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量子通信[1-3]依赖于量子纠缠的远距离分发, 但量子态传输过程中的通道损耗及退相干[4-8], 限制了其传输距离(小于500 km)[5,9]. 由于量子不可克隆原理, 其不能像经典信号一样直接放大, 因此量子中继的方案应运而生. 有多种量子系统可以作为量子节点, 例如单原子[10,11]、单离子[12]、原子系综[1]、金刚石NV色心[13]和稀土离子掺杂固态晶体[14,15]等. 其中基于冷原子系综和线性光学的Duan-Lukin-Cirac-Zoller(DLCZ)协议, 由于其能够产生并存储纠缠, 被视为最有潜力的方案之一[16]. 在该方案中, 先将一束相对于原子共振线失谐的写光脉冲作用到原子上, 经由自发拉曼散射[17], 以较低几率在空间中发射一个斯托克斯光子, 并在原子中存储一个与其关联的自旋波. 经过一段时间存储以后, 一束强的读光作用于原子, 将自旋波转换为反斯托克斯光子读出. 在此过程中读出效率是量子中继能否实用化的一个重要指标. 而且读出效率会影响两个相邻中继器节点之间的每一次纠缠交换, 据理论估计, 当纠缠分发距离平均小于600 km时, 读出效率提高1%可以提高至少10%的量子纠缠分发速率[1]. 通常通过优化读光脉冲[18], 增大原子系综光学厚度(OD)[19,20]和腔增强[18,21]等方法来提高读出效率. 所谓腔增强, 就是在原子气室外放置一个中等精细度的环形腔, 在空间上约束光场, 来增加光与原子相互作用强度, 有效地提高量子存储器的读出效率. 本文进行了原子系综中光学腔增强的读出效率的实验研究, 研究了读光相对于共振线的失谐量对读出效率的影响, 结果表明: 失谐量为80 MHz时, 加腔情况下读出效率是无腔时的1.68倍. 本质恢复效率达到45%.
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实验中将磁光阱(MOT)俘获的
$ {}^{87}{\text{Rb}} $ 冷原子作为存储介质. 整个实验的重复频率为20 Hz, 如图1所示，在前42 ms内开启MOT进行原子系综的俘获, 接下来的8 ms内, 先进行8 μs的态制备, 将原子制备到后续实验所需能级上, 然后进行循环多次实验, 循环过程通过FPGA(field programmable gate array)模块来控制, 每个循环包含三个过程, 态清洗、写过程、和读过程. 实验流程为: 两束频率分别为$ \left| {5{{\text{S}}_{{1 / 2}}}, F = 2} \right\rangle \to \left| {5{{\text{P}}_{{1 / 2}}}, {F'} = 2} \right\rangle $ 和$| 5{{\text{S}}_{{1 / 2}}}, F = 2 \rangle $ $ \to $ $ \left| {5{{\text{P}}_{{1 / 2}}}, {F'} = 1} \right\rangle$ , 脉宽为$ {\text{200 ns}} $ 的圆偏振光作用到原子上, 将原子均匀地制备在$ \left| {5{{\text{S}}_{{{\text{1}} / {\text{2}}}}}, F = 1} \right\rangle $ 的Zeeman子能级. 随后一束脉宽为$ 250{\text{ ns}} $ 的左旋圆偏振的写光与原子相互作用, 其频率锁定在$\left| {5{{\text{S}}_{{1 / 2}}}, F = {\text{1}}} \right\rangle \to $ $ \left| {5{{\text{P}}_{{1 / 2}}}, {F'} = 2} \right\rangle$ 跃迁负失谐$\varDelta$ 处, 经自发拉曼散射过程发射出与$ \left| {5{{\text{P}}_{{1 / 2}}}, F = 2} \right\rangle \to \left| {5{{\text{F}}_{{1 / 2}}}, {F'} = 2} \right\rangle $ 相对应的$ \left| R \right\rangle $ $ \left( {\left| L \right\rangle } \right) $ 写出光子, 与此同时在原子系综存储一个与写出光子对应的$ \left| {{\sigma ^+}} \right\rangle $ $ \left( {\left| {{\sigma ^-}} \right\rangle } \right) $ 自旋波. 存储一段时间后, 一束脉宽为$ {\text{250 ns}} $ 的锁定频率为$\left| {5{{\text{S}}_{{1 / 2}}}, F = 2} \right\rangle \to $ $ \left| {{\text{5}}{{\text{P}}_{{1 / 2}}}, {F'} = 1} \right\rangle$ 跃迁负失谐$\varDelta$ 处的右旋圆偏振的读光通过电磁感应透明过程将原子系综的自旋波读出, 转换为与$\left| {5{{\text{P}}_{{1 / 2}}}, F = 1} \right\rangle \to $ $ \left| {5{{\text{F}}_{{1 / 2}}}, {F'} = 1} \right\rangle$ 对应的$ \left| L \right\rangle $ $ \left( {\left| R \right\rangle } \right) $ 的读出光子.实验装置示意图如图2所示. 环形腔由
