Trapping of single atom and precise control of its coupling strength in micro-optical cavity

Yan Wei-Zhi; Fan Qing; Yang Peng-Fei; Li Gang; Zhang Peng-Fei; Zhang Tian-Cai

doi:10.7498/aps.72.20222220

Abstract

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1. 引　言
2. 光学微腔中单原子的俘获
3. 单原子与光学微腔耦合强度的调控
4. 总　结

References

Abstract

Cavity quantum electrodynamic system with strongly coupled single atoms provides a good platform for studying quantum information processing, quantum simulation, quantum network, and distributed quantum computing. Cooling and trapping single atoms is a crucial technique in the quantum technology. At present, in a high-finesse cavity with finite space, cooling and trapping single atoms is a big challenge, even though it is a mature technique for free space. Great efforts have been made to cool and trap single atoms inside a cavity, and for a trapped atom its lifetime has reached as long as tens of seconds. Developing a more flexible method of cooling and trapping single atoms in a cavity is still essential for a strongly coupled cavity quantum electrodynamic system. In this work, we demonstrate experimentally that a single cesium atom in a cavity can be trapped by utilizing a single optical tweezer settled in cavity mode, and its lifetime is (2.60 ± 0.18) s. The experiment is carried out in a Fabry-Perot cavity, which is assembled by two concave mirrors each with a curvature radius of 100 mm, and cavity length of 335 μm. The concave surfaces are highly reflective, and the cavity has a finesse of 6.1 × 10⁴. The 1080 nm optical tweezer with a waist of 2 μm is formed by an achromatic lens group with a numerical aperture of 0.4. At first, the precooled atomic assemble released from the magneto-optical trap (MOT) is transferred into cavity mode by an optical dipole trap with a waist of 36 μm. Then, one of the successfully transferred atoms is captured by the optical tweezer with the aid of cavity cooling mechanism. A blue detuned cavity locking laser is used as a standing-wave optical trap along the cavity axis. The signal of successfully trapped one atom is obtained by recording transmission of the cavity that will decrease owing to the strong coupling induced vacuum Rabi splitting. Finally, we demonstrate the precise manipulation of the atom-cavity coupling strength, which is achieved by scanning the position of the trapped atom step by step by using a high-precision translation stage. The system realized in this work can be used to study the dynamics of single atom-photon interactions with adjustable coupling strength. In addition, the mechanism adopted in this work is compatible with constructing tweezer arrays inside cavity mode, and thus possesses more flexibility and great potentials in cavity-based quantum entanglement and quantum simulation.

Keywords:

PACS:

42.50.-p	(Quantum optics)
37.10.De	(Atom cooling methods)
37.10.Gh	(Atom traps and guides)

Authors and contacts

1.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
2.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Li Gang, gangli@sxu.edu.cn ; Zhang Tian-Cai, tczhang@sxu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U21A6006, U21A20433, 11974223, 11974225, 12104277, 12104278), the National Key R&D Program of China (Grant No. 2021YFA1402002), and the Fund for Shanxi 1331 Project Key Subjects Construction, China.

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1. 引　言

强耦合腔量子电动力学(QED)系统是研究光与物质相互作用的重要平台, 在量子信息处理^[1-3]、量子网络^[4]、量子模拟^[5]和分布式的量子计算^[6,7]等方面具有重要的应用. 经过近30年的发展, 基于单原子的强耦合腔QED系统在量子存储^[8]、量子接口^[9]、量子纠缠^[10]等方面取得了一系列重要成果. 实现微腔内单个原子的俘获^[11,12]是基于单原子强耦合腔QED开展量子科技研究的关键技术.

