Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems

Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.

Figure 1

(a) Schematic of the physical model. The spin qubit (red circle), the phonon mode (cyan ellipse), and the Kittel magnon mode (green circle) are simultaneously coupled, with the enhanced coupling rate $\lambda e^r$ (blue trichotomous arrow) via a two-phonon driving (blue wavy arrow). (b) Schematic illustration of this proposal: a diamond particle with single NV spins in an electrical trap (top); an NV center embedded in a cantilever (middle); a YIG microsphere levitated in a magnetic trap (bottom).

Figure 2

(a) Tripartite coupling enhancement ${\lambda }_{\mathrm{eff}}/\lambda$ versus the squeezing parameter $r$. (b) The ratio ${\lambda }_{\mathrm{eff}}/g_0$ versus $r$ with different radius of the YIG sphere. (c) The ratio ${\lambda }_{\mathrm{eff}}/g_0$ versus $R$ for different $r$. (d),(e) Contour maps of ${\lambda }_{\mathrm{eff}}$ and the tripartite cooperativity $\mathcal{C}$ versus $R$ and $r$. The dashed line in (d) indicates the value of 1 MHz. The dashed line in (e) indicates the value of 1.

Figure 3

Quantum dynamics of the NV spin, the Kittel magnon, and the center-of-mass motion (a) without mechanical amplification ($r=0$), (b),(c) with $r=3$, and (d) with $r=4.5$. The magnon decay rate is ${\gamma }_K\sim 5\lambda$ in (a) and (b), while it is ${\gamma }_K\sim 50\lambda$ in (c) and (d). The other parameters are $g_0\sim 30\lambda$, ${\gamma }_s\sim 0.05\lambda$, ${\mathrm{\Gamma }}_m\sim 1.1\lambda$, $R_s=10\mathrm{nm}$, $R=50\mathrm{nm}$, and $d=5\mathrm{nm}$. The results are obtained with the red detuning ${\delta }_K\sim {\delta }_{\mathrm{NV}}-{\mathrm{\Delta }}_m$ and initial state $|e,0,0⟩$.

Figure 4

(a) Entanglement versus time for different squeezing parameters $r$, quantified by the minimum residual contangle $E_l^{A|B|C}$ without decay. (b) Entanglement versus time with two entanglement measures, minimum residual contangle $E_l^{A|B|C}$ and three-tangle $E_{\tau }^{A|B|C}$. The initial state of the system and the parameters $\{g_0,r_0\}$ are consistent with those in Fig. 3. The squeezing parameter is $r=4.5$.