Recent excitement in the quantum spin ice community has come from the experimental discovery of pseudospin-1/2breathing pyrochlores, including Ba₃Yb₂Zn₅O₁₁, in which inversion symmetry is broken by the `up’ and `down’ tetrahedra taking different physical sizes. We show here that the often-neglected J_z± coupling between Kramers ions, in combination with the breathing nature of the lattice, can produce an imaginary ring flip term. This can lead to an unconventional ‘U(1)_π/2 phase’, corresponding to a maximally dense packing of visons on the lattice. Coherent dynamics persist in all phases, together with an emergent QED description, in a manner reminiscent of fragmentation in spinon crystals. We characterize the enlarged QSI phase diagram and its excitations, showing that the imaginary ring flip acts both as a chemical potential for visons and as an effective three-photon vertex akin to strong light-matter coupling. The novel coupling causes a structured high-energy continuum to emerge above the photon dispersion, which is naturally interpreted as three photon up-conversion in a nonlinear optical crystal.

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