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Modern Physics Letters A

Evolution of Rényi-2 quantum correlations in a double cavity–magnon system

Abdelkader Hidki, Abderrahim Lakhfif, Jamal El Qars, Mostafa Nassik

Published Mar 7, 2023• 3 citations
Publisher

Abstract

This work reports on the stationary evolution of three different kinds of quantum correlations between two distant magnon modes. The system at hand consists of two spatially separated cavities, where each cavity has a microwave (MW) cavity and a magnon mode. The two cavities are coupled to each other via the photon-tunneling process, and both are exposed to the output field of a squeezed vacuum MW fields source. By calculating the covariance matrix fully describing the state of the two magnon modes, we give the explicit expressions of the measures of correlations defined via the Rényi-2 entropy, i.e. the Gaussian quantum steering [Formula: see text], Gaussian Rényi-2 entanglement [Formula: see text] and Gaussian Rényi-2 mutual information [Formula: see text]. We find that, the quantum steering is always upper bounded by the entanglement, which is in turn always upper bounded by half of the total correlations. The obtained results are consistent with the hierarchical Rényi-2 quantum correlations established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117, 220502 (2016)], i.e. they fulfill the hierarchical inequality [Formula: see text]. The influences of the squeezing parameter, the environmental temperature, the cavity–magnon coupling and the cavity–cavity coupling on the correlations are studied in detail.