由于空间受限、介入性差和系统的复杂性, 在微腔中单原子的冷却及俘获存在一定困难. 国内外研究者在腔内单原子的控制方面进行了系列研究, 提出了多种原子的冷却机制、传输及俘获方式. 腔内冷却机制包括腔内多普勒和西西弗斯冷却^[13-15]、腔致冷却^[16]、一维拉曼边带冷却^[17-19]、真空诱导的三维冷却^[20]等. 腔内原子的俘获方式从最初的热原子束^[21]、原子自由落体^[22,23]、原子喷泉^[24,25]等不可控的方式, 到腔内驻波阱俘获单原子^[26,27]及原子传输带结合腔内三维光晶格俘获单原子^[28]等. 腔内三维光晶格使得原子的外态被很好的控制^[29], 单原子寿命从几十毫秒逐渐延长至几十秒的量级^[29-32].

本文在实验上实现了微光学腔内单原子的俘获和耦合强度的操控. 通过在长度为336 µm的光学法布里-珀罗(F-P)腔内构建单个微尺度光学偶极阱(光镊), 实现了腔内单个原子的俘获, 俘获寿命为(2.60 ± 0.18) s, 从而获得了稳定的单原子与光学腔强耦合的腔QED系统. 实验中腔内单原子的俘获方式与现有基于三维光晶格的方式有较大区别: 首先, 原子在腔内的俘获位置由光学阱的位置唯一确定, 避免了对原子位置的二次调节; 其次, 本实验的光镊构建方式可进一步用于光偶极阱阵列的构建, 在腔内确定数目的原子装载及寻址方面具有更大的拓展优势. 该系统能够在三维方向上精确调节原子的位置, 从而实现原子与光学腔耦合强度的精确控制, 我们测量了不同耦合强度下的单原子真空拉比分裂谱. 此外, 该系统能够用于研究不同耦合强度下的单原子与光子相互作用的动力学特性^[33,34].

2. 光学微腔中单原子的俘获

实验装置如图1(a)所示, 水平放置的F-P腔由两面曲率半径为100 mm, 透射率分别为10^–5和10^–4的超高反射率镜片构成. 腔长为336 μm, 腔模腰斑半径为33.3 μm. 该系统腔QED的参数为(g, κ, γ) = 2π ×(8.6, 5.2, 2.6) MHz, 其中g为原子-腔的最大耦合强度(与铯原子6S_1/2|F = 4, m_F = ±4 $\rangle$ ↔6P_3/2|F' = 5, m_F = ±5 $\rangle$ 跃迁耦合), κ为腔场衰减率, γ为原子的极化衰减率.

$图 1 (a)实验装置示意图. 微光学F-P腔水平放置, 磁光阱(MOT)位于左侧约8 mm处, MOT释放后的铯原子团经光学“传送阱”(蓝色光束, transfer beam)传输至腔模内. 垂直于腔轴的四束对射光(紫色光束, PGC)用于腔内原子冷却, 单个光镊(红色光束, trap beam)用于俘获单个原子. (b)原子传输过程中的光学“传送阱”(36 μm ODT, transfer beam)和光镊(2 μm ODT, trap beam)引起的MOT与腔模之间势能的空间分布, 其阱深分别为–229 μK和–800 μK\r\nFig. 1. (a) Schematic experimental setup. The micro-sized optical F-P cavity is located horizontally, magneto-optical trap (MOT) is about 8 mm to the left. The cesium atoms released from the MOT are transferred into the cavity mode by an optical “conveyor trap” (blue beam, transfer beam) and an optical tweezer (red beam, trap beam) counter-propagating with the belt is used to trap a single atom. Four beams perpendicular to the cavity axis (purple beams, PGC) are for intra-cavity atom cooling. (b) The potential associated with the optical “conveyor trap” (36 μm ODT, transfer beam) and the optical tweezer (2 μm ODT, trap beam) between the MOT and the cavity mode. The corresponding well depths are –229 and –800 μK, respectively.$

图 1 (a)实验装置示意图. 微光学F-P腔水平放置, 磁光阱(MOT)位于左侧约8 mm处, MOT释放后的铯原子团经光学“传送阱”(蓝色光束, transfer beam)传输至腔模内. 垂直于腔轴的四束对射光(紫色光束, PGC)用于腔内原子冷却, 单个光镊(红色光束, trap beam)用于俘获单个原子. (b)原子传输过程中的光学“传送阱”(36 μm ODT, transfer beam)和光镊(2 μm ODT, trap beam)引起的MOT与腔模之间势能的空间分布, 其阱深分别为–229 μK和–800 μK

