Magnon-rotation enhanced nonreciprocity of multipartite entanglement in a magnomechanical system

TL;DR

The work addresses nonreciprocal entanglement in a four-mode cavity magnomechanical system by leveraging the Barnett effect, which shifts the frequency of the rotating magnon mode to induce direction-dependent correlations. Using linearized quantum Langevin dynamics and covariance-matrix methods, the authors quantify bipartite entanglement via logarithmic negativity and tripartite entanglement via minimal residual contangle, revealing substantial enhancement of entanglement and squeezing under thermal noise. They show that magnon–magnon coupling $J$ further strengthens inter-mode entanglement and that nonreciprocal entanglement can be tuned and made robust by adjusting detunings, Barnett shift $\Delta_B$, and drive parameters. The results suggest practical routes for directional quantum information processing in hybrid magnonic systems and highlight the Barnett effect as a powerful resource for robust, nonreciprocal quantum correlations in macroscopic platforms.

Abstract

Nonreciprocal physics is attracting significant interest in quantum information processing. In this work, we propose a scheme to investigate the nonreciprocity of bi- and tripartite entanglement and generate squeezed states in a magnomechanical system. This is achieved through the Barnett effect, which originates from the rotation of the first magnon mode. The system consists of two YIG spheres, each supporting a magnon mode that represents collective spin motion, positioned inside a microwave cavity (MC). We show that the Barnett effect enhances entanglement under thermal effects and generates squeezed states for the two magnon modes and the photon mode. Moreover, we show that magnon-magnon coupling enhances entanglement between different two modes.

Figures (7)

• Figure 1: (a) This schematic illustrates the hybrid four-mode cavity magnomechanical system. Two YIG samples are positioned within a microwave cavity at points of maximum magnetic field for the cavity mode. They are concurrently exposed to uniform bias magnetic fields that excite magnon modes and couple them to the cavity mode. The bias magnetic fields are oriented to activate the magnetostrictive (magnon-phonon) interaction in only one YIG sample (YIG1). This coupling can be further enhanced by directly driving the magnon mode with an external microwave source (not shown). The rotating YIG sphere with an angular frequency $\Delta_B$ will create an emergent magnetic field $\mathsf{H}_B$ that causes the magnon(1) to experience a frequency shift. (b) The diagram illustrates the constant coupling between the directly interacting modes. The cavity mode is linearly coupled to the two magnon modes, $\mathsf{m}_1$ and $\mathsf{m}_2$, with coupling constants $\mathsf{g}_1$ and $\mathsf{g}_2$, respectively. The two magnon modes are also coupled by a strong coupling $\mathsf{J}$. Additionally, magnon mode $\mathsf{m}_1$ interacts with the mechanical mode $\mathsf{b}$ via a nonlinear magnetostrictive interaction, which is characterized by an effective coupling rate $\mathsf{G}$. This interaction facilitates magnomechanical entanglement li2018magnon, which can, in turn, be used to entangle the two magnon modes. Indirect couplings are not depicted in this scheme. (c) A plot of $\mathsf{H}_B$ versus $\Delta_B$ for different rotations of the magnon around the $z$-axis.
• Figure 2: Plot of the logarithmic negativities between different bipartite: $([\rm a_1],[\rm a_2],[\rm a])$$E_{\mathsf{m}_1\mathsf{m}_2}$, $([\rm b_1],[\rm b_2],[\rm b])$$E_{\mathsf{m}_2\mathsf{b}}$, and $([\rm c_1],[\rm c_2],[\rm c])$$E_{\mathsf{c}\mathsf{b}}$, versus the normalized detuning $\Delta_{\mathsf{c}}/\omega_{\mathsf{b}}$, the normalized magnetic field detuning $\Delta_B/\omega_{\mathsf{b}}$ and magnon-magnon coupling strength $\mathsf{J}$. In $([\rm a],[\rm b],[\rm c])$, we use $\mathsf{J}$ and $\Delta_B$ are 0. $\Delta_B > 0$ ($\Delta_B < 0$) corresponds to the magnetic field driven from the direction of $+z$ ($-z$). The green vertical strips in $([\rm a_{1,2}]-[\rm c_{1,2}])$ indicate regions of strong nonreciprocity. We select in $|\Delta_B|/\omega_{\mathsf{b}}=0.2$ (black line: $\Delta_B>0$ and red line: $\Delta_B<0$), with $\mathsf{J}=0$ in $([\rm a_{1}]-[\rm c_{1}])$ and $\mathsf{J}=\mathsf{g}_1$ in $([\rm a_{2}]-[\rm c_{2}])$. The other parameters are provided in the table \ref{['table']}.
• Figure 3: Plot of the three bipartite entanglements magnon-magnon modes $E_{\mathsf{m}_1\mathsf{m}_2}$, magnon(2)-phonon modes $E_{\mathsf{m}_2\mathsf{b}}$ and photon-phonon modes $E_{\mathsf{c}\mathsf{b}}$ versus the temperature $T$ for various values of $\Delta_B=(0,\pm0.2\omega_{\mathsf{b}})$. The other parameters are provided in the table \ref{['table']}, with $\textcolor{red}{\mathsf{J}}/2\pi=3.2\times 10^6$ Hz.
• Figure 4: Plot of the three bipartite entanglements magnon-magnon modes $E_{\mathsf{m}_1\mathsf{m}_2}$, magnon(2)-phonon modes $E_{\mathsf{m}_2\mathsf{b}}$ and photon-phonon modes $E_{\mathsf{c}\mathsf{b}}$ versus the magnon-magnon coupling strength $\mathsf{J}/\mathsf{g}_1$ for various values of $\Delta_B$. The other parameters are provided in the table \ref{['table']}.
• Figure 5: The Wigner function $W(\rm{u})$ of the cavity mode $\mathsf{c}$ (a,e), the magnon(1) mode $\mathsf{m}_1$ (b,f), the magnon(2) mode $\mathsf{m}_2$ (c,g), and the phonon mode $\mathsf{b}$ (d,h) for $\Delta_B=0.2\omega_{\mathsf{b}}>0$ (a-d) and $\Delta_B=-0.2\omega_{\mathsf{b}}<0$ (e-h), respectively. The other parameters are provided in the table \ref{['table']}, with $\mathsf{J}/2\pi=3.2\times 10^6$ Hz.