Nonreciprocal quantum coherence in cavity magnomechanics via the Barnett effect

TL;DR

This work tackles the generation of nonreciprocal quantum coherence in a cavity magnomechanical (CMM) system by exploiting the Barnett effect, which shifts the magnon frequency by $\Delta_B$ when the YIG sphere rotates. A linearized quantum Langevin model with magnon–photon coupling $J$ and magnon–phonon coupling $g$ yields a drift matrix $A$ and a steady-state covariance $V$ from the Lyapunov equation $A V + V A^T = -D$, enabling Gaussian-state coherence measures. Coherence is quantified via relative entropy for single modes and for the total three-mode state, revealing that reversing the bias ($\Delta_B$ of opposite sign) produces pronounced nonreciprocity due to stability differences; the phonon mode can accumulate more coherence than the photon or magnon modes under suitable parameters, indicating transfer of quantum coherence between modes. The results offer a tunable, on-chip path to nonreciprocal quantum resources for quantum information processing and communication.

Abstract

We theoretically investigate the quantum coherence ans its nonreciprocity in a cavity magnomechanical (CMM) syetem, which consists of a rotating yittrium iron garnet (YIG) sphere and a microwave cavity. By adjusting the direction of the magnetic field, the frequency shift of a magnon mode can be tuned from positive to negative due to the Barnett effect. This effect leads to a significant difference in the system stability and is responsible for the nonreciprocal quantum coherence. We examine how the input power, magnomechanical and magnon-photon coupling rates, decay rates of both the cavity photon modes and the magnon modes influence the quantum coherence. Through careful tuning of system parameters, nearly perfect nonreciprocity can be achieved. Our results provide a controllable mechanism for direction-dependent quantum coherence, with potential applications in nonreciprocal quantum devices and information processing.

Figures (6)

• Figure 1: (a) Schematic diagram of the proposed CMM system. It consisted of a YIG sphere and a microwave cavity. The YIG sphere with angular frequency $\Delta_B$ is subjected uniform bias magnetic field $H_0$.(b) Sketch of the interactions in the CMM system. The magnon couples to the photon mode via magnetic-dipole interaction, and to the phonon mode through magnetostrictive interaction.
• Figure 2: Quantum coherences $C_a$,$C_b$,$C_m$,$C_t$ as functions of the driving power $P$. All parameters are in the main text.
• Figure 3: Quantum coherences $C_a$,$C_b$,$C_m$,$C_t$ as functions of the $\Delta_B$ and $J$. The driving power is $P=6\times10^{-4}~\mathrm{mW}$, $\tilde{\Delta}_m=0.3\omega_b.$ And the other parameters are the same as those in Fig.\ref{['fig2']}.
• Figure 4: Bidirectional contrast ration $I$ as functions of $J$. The driving power is $P=1\times10^{-5}~\mathrm{mW}$ and the angular frequency is $\Delta_B=0.2\omega_b$. And the other parameters are the same as those in Fig.\ref{['fig3']}.
• Figure 5: Quantum coherences $C_a$,$C_b$,$C_m$ as functions of $g$.The driving power is $P=7\times10^{-4}~\mathrm{mW}$ and the magnon-photon coupling rate is $J=0.26\omega_b$. The angular frequency is $\Delta_B=-0.24\omega_b$. And the other parameters are the same as those in Fig.\ref{['fig4']}.