Fig. 1. (a) Schematic experimental setup. The micro-sized optical F-P cavity is located horizontally, magneto-optical trap (MOT) is about 8 mm to the left. The cesium atoms released from the MOT are transferred into the cavity mode by an optical “conveyor trap” (blue beam, transfer beam) and an optical tweezer (red beam, trap beam) counter-propagating with the belt is used to trap a single atom. Four beams perpendicular to the cavity axis (purple beams, PGC) are for intra-cavity atom cooling. (b) The potential associated with the optical “conveyor trap” (36 μm ODT, transfer beam) and the optical tweezer (2 μm ODT, trap beam) between the MOT and the cavity mode. The corresponding well depths are –229 and –800 μK, respectively.

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冷原子初始被俘获在位于腔模的水平一侧约8 mm处的三维磁光阱(MOT)中. MOT中制备的冷原子由传输光所形成的偶极阱(图1蓝色光束, transfer beam)传输到光学腔中^[20], 该偶极阱由一束波长为1064 nm的红失谐激光聚焦形成, 水平连接MOT和腔模, 其束腰半径为36 μm, 阱深为–229 μK, 束腰位于MOT和腔模的中间位置, 距离腔模约4 mm. 从MOT释放的铯原子被传输光俘获, 并在该激光的引导下以“荡秋千”的方式进入光学微腔内(图1(a)中灰色曲线及图1(b)为光学“传送阱”和光镊引起势能的空间分布), 最终被腔中的单个光镊(图1红色光束, trap beam)俘获. 该光镊由一束1080 nm的激光通过高数值孔径透镜组(NA = 0.4)强聚焦形成, 与传输光呈对射状态, 该光镊的阱深约为–0.8 mK, 束腰半径为2.1 μm. 如图1(b)所示, 铯原子团经光学“传送阱”传输至腔模后绝热地关断“传送阱”, 同时绝热地开启光镊, 单个铯原子最终被俘获于光镊中. 原子在两个阱中的转移过程需要原子冷却手段进行辅助, 如图1中紫色光束(PGC)所示, 四束两两对射的冷却光垂直于腔轴且与水平方向呈45°, 穿过腔模中心区域, 其束腰直径为210 μm, 位于腔模中心. 冷却光的频率相对于铯原子D2线跃迁6S_1/2|F = 4 $\rangle$ ↔6P_3/2|F' = 5 $\rangle$ 负失谐30 MHz. 与此同时, 波长为894 nm的再泵浦光(频率共振于跃迁 6S_1/2|F = 3 $\rangle$ ↔6P_3/2|F' = 4 $\rangle$ )也作用于原子, 将冷却过程中弛豫到6S_1/2|F = 3 $\rangle$ 态的原子再泵浦到6S_1/2|F = 4 $\rangle$ 态. 利用841 nm的蓝失谐光场稳定光学微腔的腔长, 该光场在腔内沿腔轴方向形成蓝失谐的驻波偶极阱, 阱深约500 μK. 原子在频率蓝移的光场中感受到的势能为正, 光强空间分布形成的偶极力将原子推向光强弱的地方. 因此, 偶极力作用使原子被束缚于驻波的波节处, 即光强最弱的地方. 基于红失谐“碰撞阻挡效应”^[35,36], 实验中单原子的制备效率约为50%.

