  With the aim to reveal universal features of hadronic matter and correlated
Dirac insulators in strong AC-electric fields, we study the $\mathcal{N}=2$
supersymmetric QCD with a finite quark mass driven by a rotating electric field
$\mathcal{E}_x+i\mathcal{E}_y= E e^{i\Omega t}$. The analysis is done in the
holographically dual D3/D7 system in the co-rotating frame, effectively. The
nonequilibrium phase diagram is determined from the threshold electric field at
which the insulator phase breaks down to a conductive phase due to the AC
version of the Schwinger mechanism. The external field induces a rotating
current $\mathcal{J}_x + i \mathcal{J}_y = J e^{i\Omega t}$ originating from
vacuum polarization and dissipative current in the insulating and conductive
phases respectively. Intriguing features are observed as the frequency $\Omega$
approaches resonance with the meson excitation energy $\Omega_{\rm meson}$.
There, the threshold minimizes and a condensate of vector mesons with
oscillating current exists even in the zero driving field limit. This state,
which we call Floquet condensate of vector mesons, is expected to be
dynamically stable realizing a non-thermal fixed point that breaks time
translational and reversal symmetries. Our finding has many similarities with
exciton BEC discussed in solid state systems, where the semiconductor is to be
replaced by materials hosting gapped Dirac electrons, e.g. 3D topological
insulators or bismuth. Vector meson Floquet condensate may also have
implications in the pre-thermalized dynamics in heavy ion collision
experiments.
