图 1  双$ \pi $脉冲作用下的光子回波静默和再现操作　(a)双$ \pi $脉冲光子回波技术的脉冲序列, 输入信号光的空间相位分布为$ \phi_0(r) $, 第一个$ \pi $脉冲对应的空间相位分布为$ \phi_1(r) $, 并且$ \phi_1(r) \neq \phi_0(r) $, 第二个$ \pi $脉冲对应的空间相位分布为$ \phi_2(r) $; (b)在自由空间的ROSE存储技术中, $ \phi_1(r) \neq \phi_0(r) $可通过控制脉冲光和控制脉冲的入射方向来实现. 例如, 图中的信号脉冲从左侧入射$ \phi_0 = {\rm{i}} k r $, $ \pi $脉冲从右侧入射$ \phi_1 = \phi_2 = -{\rm{ i }}k r $

Fig. 1.  The silence and revival of two-$ \pi $-pulse photon echo: (a) Pulse sequence of two-$ \pi $-pulse photon echo. The phase distribution of the input pulse is $ \phi_0(r) $, that of the first $ \pi $ pulse is $ \phi_1(r) $, where $ \phi_1(r) \neq \phi_0(r) $, and that of the second $ \pi $ pulse is $ \phi_2(r) $. (b) In free space ROSE, $ \phi_1(r) $ differs from $ \phi_0(r) $ due to the different propagating directions of the signal pluse and the $ \pi $ pulses. In panel (b), the signal pulse incoming from the left has $ \phi_0 = {\rm{i}} k r $, and the $ \pi $ pulses incoming from the right have $ \phi_1 = \phi_2 = -{\rm{ i}} k r $.

图 2  拟采用的光子晶体结构　(a)光子晶体结构, 光子晶体为正方晶格结构, 周期为500 nm, 其中蓝色柱子为掺铒的硅材料, 直径$ D = 200 $ nm; (b)计算得到的光子晶体能带图, 带隙在$1.21 — 1.78\;\text{µ} {\rm{m}}$范围内

Fig. 2.  Photonic crystal: (a) Structurre of the photonic crystal. The photonic crystal has a square lattice, whose period is 500 nm. The circles stands for the silicon pillars with a diameter of $ D = 200 $ nm. (b) Energy band of the photonic crystal in panel (a), showing a bandgap within 1.21–1.78$\;\text{µ} {\rm{m}}$

图 3  两种不同的光子晶体微腔. 单极子谐振模式　(a)在光子晶体中去掉一个硅柱子可以形成一个缺陷态微腔. 这样一种腔支持单极子的谐振模式, 如图(c)所示. 入射光从左上方的光子晶体波导入射耦合到光子晶体腔中, 如图(e)所示. 由于单极子谐振模式是一种类似于驻波的谐振模式, 因此无法通过调节阻抗匹配实现100%的单端输出. 六极子谐振模式: (b)把光子晶体中间的硅柱子直径增加为$ d_1 = 700 $ nm, 并且将边沿的一个硅柱子直径减小为$ d_2 = 150 $ nm, 可以形成另一种光学微腔. 这样一种光学腔支持六极子的谐振模式, 其场分布如图(d)所示. 当入射光同样从左上方的光子晶体波导耦合到光子晶体腔时, 如图(f)所示, 六单极子谐振模式类似于一个顺时针旋转的回音壁模式, 可以通过调节阻抗匹配实现能量接近100%地从左下角的端口输出

Fig. 3.  Two photonic-crystal cavities. Monopole resonace: (a) Removing a rod in the photonic crystal forms a defect cavity. One of the resonances of the structure (a) is a monopole resonance, the field distribution of which is shown in panel (c). Such a monopole mode is analogous to standing-wave resonance, and has a constant phase in space. This means that single-port output to one end of the waveguides can not be realized bu tuning the waveguide-cavity coupling, as shown in panel (e). Hexapole resonance: (b) By increasing the diameter of the central rod to 700 nm and reducing the rods at the edge to $ d_2 = 150 $ nm, one can make another kind of cavity that supports hexapole resonance. The field distribution is shown in panel (d). In such a structure the coupling between waveguides and the cavity are impedance matched, as shown in panel (f), therefore one can transfer the input light to the down-right port with an efficiency close to 100%

图 4  基于光子晶体微腔的ROSE回波量子存储　(a)用于ROSE存储的光子晶体结构; (b)信号光脉冲从左侧入射, 如图 3(d)所示, 可以在原子系统中激发出一种$ \phi_0(r) $为“顺时针”旋转的集体极化; (c)控制$ \pi $脉冲从右侧入射, 因此其激发的腔模具有的相位分布$ \phi_1(r) $为“逆时针”旋转方向; (d) 当第二个控制$ \pi $脉冲也从右侧入射后, 根据(13)式和(15)式, 原子系统的集体激发再次具有$ \phi_0(r) $的相位分布, 在$ t = 2 t_2 - 2 t_1 + t_0 $时刻会向右边的端口外辐射出一个光子回波

Fig. 4.  Protocol of ROSE quantum memory based on photonic crystal structures: (a) One photonic crystal structure that is suitable for ROSE technique; (b) a signal pulse is input from the left, and the collective atomic polarization thus has a “clockwise” spatial phase distribution $ \phi_0(r) $; (c) control $ \pi $ pulses are input from the right, therefore have a “anti-clockwise” spatial phase distribution $ \phi_1(r) $; (d) after the second $ \pi $ pulse, according the Eqs. (13) and (15), the collective atomic polarization has a phase distribution of $ \phi_0(r) $ and then emit a photon echo to the right port