$ {45^ \circ } $ 全反HR1, HR2, HR3和HR4, 反射率为80%的$ {0^ \circ } $ 耦合镜BS1和反射率为99.7%的$ {0^ \circ } $ 耦合镜BS2构成. 实验中环形腔的腔长约为3.3 m, 腔的精细度为$ {\text{13}}{\text{.5}} $ . 腔内总损耗为21%, 其中腔镜损耗为15%, 真空原子气室的损耗为6%. 将原子系综放置在HR1和HR4之间, 并且在原子系综的两端对称处放置了两个F = 800 mm的透镜, 来满足环形腔内存储实验对信号光束腰的要求, 并且将光斑束腰调至原子处. 由于环形腔内反射镜和透镜对不同偏振光折射率的不同导致的相位差, 采用一对1/2玻片和1/4玻片的玻片组对这个相位差进行补偿, 其中一个1/4玻片放置在原子一端, 另一个1/4玻片和1/2玻片放置在原子另一端.实验中读光和写光从雪茄型原子长轴方向的相反方向作用于原子系综, 原子附近腔的光路与写读光路成
$ {5.1^ \circ } $ 夹角. 对于读出光子和写出光子, 经由拉曼过程后, 沿近原子长轴方向散射进入腔内. 读出光子沿顺时针在腔内循环, 经由耦合镜BS1出腔进入读接收光路, 并且用单光子探测器SPD1收集. 写出光子沿逆时针在腔内循环, 以不同角度从耦合镜BS1出腔, 进入写接收光路, 由单光子探测器SPD2进行收集.实验过程中, 采用Pound-Drever-Hall(PDH)锁定技术对环形腔的腔长进行锁定, 需要在腔内另外引入一束锁腔光来实现腔长锁定, 于是搭建反射率为6%的
$ {45^ \circ } $ 方向入射的BS3将锁腔光与写接收光路耦合, 从写接收光路的反方向经耦合镜BS1将锁腔光引入腔内. 而锁腔光的引入会带来大量噪声, 于是在锁腔光光路中接入时序对锁腔光进行开关控制. 对环形腔进行间断锁定: 在前42 ms俘获原子阶段开启锁腔光进行腔长锁定, 在实验循环阶段8 ms内锁腔光处于关闭状态. 将锁腔光频率锁定在$ \left| {5{{\text{S}}_{{1 / 2}}}, F = 2} \right\rangle \to \left| {5{{\text{P}}_{{1 / 2}}}, {F'} = {\text{1}}} \right\rangle $ 红失谐480 MHz处, 频率远失谐于读出光子和写出光子, 使散射进入接收光路的少量光子能够被接收光路的滤波器过滤掉.要想实现读出效率的增强, 必须使读出光子和写出光子在腔内模式共振, 而且还要与锁腔光的模式共振. 在实验中, 在锁腔光的光路中接入声光调制器来控制锁腔光的频率, 因此只需先将读出与写出光子模式调至共振, 移动锁腔光频率使其与读出写出光子模式共振, 即可实现三模共振.
实验中要想调节读出光子与写出光子的共振, 须在腔内引入两束光来模拟读出光子和写出光子, 于是在读接收和写接收光路各放置一个Flipper, Flipper内安装
$ {45^ \circ } $ 入射的全反镜, Beam1和Beam2经过Flipper后, 沿读接收和写接收光路反向传播, 由耦合镜BS1进入腔内, 将Beam1和Beam2的频率分别锁定至读出光子和写出光子频率, 此时光路引入完成. 腔内光的频率确定时, 需要调整腔长来使模式共振, 于是将BS2固定在平移架上, 通过调整平移架来调整腔长, 使读出光子与写出光子腔模重合. 再通过声光调制器来调节锁腔光频率, 使锁腔光与读出写出光子模式共振, 此时便实现三模共振.实验中腔长满足如下条件, 即腔长
$L = n{\lambda _{\text{R}}} = $ $ m{\lambda _{\text{W}}}$ (m, n为整数), 读出光子波长$ {\lambda _{\text{R}}} = {c / {{\nu _{\text{R}}}}} $ , 写出光子波长$ {\lambda _{\text{W}}} = {c / {{\nu _{\text{W}}}}} $ , 在实验中使用铷原子 D1线作为存储能级, 写出与读出信号频率相差$\Delta \nu = $ $ {\nu _{\text{W}}} - {\nu _{\text{R}}} = 6.02{\text{ GHz}}$ . 则腔长$ L $ 为可以得出腔长L约为49.8 mm的整数倍.
