Barnett Effect-Induced Nonreciprocal Entanglement and Gaussian interferometric power in Magnomechanics with Optical Parametric Amplifier

TL;DR

The study tackles nonreciprocal quantum resources in a cavity magnomechanical system by leveraging the Barnett effect, which introduces a rotation-induced magnon frequency shift $\Delta_B$, in conjunction with an optical parametric amplifier (OPA) to control entanglement and Gaussian interferometric power (GIP). By linearizing quantum Langevin dynamics and solving the Lyapunov equation to obtain the steady-state covariance matrix, the authors quantify bipartite entanglement via logarithmic negativity $\mathcal{E}_{ij}$ and GIP via $\mathcal{P}(\sigma)$, while introducing a bidirectional contrast ratio $\hat{N}_{ij}$ to capture nonreciprocity. Systematic parameter sweeps over detunings $\Delta_n,\Delta_m$, Barnett shift $\Delta_B$, magnon–photon coupling $\mathcal{J}$, magnomechanical coupling $\mathcal{G}$, and OPA gain $\chi$ and phase $\beta$ reveal regimes where ideal nonreciprocity is achievable and robust against thermal noise up to elevated temperatures. The results indicate that increasing OPA gain $\chi$ and tuning the detunings enable strong, thermally robust nonreciprocal entanglement and GIP, offering a viable path toward nonreciprocal single-phonon devices for quantum information processing and communication.

Abstract

Nonreciprocity is a powerful tool in quantum technologies. It allows signals to be sent in one direction but not the other. In this article, we propose a method for achieving non-reciprocal entanglement and Gaussian interferometric power (GIP) via the Barnett effect. The YIG is coupled to a microwave cavity that interacts with an optical parametric amplifier (OPA). Due to the Barnett effect, giant nonreciprocal entanglement can emerge. By fine-tuning the cavity detuning, the GIP can exhibits nonreciprocal behavior. All entanglements with ideal nonreciprocity can be achieved by tuning the photon frequency detuning, appropriately choosing the cavity-magnon coupling regime, the nonlinear gain, and the phase shift of the OPA. Interestingly, the amount of entanglement nonreciprocity and its resilience to thermal occupation are remarkably enhanced by increasing the gain of the OPA. This nonreciprocity can be significantly enhanced even at relatively high temperatures. Our research offers a pathway for the realization of nonreciprocal single-phonon devices, with potential applications in quantum information processing and quantum communication. This proposed scheme could pave the way for the development of novel nonreciprocal devices that remain robust under thermal fluctuations.

Figures (9)

• Figure 1: (a) Schematic representation of the CMM system, consisting of a microwave cavity coupled to a YIG sphere and equipped with an OPA. The YIG sphere, which supports both a magnon mode $m$ and a phonon mode $b$, is magnetized by an external bias magnetic field $H_0$. When the sphere rotates at an angular frequency $\Delta_B$, it generates an emergent magnetic field $H_B$, leading to a frequency shift in the magnon mode.
• Figure 2: Variation of logarithmic negativity $\mathcal{E}_{nm}$ between the microwave-magnon modes (the orange solid), $\mathcal{E}_{mb}$ between the magnon-phonon modes (the yellow solid), and $\mathcal{E}_{nb}$ between the microwave-phonon modes (the violet solid) as a function of the cavity mode detunings $\Delta_n$ (a) and the magnon mode detunings $\Delta_m$ (b), with $\chi=0.6 \kappa_n$ and $\beta=\pi$. The remaining parameters are detailed in the text.
• Figure 3: Plot of the logarithmic negativity $\mathcal{E}_{nm}$ between the microwave-magnon modes (the orange solid), $\mathcal{E}_{mb}$ between the magnon-phonon modes (the yellow solid), and $\mathcal{E}_{nb}$ between the microwave-phonon modes as a function of the phase shift of OPA (a), and the angular frequencies shift $\Delta_B$ (b). The nonreciprocity of entanglement $\hat{N}_{nm}$ between the microwave-magnon modes, $\hat{N}_{mb}$ between the magnon-phonon modes, and $\hat{N}_{nb}$ between the microwave-phonon modes as a function of the phase shift of OPA (a), the angular frequencies shift $\Delta_B$ (b), between the three bipartitions as a function of the nonlinear gain $\chi$ (c), and as a function of the phase shift $\beta$ (d). Where $\Delta_n = -1.3 \omega_b$. The other parameters are the same in Figure \ref{['F1']}.
• Figure 4: (a) Plot of the logarithmic negativity $\mathcal{E}_{nm}$, $\mathcal{E}_{mb}$, and $\mathcal{E}_{nb}$ as a function of the normalized magnon-phonon coupling $\mathcal{J}$. (b) The variations of the nonreciprocity of entanglement between the cavity mode and the magnon mode $\hat{N}_{nm}$, (c) between the magnon mode and the phonon mode $\hat{N}_{mb}$, and between the cavity mode and the phonon mode $\hat{N}_{nb}$ (d) as a function of the normalized magnon-phonon coupling $\mathcal{J}$. With $\Delta_B=0.3 \omega_b$.
• Figure 5: Bidirectional contrast ratio $\hat{N}$ between the photon and the magnon modes $\hat{N}_{nm}$ (a), the magnon and the phonon modes $\hat{N}_{mb}$ (b), and between the photon and phonon modes $\hat{N}_{nb}$ (c), as a function of photon frequency detuning. The other parameters are the same as those in Figure \ref{['F1']}.