图 1  (a) 双原子系统的模型图, 两原子受到一个方向与${r_{12}}$成${\theta _{\text{L}}}$, 频率为${\omega _{\text{L}}}$的激光场驱动. 两个探测器分别位于${{\boldsymbol{R}}_1}$和${{\boldsymbol{R}}_2}$, 与原子轴成${\theta _1}$和${\theta _2}$处探测原子发射的光子; (b) 原子能级图, 显示了原子1, 2的跃迁频率${\omega _1}$和${\omega _2}$, 自发辐射速率${\gamma _1}$, ${\gamma _2}$, 以及激光耦合强度等

Fig. 1.  (a) Schematic of the two-atom system, the atoms are driven by a laser field with frequency ${\omega _{\text{L}}}$ at an angle ${\theta _{\text{L}}}$ with respect to the interatomic vector ${r_{12}}$, detectors are placed at positions ${{\boldsymbol{R}}_1}$ and ${{\boldsymbol{R}}_2}$, detecting photons emitted by the atoms at angles ${\theta _1}$ and ${\theta _2}$ relative to the atomic axis; (b) presents the atomic energy level diagram, displaying the transition frequencies ${\omega _1}$ and ${\omega _2}$ of atoms 1 and 2, spontaneous emission rates ${\gamma _1}$ and ${\gamma _2}$, as well as laser coupling strengths.

图 2  对角化处理后两原子能级分布　(a) 非全同原子能级分布, 对称态与反对称态存在耦合; (b)全同原子能级分布, 激光只驱动对称态$\left| s \right\rangle $

Fig. 2.  Energy level distribution of two atoms after diagonalization: (a) Non-identical atomic energy level distribution, with coupling between symmetric and antisymmetric states; (b) identical atomic energy level distribution, where the laser drives only the symmetric state $\left| s \right\rangle $.

图 3  激光选择性驱动$\left| s \right\rangle $态和$\left| a \right\rangle $态条件　(a) ${r_{12}} = \lambda /2$; (b) ${r_{12}} = \lambda $

Fig. 3.  Conditions for laser-selective driving of $\left| s \right\rangle $ state and $\left| a \right\rangle $ state: (a) ${r_{12}} = \lambda /2$; (b) ${r_{12}} = \lambda $.

图 4  全同原子能级布居分布, $\varDelta = 0$, ${\varDelta _{\text{L}}} = 0$, ${r_{12}} = 0.5\lambda $, ${\gamma _1} = {\gamma _2}$　(a) 原子能级布居随$\varOmega $的变化, 激光入${\theta _{\text{L}}} = {\text{π }}/2$; (b) 原子能级布居随激光入射角${\theta _{\text{L}}}$的变化, $\varOmega = 0.5\gamma $

Fig. 4.  Energy level population distribution of identical atoms with $\varDelta = 0$, ${\varDelta _{\text{L}}} = 0$, ${r_{12}} = 0.5\lambda $, ${\gamma _1} = {\gamma _2}$: (a) The atomic energy level population as a function of $\varOmega $ with laser incidence at ${\theta _{\text{L}}} = {\text{π }}/2$; (b) the change in atomic energy level population with the laser incidence angle ${\theta _{\text{L}}}$, for $\varOmega = 0.5\gamma $.

图 5  非全同原子能级布居分布, ${\theta _{\text{L}}} = {\text{π }}/2$, $\varOmega = 0.5\gamma $, ${\omega _2} = $$ {\omega _{\text{L}}}$, ${r_{12}} = 0.5\lambda $　(a) 原子能级布居随$\varDelta $的变化, ${\gamma _1} = {\gamma _2}$; (b) 原子能级布居随耗散比${\gamma _1}/{\gamma _2}$的变化, $\varDelta = 0$

Fig. 5.  Energy level population distribution for non-identical atoms with ${\theta _{\text{L}}} = {\text{π }}/2$, $\varOmega = 0.5\gamma $, ${\omega _2} = {\omega _{\text{L}}}$, and ${r_{12}} = 0.5\lambda $: (a) The variation of atomic energy level population with $\varDelta $, ${\gamma _1} = {\gamma _2}$; (b) the change in atomic energy level population with the dissipative ratio ${\gamma _1}/{\gamma _2}$, $\varDelta = 0$.