实验中光学微腔的频率 ${\omega _{\text{c}}}$ 与铯原子跃迁6S_1/2|F = 4 $\rangle$ ↔6P_3/2|F' = 5 $\rangle$ 共振. 一束与光学腔共振的852 nm探测光通过透射率为10^–5腔镜注入, 在弱激发情况下(腔内平均光子数远小于1)对原子进行探测, 腔透射信号由单光子探测器(SPCM)记录. 当有原子进入腔模时, 由于原子和光学腔的耦合, 原本与光学腔共振的探测光由于原子和腔强耦合产生的正交模式分裂, 使其透射降低. 图2(a)为SPCM记录的腔内单原子被俘获并逃逸的腔透射. 为了判断单个原子是否进入腔模并被成功俘获, 分别记录了空腔的透射计数(蓝色)和俘获单原子后腔透射计数(红色)的分布直方图, 如图2(b)所示, 实线为相应的泊松分布函数的拟合. 通过设定特定的阈值n, 实现对单原子成功俘获事件的定量化衡量. 当阈值设定为40时, 由泊松分布函数拟合, 计算得到实验中单原子成功俘获的判断准确率为98.5%.

$图 2 (a)腔内单原子信号; (b)腔透射计数分布直方图, 分别展示了空腔透射(蓝色)和俘获单原子后的腔透射(红色)计数分布及相应的泊松分布函数拟合(实线), 取阈值计数40作为鉴别俘获单个原子成功与否的判断标准\r\nFig. 2. (a) Transmission counts of cavity with one atom being trapped. (b) Histogram of cavity transmission counts. Histogram of the empty-cavity transmission (blue) and the cavity with a single atom trapped inside (red). The solid cures are the corresponding fittings by Poisson distribution. Photon count of 40 is taken as threshold to discriminate the trapping of single atom.$

图 2 (a)腔内单原子信号; (b)腔透射计数分布直方图, 分别展示了空腔透射(蓝色)和俘获单原子后的腔透射(红色)计数分布及相应的泊松分布函数拟合(实线), 取阈值计数40作为鉴别俘获单个原子成功与否的判断标准

Fig. 2. (a) Transmission counts of cavity with one atom being trapped. (b) Histogram of cavity transmission counts. Histogram of the empty-cavity transmission (blue) and the cavity with a single atom trapped inside (red). The solid cures are the corresponding fittings by Poisson distribution. Photon count of 40 is taken as threshold to discriminate the trapping of single atom.

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图3(a)为腔内单原子俘获的实验时序示意图. 36 μm偶极阱(ODT)将MOT释放的原子传输进腔模, 在第1100 ms被绝热地关闭, 同时腔内的单个微尺度(2 μm ODT)光镊被绝热地开启, 传输过来的原子被转移进该光镊中. 在原子转移过程中, 用侧向PGC光(图1紫色光束)辅助装载, 在红失谐PGC光的辅助碰撞下, 光镊中俘获单个原子. 光镊阱深为–0.8 mK时, 被俘获原子的轴向和径向振动频率的理论计算值分别为3.97和34.30 kHz. 完成单原子俘获后, 绝热地降低光镊的阱深, 在浅阱中对原子做第二次PGC(1130 ms时刻), 进一步冷却原子. 俘获到光镊中的原子寿命由两次探测确定: 第一次测量在俘获原子的初始t₀时刻判断原子是否被俘获住, 由第二次测量确定原子的俘获概率, 两次探测的时间间隔为t, 从而得到俘获概率随时间t的变化(图3(b)), 从而能够测量腔内原子的俘获寿命. 我们在实验上实现了平均(2.60 ± 0.18) s的腔内单原子俘获寿命. 目前, 实验获得的单原子俘获寿命主要受限于过高的原子温度以及偶极阱激光强度噪声的影响. 采用腔电磁感应透明(EIT)冷却手段^[37]降低原子温度, 同时采用光电反馈技术抑制原子谐振频率范围内的激光器噪声, 有望进一步提高原子的俘获寿命.

