Measuring nonclassicality of single-mode systems

Nonclassicality of a single-mode state can be quantified by the entanglement (potential) the state creates at the output of a beam splitter. Thus, beam splitter transformation can be utilized for obtaining single-mode nonclassicality conditions (quantifications) from two-mode entanglement criteria (measures). Here, (i) we employ this relation to quantify the single-mode nonclassicality (SMNc) of a nonlinear crystal field generating second harmonic signals. (ii) We also manage to witness the SMNc of superradiant emission, a non-Gaussian state, in a Dicke phase transition. Entanglement potential, at the beam splitter output, is obtained in terms of measurable single-mode quantities. Thus, presence of a beam splitter in an experiment is not necessary. Employing the beam splitter method, one can also utilize hybrid entanglement criteria as SMNc conditions working well in different classes of single-mode states. (iii) We also work on essentials of the entanglement-SMNc relation: one obtains the generalized squeezing condition â † â < |â 2| as the SMNc condition when an optimized form of Duan-Giedke-Cirac-Zoller criterion [PRL 84, 2722] is used at the output of the beam splitter.