AI 中文总结
该研究从第一性原理推导旋转环形腔中的量子光学模型，经系列变换得到含旋转效应的类Jaynes-Cummings哈密顿量，发现可实验观测的旋转诱导超精细位移，为非惯性腔中原子量子电动力学研究提供基础。
AI 中文摘要
本文从第一性原理出发，推导了非惯性旋转环形腔中的量子光学模型。我们从弯曲时空中的狄拉克方程开始，加入与电磁场的最小耦合，得到广义玻恩度量下的狄拉克哈密顿量。接着通过Foldy-Wouthuysen变换正式取非相对论极限，并将其投影到原子的电子、质子和中子的费米子福克空间。聚焦于氢原子，我们在偶极和长波近似下通过Power-Zienau-Woolley变换从最小耦合规范过渡到多极展开规范。在此，我们发现了系统旋转带来的额外项，包括原子跃迁的旋转诱导超精细位移，即使在小旋转速率下也可能通过实验观测到。在电偶极、二能级和旋转波近似下，我们得到了类似Jaynes-Cummings的哈密顿量，该哈密顿量也考虑了旋转效应，如旋转诱导超精细位移以及腔中反向传播模式的萨格纳克位移。
英文摘要
In this paper, we derive a quantum optics model in a non-inertial rotating ring cavity from first principles. We begin with the Dirac equation in curved spacetime, add minimal coupling to the electromagnetic field, and then find the Dirac Hamiltonian for the generalized Born metric. We then formally take the non-relativistic limit by way of Foldy-Wouthuysen transformations and project onto a fermionic Fock space for the atoms' electrons, protons, and neutrons. Focusing on a protium atom, we next move from a minimal coupling gauge to a multipole expansion gauge by taking a Power-Zienau-Woolley transformation under the dipole and long-wavelength approximations. Here, we find additional terms from the rotation of the system including a rotation-induced hyperfine shift of the atomic transition which could possibly be observed experimentally even for small rotation rates. Making the electric dipole, two-level, and rotating-wave approximations, we arrive at a Jaynes-Cummings-like Hamiltonian which also accounts for rotational effects, such as the rotation-induced hyperfine shift and the Sagnac shift for the cavity's counterpropagating modes.
Comments25 pages, 1 figure
