哪种跃迁可用于中层大气磁强计的钠无镜激光？
Which transition can be used in sodium mirrorless lasing for mesospheric magnetometry?
AI总结：
本文针对中层大气磁强计的钠无镜激光，通过闭式推导明确了可维持粒子数反转的跃迁路径，给出了泵浦形式、功率分配及短暂窗口的关键设计结论，结果可推广至其他原子物种。
AI中文摘要：
中层大气钠层的定向无镜激光已被提出作为克服激光导星荧光各向同性的方法，且已在单元级类似系统和远程磁强计应用中得到验证。钠原子能级梯上的多条跃迁路径会竞争相同的泵浦光子，而哪条路径能维持粒子数反转以及在何种泵浦形式下维持，通常通过多能级速率模型的数值扫描来确定。本文从原子数据出发，以闭式形式解答了该问题，得到三个与设计相关的结果：（1）$u\to l$的级联反转要求$\tau_u/\tau_l>(g_u/g_l)b_{ul}$，该不等式重现了完整的连续波分类，包含$4P_{3/2}\to4S_{1/2}$（2.21μm）、$4P_{3/2}\to3D_{5/2}$（9.1μm）和精细结构伴线$4S_{1/2}\to3P_{1/2}$（1138nm），排除$4D_{5/2}\to4P_{3/2}$（2.34μm）和$3D_{5/2}\to3P_{3/2}$（819nm），且显示2.34μm谱线仅差9%即可满足条件，这就是它可短暂获得的原因；（2）速度选择性会反转初始方案的排名，因为对单步泵浦精确的多普勒平均处理，会低估两步泵浦的参与因子，其量级为多普勒宽度与自然宽度的比值，约$10^2$，两束泵浦光功率均分恰好为最优；（3）2.34μm谱线的短暂窗口在约$2\tau(4P)\neq210$ns后关闭，由储层寿命而非泵浦决定。每个结论均可追溯到寿命、分支比或线宽，无需重新运行模型即可推广到其他物种。
英文摘要：
Directed mirrorless lasing from the mesospheric sodium layer has been proposed as a way to overcome the isotropy of laser-guide-star fluorescence, with demonstrated cell-scale analogues and a demonstrated stand-off magnetometry application. Several transition paths on the Na ladder compete for the same pump photons, and which of them can sustain a population inversion---and under what pumping format---is usually settled by numerical scans of a multi-level rate model. Here the same question is answered in closed form, and three design-relevant results follow from the atomic data alone. (1) A cascade inversion on $u\to l$ requires $τ_u/τ_l>(g_u/g_l)b_{ul}$. The inequality reproduces the full continuous-wave classification---admitting $4P_{3/2}\to4S_{1/2}$ (2.21~\textmu m), $4P_{3/2}\to3D_{5/2}$ (9.1~\textmu m) and the fine-structure companion $4S_{1/2}\to3P_{1/2}$ (1138~nm), excluding $4D_{5/2}\to4P_{3/2}$ (2.34~\textmu m) and $3D_{5/2}\to3P_{3/2}$ (819~nm)---and shows the 2.34~\textmu m line to miss by only 9\%, which is why it is transiently accessible. (2) Velocity selectivity reverses the naive scheme ranking because a Doppler-averaged treatment, exact for one-step pumping, underestimates two-step pumping by a participation factor of order the Doppler-to-natural width ratio, $\sim$$10^{2}$; equal division of power between two pump beams is exactly optimal. (3) The transient window on 2.34~\textmu m closes after $\sim$2$τ(4P)\approx210$~ns, set by the reservoir lifetime rather than by the pump. Each conclusion is traceable to a lifetime, a branching ratio or a linewidth, and transfers to another species without rerunning a model.
