Entanglement and violation of classical inequalities in the Hawking radiation of flowing atom condensates

We consider a sonic black-hole scenario where an atom condensate flows through a subsonic–supersonic interface. We discuss several criteria that reveal the existence of non-classical correlations resulting from the quantum character of the spontaneous Hawking radiation (HR). We unify previous general work as applied to HR analogs. We investigate the measurability of the various indicators and conclude that, within a class of detection schemes, only the violation of quadratic Cauchy–Schwarz inequalities can be discerned. We show numerical results that further support the viability of measuring deep quantum correlations in concrete scenarios