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在腔增强读出效率增强过程中, 会有这么一个问题. 当腔模与原子线共振时, 会导致原子共振峰劈裂, 共振峰的劈裂使腔膜不能与原子线很好的共振, 影响腔对读出效率的增强效果, 失谐时共振峰劈裂的大小为
$ {g^2}/\varDelta $ , g为单光子拉比频率$g = $ $ \mu \sqrt {{{{\omega _{\text{c}}}} / {(2{\varepsilon _0}\hbar V)}}}$ , 由此式可以看出, 腔模与原子线失谐越大共振峰劈裂越小.由于原子能级的劈裂, 当读光作用到原子上时, 产生的读出光子也会在频率上分开成两个模式, 这两个模式的中心对应于
$\left| {5{{\text{P}}_{{1 / 2}}}, F = 1} \right\rangle \to $ $ \left| {5{{\text{F}}_{{1 / 2}}}, {F'} = 1} \right\rangle$ 跃迁失谐$ \varDelta $ 处, 这两个模式劈裂的大小也为$ {g^2}/\varDelta $ . 在实验中读光的失谐会影响读出光子频率, 而实验中三模共振的调节过程会将两个劈裂的模式的中心与腔模调至共振, 这样通过增加读光与原子跃迁线的失谐, 可以减小两个模式之间的频率分裂, 使两个模式更为靠近, 当这两个模式都包含在腔模式内时, 可观察到读出效率被增强. 实验中写出光子与腔共振, 也会随着腔模的劈裂而分开, 所以选择将写光和读光同步失谐, 来减小劈裂对写出光子的影响.在读光失谐过程中发现: 随着读光失谐变大, 读出效率的饱和功率随之增加, 刚开始饱和功率增加较为平缓, 当读光失谐继续增加, 饱和功率的增加速度逐渐变大. 本文研究了读光相对于原子共振线的失谐对恢复效率增强的影响. 如图3表明: 在有环形腔的情况下, 随着读光失谐变大读出效率逐渐变大. 当失谐大于80 MHz时, 读出效率趋于平缓. 在80 MHz时读出效率相比于无腔时增强了1.68倍, 对应的本质效率为45%.
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本文在自由空间DLCZ量子存储方案的基础上, 开展了光学腔增强DLCZ量子记忆读出效率的实验研究. 通过读光失谐来调节腔膜与原子线之间的失谐, 减小腔膜与原子线共振造成的共振峰劈裂, 进而减小劈裂对读出效率腔增强的影响. 经研究得知: 当失谐大于80 MHz时, 读出效率趋于平缓, 当读光的失谐量为80 MHz时, 读出效率相比于无腔时增强了1.68倍, 对应的本质效率为
$ 45{{\% }} $ .
