AI 中文总结
该研究构建了自由空间有限强场激光脉冲的连续模式量子光学表示，实现了相干与非经典脉冲的统一处理，为量子光学计算提供了能量一致的脉冲接口。
AI 中文摘要
我们构建了自由空间中有限近轴激光脉冲的能量一致的量子光学表示，该构建基于连续模式描述，为相干和非经典强场驱动源的统一处理提供了一步。从平面波量子化出发，我们构造了横向矢量模式约化，其中所选模式可再现任意归一化的空间-偏振分布。对于相干脉冲，测得的脉冲能量和完整实验室解析信号确定了频率相关的相干态位移(α(ω))，而无需引入物理量子化体积。对于非经典脉冲，相同的一阶场数据和总能量无法唯一确定量子态，需要额外的关联信息或模型假设。我们通过正常和反常协方差核纳入此信息，并讨论基于g⁽²⁾的压缩脉冲诊断。我们还推导了数值频率箱离散化的相位敏感收敛准则。一个可精确求解的连续模式自由电子应用表明，相干位移再现了半经典平均轨迹，而场协方差决定了电子波包宽度。该框架提供了测得的自由空间脉冲与量子光学计算之间便捷、能量一致的接口。
英文摘要
We formulate an energy-consistent quantum-optical representation of finite paraxial laser pulses in free space. The formulation is based on a continuous-mode description and provides a step toward a unified treatment of coherent and nonclassical strong-field drivers. Starting from plane-wave quantization, we construct a transverse vector-mode reduction in which the selected mode can reproduce an arbitrary normalized spatial--polarization profile. For a coherent pulse, the measured pulse energy and full laboratory analytic signal determine the frequency-dependent coherent-state displacement $(α(ω))$, without introducing a physical quantization volume. For nonclassical pulses, the same first-order field data and total energy do not uniquely specify the quantum state. Additional correlation information or model assumptions are required. We incorporate this information through normal and anomalous covariance kernels and discuss $g^{(2)}$-based diagnostics of squeezed pulses. We also derive a phase-sensitive convergence criterion for numerical frequency-bin discretizations. An exactly solvable continuum-mode free-electron application shows that the coherent displacement reproduces the semiclassical mean trajectory, whereas the field covariances determine the electron wave packet width. The framework offers a convenient, energy-consistent interface between measured free-space pulses and quantum-optical calculations.
