Monopole Josephson Effects in a Dirac Spin Liquid

Dirac Spin liquids (DSLs) are gapless featureless states, yet interesting by virtue of the effective field theory describing them -- (2+1)-dimensional quantum electrodynamics (QED$_3$). Further, a DSL is known to be a "parent state" of various seemingly unrelated ordered states, such as antiferromagnets and valence bond solids in the sense that one can obtain ordered states by condensing magnetic monopoles of the emergent gauge field. Can operators in the effective field theory, such as the emergent electric field, be externally induced and measured? In this work, we exploit the parent state picture to argue that the answer is yes. We propose a range of "monopole Josephson effects" that arise when two ordered states are separated by a region of the parent DSL. In particular, we show that one can induce an AC monopole Josephson effect, which manifests itself as an AC emergent electric field in the spin liquid, accompanied by a measurable spin current. Further, we show that this AC emergent electric field can be measured as a sharp tunable peak in Raman scattering. This work provides a theoretical proof of principle that emergent gauge fields in spin liquids can be externally induced, manipulated, and probed using more conventional states, which offers a generic platform for studying the exotic spin phases.