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Bilayer materials may support interlayer excitons comprised of electrons inone layer and holes in the other. In experiments, a non-zero exciton density istypically sustained by a bias chemical potential, implemented either by opticalpumping or by electrical contacts connected to the two layers. We show that ifcharge can tunnel between the layers, the chemical potential bias means that anexciton condensate is in the dynamical regime of ac Josephson effect. It hasphysical consequences such as tunneling currents and the ability to tune acondensate from bright (emitting coherent photons) to dark by experimentalcontrolling knobs. If the system is placed in an optical cavity, coupling withcavity photons favors different dynamical states depending on the bias,realizing superradiant phases.

Dynamical exciton condensates in biased electron-hole bilayers