Quantum systems are promising candidates for sensing of weak signals as they can be highly sensitive to external perturbations, thus providing excellent performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. Using numerical techniques, we further generalize these results to the case of background noise with a Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences, such as CPMG, are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.

量子系统是检测微弱信号的有希望的候选者，因为它们对外部扰动非常敏感，因此在估计外部场的参数时可提供出色的性能。但是，当尝试检测被背景噪声隐藏的微弱信号时，信噪比是比原始灵敏度更相关的指标。在关于信号和噪声的统计特性的适度假设下，我们确定了使用量子传感器在存在背景噪声的情况下检测外部信号的最佳量子控制。有趣的是，对于白色背景噪声，最佳解决方案是简单且众所周知的自旋锁定控制方案。使用数值技术，我们将这些结果进一步推广到具有洛伦兹谱的背景噪声的情况。我们表明，为了增加相关时间，基于脉冲的序列（例如CPMG）也接近用于检测信号的最佳控制，而分频取决于信号频率。这些结果表明，可以在近期的量子传感器中轻松实现最佳检测方案，而无需复杂的脉冲整形。