Emergent topological interactions induced by quantized magnetostatic fields

We propose an alternative route to canonical quantum-optics phenomena by coupling particle momenta to a static—but quantized—magnetic field (vector potential) within circuit-QED architectures. For particles confined to one and two dimensions, a global coupling to a common quantized magnetic flux (QMF) realizes an ideal Dicke-type phase transition; in two dimensions it further permits a chiral symmetry–breaking transition. In the dispersive regime, integrating out the QMF yields a distinctive orbit–orbit interaction that is nonlocal, can be topological in character, and can be mediated purely by the vector potential—without a net magnetic field. We outline concrete implementations compatible with current superconducting-circuit technology and discuss observable signatures and tunability. Our results position quantized magnetostatics as a flexible platform for engineering collective quantum phases and interactions beyond conventional light–matter settings.