We study fermionic and bosonic systems coupled to a real or synthetic static gauge field that is quantized, so the field itself is a quantum degree of freedom and can exist in coherent superposition. A natural source of a quantized magnetic flux (QMF) could be a superconducting current loop. We show that coupling to a common QMF gives rise to an emergent all-to-all interaction between particles with no classical analog, as it is topological and nonlocal (independent of interparticle distance). Moreover, the interaction persists via a quantized Aharonov-Bohm effect even when the particles lie in a nominally field-free region. The QMF mediates exchange of angular momenta between particles, and it gives rise to quantum phase transitions in both one- and two-dimensional systems, resulting in the spontaneous appearance of the chiral current and magnetic polarization. Many other interesting phenomena can be realized in this class of systems, for example, the noninteger Chern number when the magnetic flux exists in the quantum superposition of different flux states, or the nonlocal electron blockade. We show that similar physics can be realized in synthetic systems with artificial QMF, with the advantage of tunability enabling much higher strength of the synthetic QMF and the interaction of neutral particles.

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• Aharonov-Bohm effect
• Geometric & topological phases
• Nonlocality
• Quantum circuits
• Quantum phase transitions
• Synthetic gauge fields
• Topological effects in photonic systems
• Superconducting qubits