Emergent nonlocal interactions induced by quantized gauge fields in topological systems

TL;DR

This work demonstrates that promoting magnetic flux into a quantum degree of freedom yields emergent, nonlocal interactions among particles that are topological in origin and persist in field-free regions. By analyzing 1D rings and 2D electron gases coupled to a quantized flux, the authors derive exact or near-exact effective Hamiltonians, reveal momentum-space ordering and noninteger Chern numbers, and uncover quantum phase transitions analogous to Dicke or Stoner phenomena. They develop both analytical and perturbative approaches, including adiabatic elimination of the flux DOF and exact diagonalization in symmetric gauges, to expose how flux-mediated couplings generate all-to-all correlations and nonlinearities with tunable strength. The results point to a broad experimental program in superconducting circuits, photonics, and ultracold atoms for realizing tunable nonlinearities and novel topological phases arising purely from quantum fluctuations of gauge fields, with potential applications in quantum simulation of lattice gauge theories and correlated photonic materials.

Abstract

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 example is electrons on a quantum ring encircling a quantized magnetic flux (QMF) generated by a superconducting current. We show that coupling to a common QMF gives rise to an emergent interaction between particles with no classical analog, as it is topological and nonlocal (independent of interparticle distance). Moreover, the interaction persists even when the particles lie in a nominally field-free region, with the vector potential mediating the interaction. We analyze several one- and two-dimensional model systems, encompassing both real and synthetic gauge fields. These systems exhibit unusual behavior, including strong nonlinearities, non-integer Chern numbers, and quantum phase transitions. Furthermore, synthetic gauge fields offer high tunability and can reach field strengths that are difficult to realize with real magnetic fields, enabling engineered nonlinearities and interaction profiles.

Figures (10)

• Figure 1: (a) Electrons on a QR (thin circle) coupled to the QMF created by the supercurrent loop (bold circle). JJ and a cross mark the Josephson junction; (b) Electrons on two separate QRs (thin circles) coupled nonlocally through the QMF created by the supercurrent loop (bold circle). QRs could be inside or outside the supercurrent loop, as long as they encircle a common magnetic flux.
• Figure 2: (a) Electrons on different QRs coupled to the QMF created by the flux qubit. (b) Schematic of the interaction between particle momenta mediated through the vector potential.
• Figure 3: A schematic of the 2DEG in the QMF of a flux qubit.
• Figure 4: Exact diagonalization of the one particle problem in the Landau gauge. All energies $E_n$ and $\Delta$ are normalized by $\hbar \omega_c$. (a) $\Delta =1$, (b) $\Delta=1/5$.
• Figure 5: A sketch of the interaction between momenta of massless particles in graphene mediated through the sublattice pseudospin.