Magnon blockade in a hybrid ferromagnet-superconductor quantum system

The implementation of a single magnon level quantum manipulation is one of the fundamental targets in quantum magnetism with a significant practical relevance for precision metrology, quantum information processing, and quantum simulation. Here we demonstrate theoretically the feasibility of using a hybrid ferromagnet-superconductor quantum system to prepare a single magnon source based on magnon blockade effects. By numerically solving the quantum master equation, we show that the second-order correlation function of the magnon mode depends crucially on the relation between the qubit-magnon coupling strength and the driving detuning, and simultaneously signatures of the magnon blockade appear only under quite stringent conditions of a cryogenic temperature. In addition to providing perception into the quantum phenomena of magnon, the study of magnon blockade effects will help to develop novel technologies for exploring the undiscovered magnon traits at the quantum level and may find applications in designing single magnon emitters.

Figure 1

(a) Schematic illustration of the hybrid ferromagnet-superconductor quantum model, in which a single-crystalline ferromagnetic YIG sphere and a transmontype superconducting qubit are installed in a microwave cavity [15]. The qubit is driven by a monochromatic drive field (with strength $\mathrm{\Omega }$) and a weak probe field (with strength ${\xi }_p$) is applied into the YIG sphere to observed the magnon blockade effects. The qubit and magnons can be effectively coupled via the exchange of virtual cavity photons (with the coupling strength $g_{qm}$). A static magnetic field $B_z$ aligned along the hard magnetization axis [100] of the YIG sphere can be used to adjust the frequency of the Kittel (magnon) mode. (b) Energy levels of the qubit-magnon quantum system with a two-magnon state involved for the Kittel mode. The coupling between the magnon mode and the qubit induces the vacuum Rabi splitting of the dressed states.

Figure 2

The steady-state equal-time second-order correlation function ${\text{log}}_{10}{g}^{\left(2\right)}\left(0\right)$ is plotted varies with (a) the driving detuning $\mathrm{\Delta }/\gamma$ (here, for convenience, $\gamma =2\pi \times 1$ MHz used to scale the frequencies throughout the article) and the effective qubit-magnon coupling strength $g_{qm}/\gamma$. (b) The control field strength $\mathrm{\Omega }/\gamma$ and the probe field strength ${\xi }_p/\gamma$, respectively. We use $\mathrm{\Omega }/\gamma =0.1$ ($P_d\simeq 0.037\mu \mathrm{W}$) and ${\xi }_p/\gamma =0.001$ (the probe power $P_p\simeq 0.0037$ nW) in (a), and $\mathrm{\Delta }/\gamma =21$ and $g/\gamma =21$ in (b). The other system parameters we take are ${\kappa }_m/\gamma =1.4, {\kappa }_q/\gamma =1.2$, and $n_{\text{th}}=0$.

Figure 3

The equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ versus the detuning $\mathrm{\Delta }/\gamma$ under the different values of the control field strength $\mathrm{\Omega }/\gamma =(0.1,2,10)$ in (a) and the probe field strength ${\xi }_p/\gamma =(0.033,0.06,1)$ in (c). The dependence of $g^{\left(2\right)}\left(0\right)$ on $\mathrm{\Omega }/\gamma$ and ${\xi }_p/\gamma$ are plotted in (b) and (d) for $\mathrm{\Delta }/\gamma =(14.8,0,21)$, respectively. We use ${\xi }_p/\gamma =0.001$ in (a) and (b), $\mathrm{\Omega }/\gamma =0.1$ in (c) and (d), and the other parameters are the same as those in Fig. 2.

Figure 4

The equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ as a function of the effective qubit-magnon coupling strength $g_{qm}/\gamma$ under the different thermal magnon occupation number $n_{\text{th}}=(0,{10}^{-4},{10}^{-3})$. We use $(\mathrm{\Delta },\mathrm{\Omega },{\xi }_p)/\gamma =(21,0.1,0.001)$, and the other parameters are the same as those in Fig. 2.