Controlled Unidirectional Reflection in Atomic Lattices of Parity-Time Anti-Symmetry

Artificial optical materials have attracted great attentions in the past few decades for achieving various properties and functionalities not available in the natural media. Photonic crystals and left-handed materials are two prominent meta-materials promising the possibility of stretching usual rules and dis- playing new paradigms of light propagation and interaction. They have been exploited to design and realize various all-optical, optoelectronic, and opto-mechanical devices, though cannot be directly used to implement unidirectional light transport, a more difficult task than others. Only in recent years significant progresses have been made by considering moving photonic crystals of cold atoms and solid materials with parity-time (PT) symmetry. As compared to traditional photonic crystals, PT-symmetric materials are periodically modulated not only in terms of real parts but also imaginary parts of refractive indices, ex- hibiting a delicate balance of gain and loss alternately along the modulation direction with n(z) =n∗(−z). Very recently, PT-anti- symmetric materials are also considered, which require a more involved balance of positive and negative real refractive indices with n(z) = −n∗(−z) instead. Here we assume that cold 87Rb atoms trapped in 1D optical lattices – whose density modulation is dominated by a COSINE term - are driven into the four-level N configuration with a far-detuned dressing field applied to induce the dynamic shift of one ground level. We find that a probe field may experience the PT-anti-symmetric susceptibility with χ(z) = −χ∗(−z) when this dressing field has a traveling-wave (TW) and a standing-wave (SW) component so that the dynamic frequency shift is modulated as a SINE function along the lattice direction