Nelson-Barr ultralight dark matter

We show that, in the Nelson-Barr solution to the strong CP-problem, a naturally light scalar can arise. It gives rise to a completely new phenomenology beyond that of the celebrated QCD axion, if this field constitutes dark matter, as the elements of the Cabibbo-Kobayashi-Maskawa matrix vary periodically in time. We also discuss how the model can be tested using quantum sensors, in particular using nuclear clocks, which leads to an interesting synergy between different frontiers of physics.