Lecture Notes: Probing ultralight axion-like particles with quantum technology

We review the physics of ultralight axion-like particles (ALPs) as dark matter candidates and the experimental strategies used to search for them with precision and quantum technologies. In the ultralight regime, the enormous occupation number of the dark matter field motivates a classical description in terms of a coherently oscillating background, leading to distinctive, time-dependent signatures in laboratory observables. We discuss the effective field theory framework governing ALP interactions with Standard Model fields, and show how different operators give rise to qualitatively different experimental signals. The lecture notes cover both conversion-based searches enabled by the axion-photon coupling, such as haloscopes and helioscopes, and precision experiments sensitive to oscillations of fundamental constants and material properties. These include atomic and nuclear clocks, optical cavities, laser and unequal time-delay interferometers, and mechanical or solid state resonators. Emphasis is placed on the physical origin of the sensitivity of each platform, the role of coherence, bandwidth, and noise, and the complementarity between different technologies across a wide range of ALP masses. Together, these approaches provide broad and overlapping coverage of ultralight dark matter parameter space and define a rapidly evolving experimental programme with strong discovery potential.