  The behavior of quark matter with both external electric field and chiral
chemical potential is theoretically and experimentally interesting to consider.
In this paper, the case of simultaneous presence of imaginary electric field
and chiral chemical potential is investigated using the lattice QCD approach
with $N_f=1+1$ dynamical staggered fermions. We find that overall both the
imaginary electric field and the chiral chemical potential can exacerbate
chiral symmetry breaking, which is consistent with theoretical predictions.
However we also find a non-monotonic behavior of chiral condensation at
specific electric field strengths and chiral chemical potentials. In addition
to this, we find that the behavior of Polyakov loop in the complex plane is not
significantly affected by chiral chemical potential in the region of the
parameters consider in this paper.