图 6  全同原子${g^{(2)}}({\boldsymbol{R}}, {\boldsymbol{R}})$关联值随探测角的分布, ${\varDelta _{\text{L}}} = 0$　(a) ${\theta _{\text{L}}} = {\text{π }}/2$, ${r_{12}} = 0.5\lambda $, $\varOmega = 0.1\gamma $; (b) 红线${\theta _{\text{L}}} = {\text{π }}/2$, 蓝线${\theta _{\text{L}}} = {\text{π }}$, ${r_{12}} = 0.5\lambda $, $\varOmega = 0.5\gamma $; (c) ${\theta _{\text{L}}} = {\text{π }}/2$红线, ${\theta _{\text{L}}} = {\text{π }}/3$蓝线, ${\theta _{\text{L}}} = 2{\text{π }}/3$绿线, ${r_{12}} = 0.5\lambda $, $\varOmega = 0.5\gamma $; (d) ${\theta _{\text{L}}} = {\text{π }}/2$红线, ${\theta _{\text{L}}} = {\text{π }}$蓝虚线, ${\theta _{\text{L}}} = {\text{π }}/3$绿线. ${r_{12}} = \lambda $, $\varOmega = 0.5\gamma $

Fig. 6.  Distribution of the second-order correlation function ${g^{(2)}}({\boldsymbol{R}}, {\boldsymbol{R}})$ for identical atoms as a function of the detection angle with ${\varDelta _{\text{L}}} = 0$: (a) For ${\theta _{\text{L}}} = {\text{π }}/2$, ${r_{12}} = 0.5\lambda $, and $\varOmega = 0.1\gamma $; (b) for ${\theta _{\text{L}}} = {\text{π }}/2$ represented by the red line and ${\theta _{\text{L}}} = {\text{π }}$ by the blue line, with ${r_{12}} = 0.5\lambda $ and $\varOmega = 0.5\gamma $; (c) for ${\theta _{\text{L}}} = {\text{π }}/2$ shown as the red line, ${\theta _{\text{L}}} = {\text{π }}/3$ as the blue line, and ${\theta _{\text{L}}} = 2{\text{π }}/3$ as the green line, with ${r_{12}} = 0.5\lambda $ and $\varOmega = 0.5\gamma $; (d) for ${\theta _{\text{L}}} = {\text{π }}/2$ by the red solid line, ${\theta _{\text{L}}} = {\text{π }}$ by the blue dashed line, and ${\theta _{\text{L}}} = {\text{π }}/3$ as the green line, with ${r_{12}} = \lambda $ and $\varOmega = 0.5\gamma $.

图 7  非全同原子${g^{(2)}}({\boldsymbol{R}}, {\boldsymbol{R}})$关联值随探测角的分布, ${r_{12}} = 0.5\lambda $, $\varOmega = 0.5\gamma $　(a) ${\theta _{\text{L}}} = {\text{π }}/2$, ${\gamma _1} = {\gamma _2}$, ${\omega _{\text{L}}} = {\omega _2}$, 蓝线$\varDelta = 0.75\gamma $, 绿线$\varDelta = - 0.75\gamma $; (b) ${\theta _{\text{L}}} = {\text{π }}/2$, ${\gamma _1} = {\gamma _2}$, ${\omega _{\text{L}}} = {\omega _1}$, 蓝线$\varDelta = 0.75\gamma $, 绿线$\varDelta = - 0.75\gamma $; (c) ${\theta _{\text{L}}} = {\text{π }}$, ${\gamma _1} = {\gamma _2}$, ${\omega _{\text{L}}} = {\omega _1}$, 蓝线$\varDelta = 0.75\gamma $, 绿线$\varDelta = - 0.75\gamma $; (d) ${\theta _{\text{L}}} = {\text{π }}/2$, $\varDelta = 0$, ${\gamma _1} = {\gamma _2}$红线, ${\gamma _1} = 2{\gamma _2}$蓝线, ${\gamma _1} = 10{\gamma _2}$绿线

Fig. 7.  Distribution of the second-order correlation value ${g^{(2)}}({\boldsymbol{R}}, {\boldsymbol{R}})$ for distinguishable atoms as a function of the detection angle with ${r_{12}} = 0.5\lambda $ and $\varOmega = 0.5\gamma $: (a) ${\theta _{\text{L}}} = {\text{π }}/2$, ${\gamma _1} = {\gamma _2}$, ${\omega _{\text{L}}} = {\omega _2}$, the blue line corresponds to $\varDelta = 0.75\gamma $ and the green line to $\varDelta = - 0.75\gamma $; (b) ${\theta _{\text{L}}} = {\text{π }}/2$, ${\gamma _1} = {\gamma _2}$, ${\omega _{\text{L}}} = {\omega _1}$, the blue line is for $\varDelta = 0.75\gamma $ and the green line for $\varDelta = - 0.75\gamma $; (c) ${\theta _{\text{L}}} = {\text{π }}$, ${\gamma _1} = {\gamma _2}$, ${\omega _{\text{L}}} = {\omega _1}$, the blue line is for $\varDelta = 0.75\gamma $ and the green line for $\varDelta = - 0.75\gamma $; (d) with ${\theta _{\text{L}}} = {\text{π }}/2$ and $\varDelta = 0$, the red line is for ${\gamma _1} = {\gamma _2}$, the blue line for ${\gamma _1} = 2{\gamma _2}$, and the green line for ${\gamma _1} = 10{\gamma _2}$.