Even and odd trio coherent states antibunching and violation of Cauchy- Schwarz inequalities

Recently, in addition to various kinds of known nonclassical states (see, e.g., [1]), there has been introduced anew one called a trio coherent state (TCS) [2,3]. The TCS, a gen-eralization of the pair coherent state [4], has been shown to manifest intriguing nonclassical properties [2], including mul-timode and higher-order effects [3]. A scheme to generate the TCS has also been suggested in [2]. Following the way the pair coherent state goes to the event/odd pair coherent states [5], we shall consider in this paper the so-called even/odd trio co-herent states (ETCS/OTCS) which are simple superpositions of tow macroscopically distinguishable TCSs. The study of ETCS/OTCS , in parallel with different kinds of superposition states such as even/odd coherent states [6], even/odd nonlin-ear coherent states [7], even/odd pair coherent states [5],etc, proves highly meaningful because such states serve as a pro-totype of ‘Schrödinger cat states’ [8] which exhibit quantum interferences due to the superposition principle, a cornerstone principle distinguishing the quantum from the classical world

see here for details