Nonreciprocal and enhanced Goos-Hänchen shifts in the cavity-assisted atomic lattice of parity-time antisymmetry

We propose a scheme for realizing nonreciprocal and largely enhanced Goos-Hänchen (GH) shifts in a lattice of cold atoms exhibiting the parity-time (<i>P</i><i>T</i>) antisymmetric susceptibility when driven by a probe beam and a coupling beam. This atomic lattice in the free space allows to attain unidirectionally detectable nonreciprocal GH shifts for reflected probe beams provided a Bragg bright resonance is tuned to overlap with an exceptional point. Placing this atomic lattice in an optical cavity, we can further attain bidirectionally detectable nonreciprocal GH shifts for reflected probe beams, benefiting from the interplay between a Bragg bright resonance and a cavity dark resonance. Nonreciprocal GH shifts in our cavity-assisted <i>P</i><i>T</i>-antisymmetric atomic lattice exhibit the advantages of dynamic tunability and reversibility, while enhanced up to hundreds of probe wavelengths, in the case of nonzero detectable reflections.