Simultaneous blockade of a photon, phonon, and magnon induced by a two-level atom

The hybrid microwave optomechanical-magnetic system has recently emerged as a promising candidate for coherent information processing because of the ultrastrong microwave photon-magnon coupling and the long life of the magnon and phonon. As a quantum information processing device, the realization of single excitation holds special meaning for the hybrid system. In this paper, we introduce a single two-level atom into the optomechanical-magnetic system and show that an unconventional blockade due to destructive interference cannot offer a blockade of both the photon and magnon. Meanwhile under the condition of single excitation resonance, the blockade of the photon, phonon, and magnon can be achieved simultaneously even in a weak optomechanical region, but the phonon blockade still requires the cryogenic temperature condition.

Figure 1

(a) Sketch of the system. A two-level atom is placed inside a microwave cavity with a movable mirror. A YIG sphere is placed near the maximum magnetic field of the cavity mode and in a uniform bias magnetic field, which establishes the magnon-photon coupling. (b) Energy-level diagram under the Hamiltonian Eq. (3), where $|g\left(e\right),n_{+},n_{-},n_b\rangle$ denotes lower-level $g$ (upper-level $e$), and $n_j(j=+,-,b)$ is the number of the mode $(a_{+},a_{-},b)$. The eigenstates are drawn on the right-hand side.

Figure 2

The evolution of probabilities $P_{g100}$ (a) and $P_{g200}$ (b) with original Hamiltonian $H$ (red line) and effective Hamiltonian $H_{\mathrm{eff}}$ (blue squares), respectively, where $P_{g100}={\left|C_{g100}\right|}^2$, $P_{g200}={\left|C_{g200}\right|}^2$. The parameters are $\eta =5\kappa$, ${\eta }_a=6/\sqrt{2}\kappa$, $G_m=200\kappa$, and ${\mathrm{\Omega }}_e=0.1\kappa$.

Figure 3

(a) Equal-time second correlation function for modes $a_{+}$ (red solid, red square), $a_{-}$ (blue dashed, blue dot), and $b$ (black asterisk) versus detuning $\mathrm{\Delta }$, where lines and marks represent analytical and numerical solutions, respectively. (b) The average particle number. The relative probability population function $y$ (c)–(f) corresponding to the mark point A–D in (a), where red (light gray) and blue (dark gray) bars represent supermode $a_{+}$ and $a_{-}$, respectively. The parameters are ${\eta }_a=40/\sqrt{2}\kappa$, $\eta =15\kappa$, ${\kappa }_b=0.05\kappa$, ${\mathrm{\Omega }}_e=0.1\kappa$, $G_m=800\kappa$, and $n_{th}=0$.

Figure 4

(a) Equal-time second-order correlation function for modes $a$ (solid line), $m$ (dots). (b) Average number for optical mode $a$ (solid line) and magnetic mode $m$ (dots) as functions of detuning $\mathrm{\Delta }$. The other parameters are the same as in Fig. 3.

Figure 5

Time-delay second-order correlation function for supermode $a_{+}$ (red solid line) and $a_{-}$ (blue dashed line) in (a), and for optical mode (blue solid line), magnetic mode (orange dashed line), and mechanical mode (black dotted line) in (b). We set $\mathrm{\Delta }={\beta }_1$, and other parameters are the same as in Fig. 3. The inset in panel (b) shows the partial enlarged detail.

Figure 6

(a) Contour plot ${\text{log}}_{10}^{}{g}_a^2\left(0\right)$ as function of ${\eta }_a$ and $\mathrm{\Delta }$. (b) $g_a^2\left(0\right)$ change with $\mathrm{\Delta }$ for several values of ${\eta }_a=40/\sqrt{2}\kappa$ (black solid line), $17.7\kappa$ (orange dashed line), $0.5\kappa$ (green dotted line). The other parameters are the same as in Fig. 3.

Figure 7

(a) Equal-time second-order correlation function for mode $a$ (blue solid line), $m$ (orange dots), and $b$ (black dotted line). We set $\eta =0.2\kappa$, ${\mathrm{\Omega }}_e=0.8\kappa$, ${\eta }_a=20/\sqrt{2}\kappa$, and ${\kappa }_b=\kappa$ in panel (a). The other parameters are same as in Fig. 3. (b) Equal-time second-order correlation function versus thermal phonon population. We set $\mathrm{\Delta }={\beta }_1$, and the other parameters are the same as in panel (a).