Exponentially Enhanced Tripartite Coupling in Quantum Nonlinear Magnonics

TL;DR

This work addresses the challenge of achieving strong, tunable tripartite interactions in quantum magnonics by coupling a three-level NV center to Kerr magnons in two YIG spheres. Through adiabatic elimination of the NV ground state, a tripartite interaction among magnons and an NV qubit is induced, which is further exponentially enhanced by jointly squeezing the two magnon modes via Kerr nonlinearity, yielding a coupling scaling of $G_s/G_k = (1/4) e^{2\xi}$ and a cooperativity boost of $C_s/C_k = (1/64) e^{6\xi}$. This accelerated dynamics enables fast generation of tripartite entanglement and enables noise-resilient perfect magnon blockade, as demonstrated analytically and numerically. The results position the NV center as a promising interface for engineering many-body interactions in quantum magnonics and suggest avenues for exploring entanglement and correlations in hybrid quantum platforms, with potential extensions to spin-magnon-phonon and superconducting-spin-magnon systems.

Abstract

Strong and controllable tripartite interactions play a pivotal role in quantum information and nonlinear quantum optics, yet challenging to realize. In this work, we propose a hybrid system consisting of a nitrogen-vacancy (NV) center coupled to Kerr magnons (magnons with Kerr nonlinearity) in two yttrium-iron-garnet spheres. By adiabatically eliminating the ground state of the NV qutrit in the dispersive regime, an effective tripartite interaction among magnons and an NV qubit encoded in its excited states is obtained. In the strong driving limit, Kerr magnons can be linearized and give rise to degenerate parametric amplification for squeezing magnons. As a result, both the tripartite interaction and cooperativity are exponentially enhanced twice, which is about $\exp(ξ)$ times than schemes only involving single-squeezing. Hence, our proposal is more experimentally feasible because modest squeezing parameter is sufficient. With this amplified tripartite coupling strength, the system dynamics are greatly accelerated, leading to fast generation of tripartite entanglement. In addition, noise-resilient perfect magnon blockade can be achieved, well predicted by both the analytical approach and numerical simulation with quantum master equation. Our results suggest that the NV center represents a promising interface for engineering many-body interactions in quantum magnonics, offering a versatile platform for exploring fundamental quantum phenomena such as entanglement and correlations.

Figures (6)

• Figure 1: (a) Schematic of the hybrid system consisting of an NV center coupled to Kerr magnons in two YIG spheres. magnons in each sphere are driven by a microwave field with frequency $\nu_p$ and amplitude $\Omega_p$ ($p=l,r$). The transition $|g\rangle\!\leftrightarrow\!|e\rangle$ ($|g\rangle\!\leftrightarrow\!|f\rangle$) couples to the magnons in the left (right) sphere. (b) Effective tripartite interaction between the the magnons in two spheres and the NV qubit formed by two excited states of the NV qutrit, obtained by adiabatic elimination of the ground state $|g\rangle$ in the dispersive regime. (c) Exponentially enhanced tripartite interaction arising from magnon squeezing in both spheres, induced by the Kerr nonlinearity.
• Figure 2: (a) Coupling ratio $G_s/G_k$ and (b) cooperativity ratio $C_s/C_k$ versus the squeezing parameter $\xi$. The orange curve denotes the joint squeezing and the blue curve denotes the single squeezing.
• Figure 3: The ideal occupation of (a) the left squeezed-magnon $\langle m_{s,l}^\dag m_{s,l}\rangle$, (b) the right squeezed-magnon $\langle m_{s,r}^\dag m_{s,r}\rangle$, and (c) the NV qubit $\langle \sigma_+\sigma_-\rangle$ as a function of the dimensionless evolution time $G_k t$. (d) The nonideal occupation of the left squeezed-magnon ($\langle m_{s,l}^\dag m_{s,l}\rangle$), the right squeezed-magnon ($\langle m_{s,r}^\dag m_{s,r}\rangle$), and the NV qubit ($\langle \sigma_+\sigma_-\rangle$) as a function of the dimensionless evolution time $G_k t$, where $\kappa_l/2\pi=\kappa_r/2\pi=100$ kHz, $\gamma_q/2\pi=1$ kHz and $\xi=2$. In (a)-(d), the resonant condition $\omega_{s,l}+\omega_q=\omega_{s,r}$ is chosen, the system is initially prepared in the state $|\psi\rangle = |1_l,0_r,f_q\rangle_l$, and $G_k=0.5$ MHz.
• Figure 4: (a) Tripartite entanglement versus time for different detuning quantified by the residual tangle $\tau_{A|B|C}$. (b) Tripartite entanglement versus time for different squeezing parameters $r$ by the residual tangle $\tau_{A|B|C}$. (c) Tripartite entanglement versus time for different decay rate of the system quantified by the residual tangle $\tau_{A|B|C}$ (d) Tripartite entanglement versus time quantified by the residual tangle $\tau_{A|B|C}$ and the minimum residual contangle $E_{\tau}^{i|j|k}$. Other parameters are the same as those in Fig. \ref{['figure2']}.
• Figure 5: The equal-time second-order correlation function $g^{(2)}(0)$ and the steady-state probabilities are plotted as functions of the normalized frequency detuning $\Delta/G_k$, with $\omega_q=10G_k$ and $\Omega_p/2\pi=0.05$ MHz. Panels (a, d) correspond to $\xi=0$, with $\omega_{s,l}=-399.805G_k$ and $\omega_{s,r}=15.016G_k$; panels (b, e) correspond to $\xi=1$, with $\omega_{s,l}=-446.250G_k$ and $\omega_{s,r}=153.887G_k$; and panels (c, f) correspond to $\xi=2$, with $\omega_{s,l}=-776.732G_k$ and $\omega_{s,r}=1142.064G_k$. Other parameters are the same as those in Fig. \ref{['figure2']}. These parameter choices are made to satisfy the optimal blockade condition in Eq. (\ref{['equ35']}).