Anti-correlated phonons with two-mode Gaussian squeezed state

Abstract

We study the cross-correlation between two bosonic modes of a two-mode displaced squeezed thermal state. By calculating the equal-time second-order cross-correlation function, we find that strong anticorrelation between the two bosonic modes can be observed. The mechanism of anticorrelation between the two bosonic modes is the interference between two coherent displacements and a squeeze operation. The optimal values of the two displacements and the squeezing parameter for achieving the minimum value of is derived. As an example, we explore the anticorrelation between phonons in a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. The two-mode displaced squeezed thermal state of the two mechanical oscillators can be achieved if the squeezing amplitude and the mean phonon occupation number of the two mechanical environments are not very large. Furthermore, we find that the two-time second-order correlation function has multiple minima if the frequency difference of the two mechanical oscillators is large. Our results provide us with a tool to generate anticorrelated photons and phonons which may have potential applications in quantum information networks.