Nuclear magnetic resonance is a promising experimental approach to search for ultra-light axion-like dark matter. Searches such as the cosmic axion spin-precession experiments (CASPEr) are ultimately limited by quantum-mechanical noise sources, in particular, spin-projection noise. We discuss how such fundamental limits can potentially be reached. We consider a circuit model of a magnetic resonance experiment and quantify three noise sources: spin-projection noise, thermal noise, and amplifier noise. Calculation of the total noise spectrum takes into account the modification of the circuit impedance by the presence of nuclear spins, as well as the circuit back-action on the spin ensemble. Suppression of the circuit back-action is especially important in order for the spin-projection noise limits of searches for axion-like dark matter to reach the quantum chromodynamic axion sensitivity.

核磁共振是寻找超轻轴子状暗物质的一种很有前途的实验方法。诸如宇宙轴子自​​旋进动实验 (CASPER) 之类的搜索最终会受到量子力学噪声源的限制，尤其是自旋投影噪声。我们讨论如何可能达到这种基本限制。我们考虑磁共振实验的电路模型并量化三个噪声源：自旋投影噪声、热噪声和放大器噪声。总噪声谱的计算考虑了由于核自旋的存在而导致的电路阻抗的修改，以及自旋系综上的电路反作用。