loops between the microwave instruments (analog signal generator and network analyzer) and their corresponding lines. Attenuators (not shown) are added between every connection to reduce cable resonances. All instruments are synchronized with a SRS FS725 Rubidium frequency standard (not shown). Measurement controlling and data processing are done by MATLAB running on a measurement computer. Communications between the measurement computer and the instruments are realized through IEEE-488 GPIB buses.

Power attenuation
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In our experiments, we drive the system strongly with a signal created by the signal generator at room temperature. We can control the signal power at the generator, but to get the power $P_{\rm in}$ at the input of the cavity we need to make an estimation of the attenuation in the cavity input line.

In both spectroscopy and relaxation experiments, we use the same line to connect the ports 1a to 1c and 1b to 1c (see Fig. \[fig:mschema\]). There are several attenuators placed in this line at the different temperature levels of the refrigerator, providing a total of $68\ \textrm{dB}$ attenuation. Then for the semi-rigid cables of this rf line we have $9\ \textrm{dB}$ of additional attenuation (calculation includes the temperature dependence of attenuation). Further on, as 