Geometric phase effects in dipole superfluids: vortex lattices and singular domain walls

We explore the response of dipole superfluids to an applied electromagnetic field, drawing parallels to the Meissner effect in conventional superconductors.[1] While superconductors, consisting of electric monopoles, interact with magnetic fields via the Aharonov-Bohm phase, magnetic-dipole superfluids---composed of charge-neutral particles with magnetic dipole moments---interact with electric fields through the Aharonov-Casher phase, where spatially modulating electric fields act as pseudo-magnetic fields. This leads to a distinct response compared to conventional superconductors. We develop a phenomenological theory to describe this behavior, revealing that the magnetic-dipole superfluid under a pseudo-magnetic field forms a vortex lattice, separated by singular domain walls where the pseudo-magnetic field and the polarization charge density diverge. A similar effect is predicted in electric-dipole superfluids, where electric and magnetic roles are reversed, establishing the singular domain wall formation as a fundamental property of dipole condensates.