  The Kondo effect is one of the most studied examples of strongly correlated
quantum many-body physics. Another type of strongly correlated physics that has
only recently been explored in detail (and become experimentally accessible) is
that of ultrastrong coupling between light and matter. Here, we study a system
which we denote as "Kondo QED") that combines both phenomena, consisting of a
two-impurity Anderson model ultra-strongly coupled to a single-mode cavity.
While presented as an abstract model, it is relevant for a range of future
hybrid cavity-QED systems. Using the hierarchical equations of motion approach
we show that the ultrastrong coupling of cavity photons to the electronic
states (impurity) noticeably suppresses the electronic Kondo resonance due to
the destruction of many-body correlations of the Kondo cloud. We observe this
transfer of correlations from the Kondo cloud to the cavity by computing the
entropy and mutual information of the impurity-cavity subsystems. In addition,
in the weak lead-coupling limit and at zero-bias, the model exhibits a
ground-state photon accumulation effect originating entirely from
counter-rotating terms in the impurity-cavity interaction. Interestingly, in
the strong lead-coupling limit, this accumulation is ``Kondo-enhanced'' by new
transition paths opening when increasing the hybridization to the leads. This
suggests a new mechanism for the generation of real photons from virtual
states. We further show that the suppression of the Kondo effect is stable
under broadening of the cavity resonance as a consequence of the interaction to
an external bosonic continuum. Our findings pave the way for the simultaneous
control of both the Kondo QED effect and a photon accumulation effect using the
ultrastrong coupling of light and matter.

Quantum Physics;Strongly Correlated Electrons