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The theory of dynamical Coulomb blockade is extended to tunneling elementsdriven by a time-dependent voltage. It is shown that for standard set-ups wherean external voltage is applied to a tunnel junction via an impedance,time-dependent driving entails an excitation of the modes of theelectromagnetic environment by the applied voltage. Previous approaches for acdriven circuits need to be extended to account for the driven bath modes. Aunitary transformation involving also the variables of the electromagneticenvironment is introduced which allows to split-off the time-dependence fromthe Hamiltonian in the absence of tunneling. This greatly simplifiesperturbation-theoretical calculations based on treating the tunnelingHamiltonian as a perturbation. In particular, the average current flowing inthe leads of the tunnel junction is studied. Explicit results are given for thecase of an applied voltage with a constant dc part and a sinusoidal ac part.The connection with standard dynamical Coulomb blockade theory for constantapplied voltage is established. It is shown that an alternating voltage sourcereveals significant additional effects caused by the electromagneticenvironment. The hallmark of dynamical Coulomb blockade in ac driven devices isa suppression of higher harmonics of the current by the electromagneticenvironment. The theory presented basically applies to all tunneling devicesdriven by alternating voltages.

Dynamical Coulomb blockade of tunnel junctions driven by alternating voltages