Optical PT-symmetry and PT-antisymmetry in coherently driven atomic lattices

We study an ensemble of ultracold atoms trapped in the one-dimensional optical lattices under the N level configuration to examine the absorption and dispersion properties modulated into different ways along the lattice direction z. We find these trapped atoms with a Gaussian density distribution in each period may exhibit either symmetry chi(p)(z) = chi(p)*(-z) or antisymmetry chi(p)(z) = -chi(p)*(-z) of parity-time (PT) in terms of the probe susceptibility. Such intriguing twofold modulations of real (chi'(p)) and imaginary (chi ''(p)) susceptibilities with a pi/2 phase shift are attained by spatially modulating intensities or frequencies of one driving field in a suitable way. The PT-symmetric or PT-antisymmetric atomic lattices correspond in fact to complex photonic crystals and may be extended to develop functional devices like photonic diodes and transistors, a task impossible for real photonic crystals. (C) 2016 Optical Society of America