that would have been hidden otherwise. This type of active cooling protocol was required to obtain the detailed, clean data in Fig. \[fig:3\], where we could clearly resolve resonances separated by only 270 MHz (13 mK). In fact, the necessity of active cooling becomes even more evident in the next section where, without the cooling pulse, the observed level of detail could not have been resolved over such a large parameter space in practical acquisition times.

![image](Fig5_Oliver_final_red_size.png){width="5in"}

Amplitude Spectroscopy {#sec:AS}
======================

Frequency-dependent absorption and emission spectroscopy has long played a fundamental role in the characterization of quantum systems. The development of coherent microwave (maser) and optical (laser) sources, high-intensity radiation with tunable, narrow spectral linewidth, has further enabled targeted absorption spectroscopy of atoms and molecules with high frequency resolution [@Schawlow82a; @Thompson85a]. However, the application of broadband frequency spectroscopy is not universally straightforward. This is particularly relevant for artificial atoms engineered from solid-state materials which, when cooled to cryogenic temperatures, assume quantized energy levels that extend into microwave and millimeter wave regimes (10-300 GHz). Although certainly not an impossible task, a broadband frequency-based spectroscopic study of these atoms in excess of around 50 GHz becomes extremely challenging and expensive to implement 