The Search for Modulated Superconductivity

In the mid 60's, theoretical physicists came to the conclusion that a strong magnetic field could lead to a superconducting state where magnetism and superconductivity are interleaved on the nano-scale: tidal wave like domain walls spontaneously form in the superfluid order, trapping unpaired spins. Over the past 50 years, our theoretical understanding of this proposal has greatly advanced, yet we still have not found definitive experimental evidence of the modulated superconducting state (also known as the FFLO state, after the initials of the theorists who anticipated it). I will describe the current state of this search, with a particular focus on how experiments with ultracold atoms are about to find it.