DOI
10.1142/s021773232350044x

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International Journal of Modern Physics B•Feb 4, 2023•5 citations
This work reports on the stationary evolution of three different kinds of quantum correlations between two distant magnon modes. The system at hand consists of two spatially separated cavities, where each cavity has a microwave (MW) cavity and a magnon mode. The two cavities are coupled to each other via the photon-tunneling process, and both are exposed to the output field of a squeezed vacuum MW fields source. By calculating the covariance matrix fully describing the state of the two magnon modes, we give the explicit expressions of the measures of correlations defined via the Rényi-2 entropy, i.e. the Gaussian quantum steering [Formula: see text], Gaussian Rényi-2 entanglement [Formula: see text] and Gaussian Rényi-2 mutual information [Formula: see text]. We find that, the quantum steering is always upper bounded by the entanglement, which is in turn always upper bounded by half of the total correlations. The obtained results are consistent with the hierarchical Rényi-2 quantum correlations established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117, 220502 (2016)], i.e. they fulfill the hierarchical inequality [Formula: see text]. The influences of the squeezing parameter, the environmental temperature, the cavity–magnon coupling and the cavity–cavity coupling on the correlations are studied in detail.
In a two-mode Gaussian state [Formula: see text], we report on stationary evolution of three measures of correlations defined via the Rényi-2 entropy, i.e. quantum mutual information (QMI) [Formula: see text], the Gaussian–Rényi-2 entanglement (GR2E) [Formula: see text] and Gaussian quantum steering (GQS) [Formula: see text]. We evaluate analytical expression of the covariance matrix fully describing the state [Formula: see text]. Further, we study, under influences of parameters characterizing the state at hand and its environment, the behavior of the three considered measures. We find that quantum steering [Formula: see text] is always upper bounded by (GR2E) [Formula: see text], which in turn is found always upper bounded by half of the QMI [Formula: see text]. This therefore satisfies the hierarchical relation [Formula: see text] established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117 (2016) 220502]. Importantly, we find that both GR2E [Formula: see text] and GQS [Formula: see text] are strongly affected by the thermal effects. Remarkably, when the GR2E [Formula: see text] thoroughly vanishes, the GMI [Formula: see text] exhibits a freezing behavior, and seems to be captured within a wide range of temperature.
Abstract We report on temporal evolution of three different kinds of correlations present between two mechanical resonators of two distant Fabry-Pérot cavities. The two cavities are jointly fed by a two-mode squeezed light and driven by two independent coherent lasers. We consider the initial state of the two mechanical modes as a two-mode uncorrelated thermal state. After evaluating the dynamical covariance matrix elements, we give explicit expressions of the measures of correlations defined via the Rényi-2 entropy, namely, the Rényi-2 quantum mutual information, the Gaussian Rényi-2 entanglement and the Gaussian quantum steering. We find that by an appropriate choice of the system parameters, it is possible to generate entanglement and steering via a quantum correlations transfer from squeezed light to the mechanical bi-mode state. The influence of the squeezing parameter, the optomechanical cooperativity and the environmental thermal noise on the correlations are studied thoroughly. Additionally, we show in various circumstances that the considered temporal correlations respect the hierarchical relation established in L Lami, C Hirche, G Adesso, and A Winter, (2016 Phys. Rev. Lett. 117 , 220 502).
Abstract In the two microwave (MW) cross-shaped cavity magnon system, we describe a method to produce multipartite entanglement and quantum steering. To achieve squeezed states of the magnons, a Josephson parametric amplifier (JPA) creates a squeezed vacuum field that drives the two cavities. We theoretically demonstrate that the cavity-cavity entanglement can be generated at the resonance point, however, increasing the cavity and magnon decay rates generate the cavity-magnon entanglement. By changing the squeezing parameter and increasing the decay rates, we can transfer the cavity-cavity entanglement to cavity-magnon entanglement. Furthermore, the cavity-cavity entanglement (survive up to 2.8 K) was not only found to be much stronger but also more robust as compared to cavity-magnon entanglement (survive up to 0.4 K). More importantly, the genuine photon-magnon-photon tripartite entanglement could be achieved, which is robust against thermal fluctuations and depends strongly on the squeezing parameter. Furthermore, for the current dual cavity-magnon system, two-way quantum steering is found when the optomagnonical couplings are equal. The current study offers a straightforward and practical method for achieving multipartite quantum correlations.
We theoretically investigate a scheme to entangle two squeezed magnon modes in a double cavitymagnon system, where both cavities are driven by a two-mode squeezed vacuum microwave field. Each cavity contains an optical parametric amplifier as well as a macroscopic yttrium iron garnet (YIG) sphere placed near the maximum bias magnetic fields such that this leads to the excitation of the relevant magnon mode and its coupling with the corresponding cavity mode. We have obtained optimal parameter regimes for achieving the strong magnon-magnon entanglement and also studied the effectiveness of this scheme towards the mismatch of both the cavity-magnon couplings and decay parameters. We have also explored the entanglement transfer efficiency including Gaussian quantum steering in our proposed system
We study phase-controlled quantum entanglement and one-way quantum steering in a cavity magnonic system, where two magnon modes couple to two microwave cavities driven by squeezed fields. The magnon-magnon entanglement and the steering directivity can be controlled by adjusting the ratio of the coupling strengths between cavity modes and magnon modes. In particular, the quantum entanglement and one-way quantum steering can be significantly enhanced by the squeezed vacuum field, which also exhibits robustness against temperature variations. More intriguingly, both quantum entanglement and steering between two magnon modes are susceptible to variations in the phase difference of two Josephson parametric amplifiers, and thus the phase-controlled quantum entanglement and one-way quantum steering can be achieved. Our scheme may have potential applications in quantum information.
In this paper, we investigate a system composed of two spatially separated cavities, each with a magnon mode of a yttrium iron garnet (YIG) sphere coupled to a microwave (MW) cavity and phonon modes, respectively, via linear beam splitter and magnetostrictive interactions. In addition, two-mode squeezed vacuum fields drive the two cavities. We investigate and compare the behavior of three nonclassicality indicators in two subsystems (i.e., magnon–magnon and phonon–phonon) under the influences of the temperature, the cavity–magnon damping rate, and the magnomechanical coupling rate. We use the entanglement of formation (EoF) to measure the degree of entanglement, the Gaussian quantum discord (GQD) to characterize the quantum correlations beyond entanglement and Gaussian quantum coherence (GQC) to quantify coherence. Considering that the quantifiers share the same entropic definition, we compare the three quantifiers and test the validity of the hypothesis that quantum states with nonzero discord are inherently entangled. We find, on the one hand, that both GQC and GQD exhibit freezing behavior and that they are more robust to the decoherence effect than the EoF. On the other hand, the EoF and the GQD are always upper bounded by GQC, and there is no simple dominance relationship between EoF and GQD; hence these two quantifiers should not be compared. The effect of other parameters is also discussed in detail.