$图 3 (a)实验时序示意图 (阴影填充部分表示实验中所控制光功率随时序的变化, 坐标轴未按比例绘制); (b)腔内单原子俘获概率随时间的变化 (蓝色圆点表示在t0时刻成功俘获单原子100次, 不同t时刻SPCM计数平均值低于阈值的概率; 蓝色实线为实验数据的e指数拟合, 拟合得到原子寿命为(2.60 ± 0.18) s)\r\nFig. 3. (a) Experimental time sequence (Shaded parts indicate the changes of the optical power in the experiment, and the scale of the time axis is distorted for clarity); (b) the dependence of the survival probability of single atom in the cavity on storage time (The blue dots represent the averaged probability at different storage time t at the case of successfully trapping of one atom at time t0. The probability is obtained with 100 times of experiment trial. The blue solid line indicates data fitting with an exponential function and the fitted lifetime is (2.60 ± 0.18) s).$

图 3 (a)实验时序示意图 (阴影填充部分表示实验中所控制光功率随时序的变化, 坐标轴未按比例绘制); (b)腔内单原子俘获概率随时间的变化 (蓝色圆点表示在t₀时刻成功俘获单原子100次, 不同t时刻SPCM计数平均值低于阈值的概率; 蓝色实线为实验数据的e指数拟合, 拟合得到原子寿命为(2.60 ± 0.18) s)

Fig. 3. (a) Experimental time sequence (Shaded parts indicate the changes of the optical power in the experiment, and the scale of the time axis is distorted for clarity); (b) the dependence of the survival probability of single atom in the cavity on storage time (The blue dots represent the averaged probability at different storage time t at the case of successfully trapping of one atom at time t₀. The probability is obtained with 100 times of experiment trial. The blue solid line indicates data fitting with an exponential function and the fitted lifetime is (2.60 ± 0.18) s).

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3. 单原子与光学微腔耦合强度的调控

当原子被光镊俘获后, 原子与光学微腔的耦合强度可以通过精确调节光镊的空间位置实现. F-P腔中的光场模式为基模高斯光(TEM00模)形成的驻波场, 光场强度在垂直于腔轴平面(X-Y平面)上服从高斯分布, 耦合强度在X-Y平面内也服从高斯分布:

$g(r)={g}_{0}{\text{e}}^{-{(r-{r}_{0})}^{2}/{w}^{2}} \text{, }$

(1)

式中 ${g_0}$ 为原子-腔的最大耦合强度, r表示原子的位置, r₀表示腔模中心的坐标, w为腔模束腰半径. 在沿腔轴(Z轴)方向, 用于腔锁定的841 nm光在该方向形成驻波蓝失谐偶极阱, 原子最终被束缚在蓝失谐偶极阱的节点处. 该锁腔光的频率与腔探测光频率相差11个自由光谱区, 在腔模中心处, 其驻波的波节与探测光的波腹完美重合, 耦合最大. 俘获在841 nm驻波偶极阱中的原子耦合强度g(z)沿腔轴向腔中心两侧逐渐递减, 归一化后服从关系:

$g(z)/{g_0} = \sqrt {\frac{1}{2}\left( {1 + \cos \frac{{2{\text{π }}z{\lambda _1}}}{{{\lambda _2}}}} \right)} \text{, }$

(2)

其中 ${\lambda _1}$ = 852 nm, ${\lambda _2}$ = 841 nm.

实验上原子与腔的耦合强度通过扫描真空拉比分裂谱来确定. 在此过程中, 保持腔与原子跃迁线共振, 扫描探测光与原子的频率失谐, 记录原子-光学腔耦合系统的透射即可获得真空拉比分裂谱. 当光镊位于光学腔中心时, 其俘获的单原子与光学腔耦合最大, 相应的真空拉比分裂谱如图4所示. 由理论公式^[38]

$图 4 原子与光学腔耦合最大时的真空拉比分裂谱, 拟合得到其最大的光与原子耦合强度为${{{g_0}} / {(2}}{\text{π}}) =( 8.10 \pm $$ 0.16 ){\text{ MHz}}$\r\nFig. 4. Experimental vacuum rabi splitting corresponds to the maximum atom-cavity coupling. The coupling strength between atom and cavity is ${{{g_0}} \mathord{\left/ {\vphantom {{{g_0}} {(2}}} \right. } {(2}}{\text{π)}} = \left( {8.10 \pm 0.16} \right){\text{ MHz}}$.$

