Quantum Confinement of Monopole Quasiparticles in a Quantum Spin Ice

We report direct spectroscopic evidence of correlations between monopoles in a quantum spin ice. A hierarchy of unequally spaced magnetic excitations has been observed via inelastic neutron spectroscopy in Pr$_{2}$Sn$_{2}$O$_{7}$, resembling the confinement of spin defects in low-dimensional quantum magnets. \footnote{J.~B.~Torrance and M.~Tinkham, Phys. Rev.,\textbf{187}, 2, 587 (1969)} Using a simple linear potential model to fit the excitations,\footnote{R. Coldea \textit{et al.}, Science, \textbf{327}, 177 (2010)} we have estimated the monopole pair creation energy, and calculated a lower bound for the tension between monopole-like quasiparticles. The linear potential model provides a natural explanation as to why detection of these correlations have been so elusive in the canonical dipolar spin ices. This is the first spectroscopic measurement of an effective ``Dirac string'' between magnetic monopoles.