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.

翻译：同时存在外电场和手征化学势时的夸克物质行为在理论和实验上均具有研究价值。本文采用$N_f=1+1$动态交错费米子的格点QCD方法，研究了虚电场与手征化学势同时存在的情况。我们发现，总体上虚电场和手征化学势均可加剧手征对称性破缺，这与理论预测一致。然而，在特定电场强度和手征化学势下，手征凝聚表现出非单调行为。此外，本文还发现，在所研究的参数区域内，Polyakov环在复平面上的行为未受到手征化学势的显著影响。