Off-resonant interaction of fluctuating photons in a resonator with a qubit increases the qubit dephasing rate. We use this effect to measure a small average number of intracavity photons that are coherently or thermally driven. For spectral resolution, we do this by subjecting the qubit to a Carr-Purcell-Meiboom-Gill sequence and record the qubit dephasing rate for various periods between qubit $\pi$ pulses. The recorded data is then analyzed with formulas for the photon-induced dephasing rate derived for the non-Gaussian noise regime with an arbitrary ratio of the resonator dispersive shift to decay rate. We show that the presented Carr-Purcell-Meiboom-Gill dephasing rate formulas agree well with experimental results and demonstrate measurement of thermal and coherent photon populations at the level of a few ${10}^{-4}$.

中文翻译：

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电路 QED 谐振器中小光子数的测量

谐振器中波动光子与量子位的非共振相互作用增加了量子位相移速率。我们利用这种效应来测量相干或热驱动的少量平均数量的腔内光子。对于光谱分辨率，我们通过将量子位置于 Carr-Purcell-Meiboom-Gill 序列并记录量子位之间不同周期的量子位相移率来实现这一点$\pi$脉冲。然后使用针对非高斯噪声区域导出的光子引起的相移速率公式对记录的数据进行分析，其中谐振器色散位移与衰减速率的任意比率。我们表明，所提出的 Carr-Purcell-Meiboom-Gill 移相率公式与实验结果非常吻合，并证明了在一些水平上对热光子和相干光子群体的测量。${10}^{-4}$。