An orchestra of a hundred violins plays in a vast hall. The conductor stands before them but cannot get the instruments to sound in unison: every bow moves at its own tempo, and the music crumbles into noise. The axion search problem looks much the same. These dark matter particles, thought to stream through us every second, turn into microwave photons only when the conditions line up with extreme precision. To hear that whisper you need both a sensitive microphone and a perfectly synchronized ensemble.
DALI picks up this signal with a set of parallel dielectric plates placed in a magnetic field. When an axion flies through such a plate, a faint electromagnetic wave is born on its surface. From each plate the wave travels outward, and if their phases do not match, they cancel each other. But if the plates sit at the right distances, their emissions add up like the voices of a choir singing a single note. This is coherent addition, the first amplification mechanism.
The second mechanism is resonant buildup. Between the plates and a conducting mirror, a half-open Fabry-Perot resonator forms: light bounces back and forth between the mirror and the array, reflecting many times over. With the right tuning, a wave that has made many passes reinforces itself, and a weak signal accumulates to a measurable level. The key result of the paper: these two mechanisms are independent. The coherence of the surfaces determines how much energy enters the mode in a single pass, while the quality factor of the resonator determines how many times the wave can reflect before it dies away.
The authors break the output power of the instrument into four factors: the reference power from the magnetized mirror, the transverse projection of the source onto the desired mode, the loaded quality factor, and the energy extraction coefficient through the port. It turns out that the transverse projection is the only factor that depends on the phase pattern of the plates' emission. Everything else is set by the geometry of the resonator and does not change when the array is retuned.
The practical takeaway is simple: to calibrate DALI, you do not need to model a distributed axion source. It is enough to shine an external microwave source into the instrument and measure the quality factor and the coupling coefficient, since these parameters carry over to axion excitation unchanged. Such calibration removes the main obstacle to designing next-generation haloscopes.
The orchestra has gathered in the hall again. Now the conductor knows that to make the violins sound in unison, there is no need to retrain every musician: it is enough to place the music stands correctly and choose the tempo. So it is with DALI: the coherence of the surfaces is tuned once, and the resonator does the rest of the work, building a faint axion signal up to an audible level. This opens the way to dark matter searches at frequencies where earlier detectors were deaf.
The DALI prototype uses ceramic plates of yttrium-stabilized zirconium oxide only 1 mm thick, and the quality factor grows linearly with the number of layers up to 20, regardless of whether that number is even or odd.