布居差联系起来；建立了零温腔中连通关联的精确泵浦阶次层级以及最小集体自旋扇区的奇偶性；并基准测试了少发射体激光理论中使用的二阶累积量闭合，发现其对光子数是半定量的，但在反转之上对发射体间相干性预测了错误的符号。在良腔区域，精确解对两个和三个发射体显示出近泊松统计和强线宽窄化。
英文摘要
We combine the Briegel--Englert damping basis of a lossy cavity mode with the permutation-invariant Liouville basis of \(N\) identical, incoherently pumped two-level emitters. The resulting Liouvillian is exactly block tridiagonal in a single radial field index, with atomic blocks of dimension \(\binom{N+3}{3}\). The stationary state follows from a matrix continued fraction whose asymptotic closure is a linear matrix equation that we prove to be uniquely solvable throughout the dissipative regime \(A>0\), and the same construction in the coherence-one sector yields the emission spectrum. The method is validated against direct diagonalization, weak-pump perturbation theory, and closed-system spectra, reaches \(N=16\) in tens of seconds in the few-quanta regime, and has a quantified precision limit at large photon number. We use it to derive an exact two-atom photon-balance identity that isolates the cavity-induced pair coherence and relates it to a singlet--triplet population difference; to establish an exact pump-order hierarchy of connected correlations for a zero-temperature cavity and a parity property of the minimal collective-spin sector; and to benchmark the second-order cumulant closure used in few-emitter laser theory, which we find to be semi-quantitative for the photon number but to predict the wrong sign of the inter-emitter coherence above inversion. In a good-cavity regime the exact solution shows near-Poissonian statistics and strong line narrowing for two and three emitters.
发表机构
- Munich Center for Mathematical Philosophy, LMU Munich（慕尼黑数学哲学中心，慕尼黑大学）
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