Abstract In this paper, we investigate the effect of minimal length on Einstein model of a gas of two-level atoms in thermal equilibrium with blackbody radiation at temperature T. We reformulate the classical Hamiltonian describing the interaction of atomic electrons with the electromagnetic field of blackbody radiation by employing Kempf Algebra to obtain the Hamiltonian with a minimal length. In the electric dipole approximation, we obtain the modified transition rate relations, and modified Einstein coefficients for broadband excitation. We utilize the modified quantities to obtain the modified cross-section in the resonant laser excitation. We deduce the upper bounds for the deformation parameter and minimal length.

中文翻译：

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原子激发的广义不确定性原理修正

摘要 在本文中，我们研究了最小长度对温度 T 下黑体辐射热平衡的两能级原子气体爱因斯坦模型的影响。我们重新表述了描述原子电子与黑体电磁场相互作用的经典哈密顿量辐射通过使用 Kempf 代数来获得具有最小长度的哈密顿量。在电偶极子近似中，我们获得了修正的跃迁率关系和宽带激发的修正爱因斯坦系数。我们利用修改后的量来获得谐振激光激发中修改后的横截面。我们推导出变形参数和最小长度的上限。