A theoretical particle-number conserving quantum field theory based on the concept of imaginary time is presented and applied to the scenario of a coherent atomic laser field at ultra-cold temperatures. The proposed theoretical model describes the analytical derivation of the frequency comb spectrum for an atomic laser realized from modeling a coherent atomic beam of condensate and non-condensate quantum field components released from a trapped Bose-Einstein condensate at a given repetition phase and frequency. The condensate part of the atomic vapor is assumed to be subjected to thermal noise induced by the temperature of the surrounding thermal atomic cloud. This new quantum approach uses time periodicity and an orthogonal decomposition of the quantum field in a complex-valued quantum field representation to derive and model the quantum field's forward- and backward-propagating components as a standing wave field in the same unique time and temperature domain without quantitative singularities at finite temperatures. The complex-valued atom laser field, the resulting frequency comb, and the repetition frequency distribution with the varying shape of envelopes are numerically monitored within a Monte-Carlo sampling method, as a function of temperature and trap frequency of the external confinement.

翻译：基于虚时概念提出一种理论上的粒子数守恒量子场论，并将其应用于超冷温度下相干原子激光场的场景。该理论模型描述了通过模拟从囚禁玻色-爱因斯坦凝聚体中释放的凝聚体与非凝聚体量子场分量的相干原子束，在给定重复相位与频率下实现原子激光器频率梳频谱的解析推导。假设原子蒸汽的凝聚部分受到周围热原子云温度引起的热噪声影响。这一新的量子方法采用时间周期性及量子场在复值量子场表示中的正交分解，推导并建模量子场的前向传播与后向传播分量，使其在无有限温度定量奇异性的同一独特时间与温度域中表现为驻波场。通过蒙特-卡洛采样方法，数值监测复值原子激光场、由此产生的频率梳以及随包络形状变化的重复频率分布，并将其作为温度与外部囚禁势阱频率的函数进行分析。