Hearing the light: stray field noise from the emergent photon in quantum spin ice

The decisive experimental confirmation of the $U(1)$ quantum spin liquid phase in quantum spin ice remains an outstanding challenge. In this work, we propose stray-field magnetometry as a direct probe of the emergent photons -- the gapless excitation of the emergent electrodynamics in quantum spin ice. The emergent photons are transverse magnetization waves, which, in a finite sample, form cavity modes governed by one of two sets of natural boundary conditions: 'insulating' or 'superconducting'. We find that the spectrum and spatial structure of the stray magnetic noise from the cavity modes provide a sharp qualitative signature of the underlying electrodynamics and can distinguish between the two boundary conditions. Crucially, the predicted stray-field signal levels lie comfortably within the detection range of present-day solid-state defect and SQUID magnetometry. Finally, we consider the microscopic quantum spin ice Hamiltonian on a pyrochlore lattice with a (111) surface cut and numerically show that it has an 'insulating' boundary.