Study of collective steering behavior in a double cavity optomechanical system

In this paper, we theoretically investigate, in a double cavity system, collective steering, between two mechanical modes and an optical mode, as well as between two optical modes and a mechanical mode. We explore the behavior of collective steering in terms of squeezing light, phonon tunneling force and photon hopping strength. We thus found the optimal choice for the considered parameters to improve collective steering irreducible to individual steering. In parallel, the monogamy of steering was demonstrated via the CKW-type monogamy inequalities. In addition, the study of collective steering behaviors indicates the conditions under which each considered tripartite state generates one-way and two-way steering.