We present a theoretical framework for recovering the amplitude and carrier phase of a single received RF field with a Rydberg-atom receiver, without injecting an RF local oscillator (LO) into the atoms. The key enabling mechanism is a static DC bias applied to the vapor cell: by Stark-mixing a near-degenerate Rydberg pair, the bias activates an otherwise absent upper optical pathway and closes a phase-sensitive loop within a receiver driven only by the standard probe/coupling pair and the received RF field. For a spatially uniform bias, we derive an effective four-level rotating-frame Hamiltonian of Floquet form and show that the periodic steady state obeys an exact harmonic phase law, so that the $n$th probe harmonic carries the factor $e^{inΦ_S}$. This yields direct estimators for the signal phase and amplitude from a demodulated probe harmonic, with amplitude recovery obtained by inverting an injective harmonic response map. In the high-SNR regime, we derive explicit RMSE laws and use them to identify distinct phase-optimal and amplitude-optimal bias-controlled mixing angles, together with a weighted joint-design criterion and a balanced compromise angle that equalizes the fractional phase and amplitude penalties. We then extend the analysis to nonuniform DC bias through quasistatic spatial averaging and show that bias inhomogeneity reduces coherent gain for phase readout while also reshaping the amplitude-response slope. Numerical examples validate the phase law, illustrate response-map inversion and mixing-angle trade-offs, and quantify the penalties induced by bias nonuniformity. The results establish a minimal route to coherent Rydberg reception of a single RF signal without an auxiliary RF LO in the atoms.

翻译：我们提出了一种用于恢复单接收射频场幅度和载波相位的理论框架，该框架基于里德伯原子接收机，无需向原子注入射频本振（LO）。关键实现机制是对蒸气室施加静态直流偏置：通过斯塔克混合近简并的里德伯对，该偏置激活了原本缺失的上层光学路径，并在仅由标准探测/耦合对和接收射频场驱动的接收机内闭合了一个相位敏感环路。对于空间均匀偏置，我们推导出弗洛凯形式的有效四能级旋转框架哈密顿量，并证明周期稳态服从精确谐波相位规律，使得第n阶探测谐波携带因子e^(inΦ_S)。由此可从解调后的探测谐波直接获得信号相位和幅度的估计量，幅度恢复通过反演单射谐波响应映射实现。在高信噪比条件下，我们推导了显式均方根误差（RMSE）定律，并利用它们识别出不同的相位最优和幅度最优的偏置控制混合角，同时给出了加权联合设计准则和平衡折中角，该角度可均衡分数相位和幅度惩罚。随后我们将分析扩展到非均匀直流偏置情况，通过准静态空间平均方法证明，偏置不均匀性会降低相位读出的相干增益，同时重塑幅度响应斜率。数值算例验证了相位规律，展示了响应映射反演和混合角权衡，并量化了偏置不均匀性导致的性能损失。这些结果确立了无需原子内辅助射频本振即可实现单射频信号相干里德伯接收的极简路径。