Sonic horizon dynamics of ultracold Fermi system under elongated harmonic potential

We study the phenomena of the sonic horizon in an ultracold atomic Fermi system in an elongated harmonic trap. Based on the one-dimensional Gross–Pitaevskii equation model and variational method combined with exact derivation approach, we derive an analytical formula which describes the occurrence of the sonic horizon and the associated Hawking radiation temperature. Using a pictorial demonstration of the key physical quantities we identify the features reported in prior numerical studies of a three-dimensional (3D) ultracold atomic system, proving the applicability of the theoretical model presented here. (paper)