Talbot effects induced by gain-loss modulated optical lattices in a coherent atomic medium

We investigate the electromagnetically induced Talbot effects resulting from the gain-loss modulated optical lattices constructed in a coherent four-level $N$-type atomic system. Both integer and fractional Talbot effects are studied in a parity-time ($\mathcal{PT}$) symmetric optical lattice, quasi-$\mathcal{PT}$-symmetric optical lattices, and a conventional electromagnetically induced transparency (EIT) optical lattice. Additionally, the visibilities of Talbot images from a $\mathcal{PT}$-symmetric optical lattice, quasi-$\mathcal{PT}$-symmetric optical lattices, and a conventional EIT optical lattice are examined. This study provides insights for understanding the Talbot effects in experiments based on coherent atomic systems with gain and loss properties.