We investigate the radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. In the limit of a single impurity, we show using Fermi’s golden rule that introducing (or injecting) an impurity into the medium is equivalent to ejecting an impurity that is initially interacting with the medium, since the “injection” and “ejection” spectral responses are simply related to each other by an exponential function of frequency. Thus, the full spectral information for the quantum impurity is contained in the injection spectral response, which can be determined using a range of theoretical methods, including variational approaches. We use this property to compute the finite-temperature equation of state and Tan contact of the Fermi polaron. Our results for the contact of a mobile impurity are in excellent agreement with recent experiments and we find that the finite-temperature behavior is qualitatively different compared to the case of infinite impurity mass.

中文翻译：

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射频响应和量子气体中的杂质接触。

我们研究了在有限温度下与量子气体相互作用的杂质的射频光谱。在单一杂质的极限下，我们显示出使用费米黄金定律表明，将杂质引入（或注入）到介质中等同于注入最初与介质相互作用的杂质，因为“注入”和“注入”光谱响应通过频率的指数函数简单地彼此关联。因此，量子杂质的全部光谱信息包含在注入光谱响应中，这可以使用一系列理论方法（包括变分方法）来确定。我们使用此属性来计算费米极化子的状态和Tan接触的有限温度方程。