发表机构
Università di Padova; INFN, Sezione di Padova; Università di Roma Sapienza; Istituto dei Sistemi Complessi - CNR; Università della Campania “Luigi Vanvitelli”; Università di Salerno（帕多瓦大学; 意大利国家核物理研究所帕多瓦分部; 罗马第一大学; 复杂系统研究所-国家研究委员会; 坎帕尼亚路易吉·凡维泰利大学; 萨莱诺大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有波动密度的相干玻色 - 爱因斯坦凝聚，通过相位 - 密度分解表述，在理想气体假设下确定关联函数层级，给出反常平均值模平方与凝聚密度关系，为光子凝聚提供图像并提出检验理论预测的方法。
AI 中文摘要
在巨正则系综中的玻色 - 爱因斯坦凝聚可以通过凝聚模算符\(\hat{\psi}_{\bf 0}\)的相位 - 密度分解来表述。在存在宏观凝聚数涨落的情况下，这种表示有重要意义。对于理想气体，在相位明确且凝聚密度波动的假设下表明，关联函数的完整层级由密度统计决定。在此框架下，反常平均值\(\langle \hat{\psi}_{\bf 0}\rangle\)的模平方仅提供部分凝聚密度\(\rho_{\bf 0}\)，理想玻色气体的巨正则统计下\(|\langle {\hat \psi}_{\bf 0}\rangle|^2 =(\pi/4) \rho_{\bf 0}\)，其余部分由\(\hat{\psi}_{\bf 0}\)的涨落补充，这是此情形下玻色 - 爱因斯坦凝聚的显著特征，为染料填充微腔光子实验中具有明确相位但大量涨落的光子凝聚提供了清晰物理图像，还提出了获取反常平均值模平方以检验理论预测的方法。
英文摘要
Bose-Einstein condensation in the grand canonical ensemble admits a formulation in terms of a phase-density decomposition of the condensate mode operator $\hatψ_{\bf 0}$. In the presence of macroscopic condensate number fluctuations this representation presents nontrivial implications. In particular, we show that, for the ideal gas, under the assumption of a well-defined phase and a fluctuating condensate density, the square modulus of the anomalous average $\langle \hatψ_{\bf 0}\rangle$ can provide only a fraction of the whole condensate density $ρ_{\bf 0}$ and for the grand canonical statistics of the ideal Bose gas one obtains the value $|\langle {\hat ψ}_{\bf 0}\rangle|^2 =(π/4) ρ_{\bf 0}$. The remaining part is supplemented by the (macroscopic) fluctuations of $\hatψ_{\bf 0}$, which become a distinctive feature of the BEC in this setting. This provides a transparent physical picture of a condensate of photons with a well-defined phase but large number fluctuations, as observed in dye-filled microcavity photon experiments. We also propose a way to access the square modulus of the anomalous average to test theoretical predictions.
Comments9 pages
Journal refPhys. Rev. A 114, 043704, 2026
