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Physica Scripta

Anti-correlated phonons with two-mode Gaussian squeezed state

X. Y. Zhang, Y. H. Zhou, Yanqun Guo, X. X. Yi

Published Sep 9, 2019• 1 citation
Publisher

Abstract

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 g ab ( 2 ) ( 0 ) 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.

DOI
10.1088/1402-4896/ab42aa

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We calculate exactly the quantum mechanical, temporal second-order coherence function for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. The calculation involves first the generation of the Gaussian state and subsequent measurements of two photons a time τ≥0τ\geq 0τ≥0 apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence function depends only on τττ.
In this paper, we study some quantum properties of a superposition of displaced squeezed two-mode vacuum and single-photon states, such as the second-order correlation function, the Cauchy-Schwartz inequality, quadrature squeezing, quasiprobability distribution functions and purity. This type of states includes two mechanisms, namely, interference in phase space and entanglement. We show that these states can exhibit sub-Piossonian statistics, squeezing and deviate from the classical Cauchy-Schwartz inequality. Moreover, the amount of entanglement in the system can be increased by increasing the squeezing mechanism. In the framework of the quasiprobability distribution functions we show that the single-mode state can tend to thermal state based on the correlation mechanism. Generation scheme for such states is given.
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We study the influence of the linear and nonlinear coupling processes on the correlation properties of a system composed of two bosonic modes. The coupling processes are treated as Gaussian while the modes are assumed to experience damping and fluctuations that are due to their coupling to independent squeezed vacua. We investigate under what circumstances a given type of coupling causes the creation of the first-order correlations and which causes the creation of the two-photon correlations. Distinctly different results are obtained for the linear and nonlinear couplings, especially when there are two-photon correlations present in the modes. In particular, the linear coupling process can generate the inter-mode correlations only when there are differences between the modes either in populations or two-photon correlations. The varying with the coupling strength a population difference is shown to be responsible for generation of the first-order correlations while the varying asymmetry in the two-photon correlations is found to be responsible for the generation of the inter-mode two-photon correlations. In the case of the nonlinear coupling the generation of the inter-mode correlations is insensitive to any difference between the modes. The varying with the coupling strength amplification of the population of the modes is found to be responsible for generation of the inter-mode two photon correlations while the varying amplification of the two-photon correlations results in the first-order correlations between the modes. Furthermore, in the strong coupling limit the linear coupling tends to destroy all of the inter-mode correlations, and simultaneously turns the states of the modes to be identical, either thermal or equally squeezed states. In the case of nonlinear coupling process the modes are turned to be perfectly coherent.