光学腔增强Duan-Lukin-Cirac-Zoller量子记忆读出效率的研究
Experimental study of retrieval efficiency of Duan-Lukin-Cirac-Zoller quantum memory by optical cavity-enhanced
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摘要: 量子中继是长距离纠缠分发的关键组成部分, 而基于原子系综存储的读出效率是量子中继能否实用化的一个重要指标. 本文利用冷原子系综中的自发拉曼散射过程产生Duan-Lukin-Cirac-Zoller量子记忆, 在原子系综周围搭建环形腔, 增强光与原子相互作用, 从而提高读出效率, 然而, 腔内原子的能级分裂使量子记忆的读出效率降低. 本文研究了读出效率随读光相对于原子共振线失谐量的变化关系. 结果显示: 当读光的失谐量为80 MHz时, 本质读出效率为45%, 这时腔对读出效率的增强倍数为1.68倍.Abstract:
Long-distance entanglement distribution is an important task for quantum communication, but difficult to achieve due to the loss of photons in optical fiber transmission. Quantum repeater is a scheme to solve this problem. In this scheme, the long distance of entanglement distribution is divided into several small parts, the entanglement is established first at both ends of each part, then, the entanglement distance is extended through the entanglement exchange of adjacent interval parts, in order to achieve the long distance entanglement distribution. Of them, the Duan-Lukin-Cirac-Zoller (DLCZ) protocol based on the cold atom ensemble and the linear optics which can generate and store entanglement, is regarded as one of the most potential schemes. In the process of DLCZ, retrieval efficiency is an important index of the quantum repeater, because it will influence each entanglement exchange operation between adjacent quantum repeater nodes. Generally, the retrieval efficiency is improved by optimizing the reading pulse, increasing the optical depth (OD) of the atomic ensemble and the cavity enhancement. The ring cavity constrains the light field to increase the intensity of the interaction between light and atoms, and effectively improve the retrieval efficiency of the quantum memory. In this work, atomic ensembles are placed in a ring cavity. The cavity length is 3.3 m and the fineness is 13.5. The optical loss of all ring cavity is 21%, mainly including 15% loss of other optical elements and 6% loss of the cell. In order to increase the retrieval efficiency, we need to ensure the mode resonance of read-out photon, write-out photon and locking. The cavity needs two input beams of light: one comes from the path of read-out photon and the other from the path of write-out photon in the reverse direction. The two beams are locked at the same frequency as the write-out photon and the read-out photon respectively. The cavity length is adjusted by moving the cavity mirrors’ positions through translating the frame, to make two light modes resonate. The acousto-optic modulator (AOM) is inserted into the path of the locking to control the frequency of the locking. By adjusting the AOM to change the frequency of the locking, the locking can be coincident with the write-out and read-out cavity modes. Then, the three-mode resonance can be achieved When the cavity mode resonates with the atomic line, it will lead the atomic formants to split. thereby affecting the enhancement effect of retrieval efficiency. In the experiment, the detuning of the read light will affect the frequency of the read-out photon, and further affect the detuning of the cavity mode with the resonance line of the atom. Thus, by increasing the detuning between the reading light and the atomic transition line, the frequency splitting between the two modes can be reduced, then enhance the retrieval efficiency. We study the relation between the enhancement factor of the retrieval efficiency and the detuning amount of the reading light relative to the atomic resonance line. The results show that when the detuning amount of reading light is 80 MHz, the intrinsic readout efficiency is 45%, and the readout efficiency is enhanced by 1.68 times. -
Key words:
- quantum memory /
- retrieval efficiency /
- optical ring cavity .
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图 1 (a)
$ {}^{87}{\text{Rb}} $ 原子能级. 其中左图为写过程,$ {\sigma ^+}\left( {{\sigma ^-}} \right) $ 分别代表左(右)旋圆偏振的斯托克斯光, W代表写光光场. 右图为读过程,$ {\sigma ^+}\left( {{\sigma ^-}} \right) $ 代表左(右)旋圆偏振的反斯托克斯光, R代表读光光场;$\varDelta$ 代表读光和写光相对于原子共振跃迁线的失谐; (b) 实验时序图, 图中Cleaning为态制备过程, Writing代表写过程, Reading代表读过程, Locking表示腔锁定时序, MOT代表冷原子俘获过程Figure 1. (a) Relevant
$ {}^{87}{\text{Rb}} $ atomic levels. The left is writing process,$ {\sigma ^+}\left( {{\sigma ^-}} \right) $ represents left (right) polarization of Stokes, W represents writing field. The right is reading process,$ {\sigma ^+}\left( {{\sigma ^-}} \right) $ represents left (right) polarization of anti-Stokes, R represents reading field;$\varDelta$ denotes the detuning of the reading and writing laser relative to the resonance transition; (b) time sequence of experimental cycle, Cleaning: the state cleaning process, Write: the writing process, Reading: the writing process, Locking: the locking cavity process, MOT: the cold atom preparation process.
图 2 实验装置示意图. 其中PZT代表压电陶瓷; BS为耦合镜; SPD1(SPD2)表示读接收(写接收)单光子探测器; Locking为锁腔光; Flipper为可折叠式镜架;
$ {\lambda / 2} $ 和$ {\lambda / 4} $ 分别为半玻片和四分之一玻片Figure 2. Experimental setup. PZT represents the piezoelectric ceramic transducer; BS, coupling mirror; SPD1(SPD2), read receive (write receive) single photon detector; Locking, the lock cavity light;
$ {\lambda / 2} $ and$ {\lambda / 4} $ , half wave plate and quarter wave plate. -
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