Enhancing Remote Magnon-Magnon Entanglement with Quantum Interference

TL;DR

The paper addresses generating macroscopic entanglement between two remote magnon modes in a coupled cavity-magnon system using only beam-splitter interactions. It proposes injecting single- or double-mode squeezed vacuum fields into the cavities and analyzes the steady-state Gaussian state via the covariance matrix $V$, with entanglement quantified by the logarithmic negativity $E_N$ derived from $V_{mm}$. When driven by a single SVF, entanglement arises only if the SVF is resonant with a single supermode; with two SVFs, two independent channels are activated and can interfere coherently via the supermode interface. Phase control of the SVFs enables constructive interference and enhanced robustness to dissipation and thermal noise, increasing the entanglement survival temperature from about 260 mK to 450 mK under realistic parameters.

Abstract

Cavity magnonics, owing to its strong magnon-photon coupling and excellent tunability, has attracted significant interest in quantum information science. However, achieving strong and robust macroscopic entanglement remains a long-standing challenge due to the inherently linear nature of the beam-splitter interaction. Here, we propose an experimentally feasible scheme to generate and enhance macroscopic entanglement between two remote magnon modes by injecting squeezed vacuum fields (SVFs) into coupled microwave cavities. We demonstrate that even a single SVF applied to one cavity can induce steady magnon-magnon entanglement, while applying two SVFs (the double-squeezed configuration) enables selective activation of two independent entanglement channels associated with the cavity supermodes. Remarkably, quantum interference between the two SVFs allows for phase-controlled enhancement of entanglement, resulting in significantly improved robustness against cavity dissipation and thermal noise. Under realistic parameters, the survival temperature of quantum entanglement increases from approximately $260$ mK to $450$ mK. Our results establish a versatile and controllable approach to generating and enhancing quantum entanglement through double-squeezed-field interference, opening new avenues to study and enhance macroscopic quantum physics in cavity-magnon systems with only beam-splitter interactions.

Figures (6)

• Figure 1: (a)Schematic diagram of the coupled cavity-magnon system. Two microwave cavities, connected by a coaxial cable, are respectively driven by two single-mode squeezed vacuum fields with frequency $\omega_s$, generated by two Josephson parametric amplifiers (JPAs) pumped at frequency $2\omega_s$. (b) Two supermodes with frequencies $\omega_a\pm J$, formed by two resonant cavities, are depicted. $2J$ is the separation between two supermodes. (c) The mechanism of the generation of the magnon-magnon entanglement in the single-squeezed configuration, where only one determined supermode can be activated. (d) The mechanism of the generation of the magnon-magnon entanglement in the double-squeezed configuration, where two supermode can be selectively activated, via tuning the detunings of the cavity.
• Figure 2: The degree of magnon-magnon entanglement is shown as a function of (a, b) the normalized cavity detunings and (c, d) the normalized magnon detunings in the single-squeezed configuration. In panel (a), we take $\Delta_{m_1} = -\Delta_{m_2} = 0.5J$, while in panel (b), $\Delta_{m_1} = -\Delta_{m_2} = -0.5J$. In panel (c), the cavity detunings are fixed at $\Delta_{a_1} = \Delta_{a_2} = -J$, and in panel (d), they are fixed at $\Delta_{a_1} = \Delta_{a_2} = J$. Other parameters are chosen as in Ref. tabuchi2014hybridizing: $\kappa_{a_1}/2\pi = \kappa_{a_2}/2\pi =\kappa_{a}/2\pi= 5~\mathrm{MHz}$, $\kappa_{m_1} = \kappa_{m_2} = \kappa_a / 5$, $J = 4\kappa_a$, $g_1 = g_2 = 2\kappa_a$, $r_1 = r_2 = 0.9$, and $\theta_1 = \theta_2 = 0$.
• Figure 3: The degree of magnon-magnon entanglement is shown as a function of (a, b) the normalized cavity detunings and (c, d) the normalized magnon detunings in the double-squeezed configuration. In panel (a), we take $\Delta_{m_1} = -\Delta_{m_2} = 0.5J$, while in panel (b), $\Delta_{m_1} = -\Delta_{m_2} = -0.5J$. In panel (c), the cavity detunings are fixed at $\Delta_{a_1} = \Delta_{a_2} = -J$, and in panel (d), they are fixed at $\Delta_{a_1} = \Delta_{a_2} = J$. Other parameters are the same as those in Fig. \ref{['fig2']}.
• Figure 4: The degree of magnon-magnon entanglement is plotted as a function of (a) the squeezing phases $\theta_1$ and $\theta_2$ in the double-squeezed configuration, (b) the squeezing parameter $r_1$ in the single-squeezed configuration, (c) the squeezing parameters $r_1$ and $r_2$ in the double-squeezed configuration, and (d) the squeezing parameter $r_1$ in the single-squeezed configuration. In panels (a) and (b), the squeezing phases are fixed at $\theta_1 = \theta_2 = 0$, while in panels (c) and (d), the squeezing strengths are set to $r_1 = r_2 = 0.9$. In all panels, the cavity detunings are fixed at $\Delta_{a_1} = \Delta_{a_2} = -J$, and the magnon detunings are chosen as $\Delta_{m_1} = -\Delta_{m_2} = 0.5J$. Other parameters are the same as those used in Fig. \ref{['fig2']}.
• Figure 5: The degree of magnon-magnon entanglement is shown as a function of the normalized decay rates of the two cavity modes for (a) the double-squeezed and (b) the single-squeezed configurations. Panels (c) and (d) display the corresponding cross-sectional results from (a) and (b), respectively, with $\kappa_{a_1} = 2.5\kappa$ fixed. In all panels, the cavity detunings are set to $\Delta_{a_1} = \Delta_{a_2} = -J$, and the magnon detunings are chosen as $\Delta_{m_1} = -\Delta_{m_2} = 0.5J$. Other parameters are identical to those used in Fig. \ref{['fig2']}.