图 4 原子与光学腔耦合最大时的真空拉比分裂谱, 拟合得到其最大的光与原子耦合强度为

${{{g_0}} / {(2}}{\text{π}}) =( 8.10 \pm$

$0.16 ){\text{ MHz}}$

Fig. 4. Experimental vacuum rabi splitting corresponds to the maximum atom-cavity coupling. The coupling strength between atom and cavity is

${{{g_0}} \mathord{\left/ {\vphantom {{{g_0}} {(2}}} \right. } {(2}}{\text{π)}} = \left( {8.10 \pm 0.16} \right){\text{ MHz}}$

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$T = \frac{{{\kappa ^2}({\gamma ^2} + \varDelta _{{\text{pa}}}^2)}}{{{{({g_{\text{eff}}^2} - \varDelta _{{\text{pa}}}^2 + {\varDelta _{{\text{ca}}}}{\varDelta _{{\text{pa}}}} + \gamma \kappa )}^2} + {{(\kappa {\varDelta _{{\text{pa}}}} + \gamma {\varDelta _{{\text{pa}}}} - \gamma {\varDelta _{{\text{ca}}}})}^2}}} \text{, }$

(3)

拟合得到最大的原子与光学腔的耦合强度为 ${{{g_0}} \mathord{\left/ {\vphantom {{{g_0}} {(2}}} \right. } {(2}}{\text{π )}} = \left( {8.10 \pm 0.16} \right){\text{ MHz}}$ . 其中 ${\varDelta _{{\text{pa}}}}$ 和 ${\varDelta _{{\text{ca}}}}$ 分别是探测光与原子和光学腔与原子之间的频率失谐, ${g}_{\text{eff}}$ 为原子和腔的有效耦合强度.

1080 nm光镊整个光路搭建在平移台(Newport, 型号M-562 F-XYZ)上. 该平移台由测微计(型号DM-13)控制, 调节精度为0.5 μm. 在三维方向上, 通过精确控制1080 nm光镊的位置即可控制原子的位置, 实现耦合强度的调控. 图5(a)为测量的耦合强度在径向(X和Y方向)随着位置的变化, 通过(1)式拟合得到相应的腔模束腰半径分别为w_x= (36.7±0.2) μm, w_y= (35.50±0.17) μm, 与理论计算的腰斑半径33.3 μm基本一致. 图5(b)为耦合强度在Z方向上的调节, 实验结果及拟合曲线(黄色实线)没有达到最小值0, 与(2)式的预期存在偏差. 该偏差主要来源于光镊内温度不为零的单个原子在腔轴方向运动导致的腔与原子耦合因子在空间上的平均效应; 其次, 控制光镊位置的平移台调节精度为500 nm, 很难将偶极阱恰好定位于耦合为0处(该区域为半波长量级). 通过进一步冷却原子温度以及提高平移台的精度, 可以减小该偏差, 并在实验上精确调节原子的位置, 实现单个原子与高精细度光学微腔耦合的高精度操控.

$图 5 通过扫描单原子在腔中的位置实现原子与腔耦合强度的精确调节　(a)与腔耦合的单个原子分别沿X (红色圆点)和Y (蓝色圆点)方向扫描时, 耦合强度大小随位置的变化 (红色和蓝色实线分别表示高斯函数拟合的结果); (b)单原子沿Z轴(黄色圆点)方向扫描, 原子处于腔内晶格不同节点时, 耦合强度的大小变化趋势(黄色实线表示与(2)式的预期一致)\r\nFig. 5. Manipulation of the atom-cavity coupling by scanning the position of a single atom in cavity: (a) The position is scanned along X (red circles) and Y (blue circles) axis (Red and blue solid curves are the data fitting by Gaussian functions); (b) position is scanned along cavity axis (Z-axis), the coupling strength with atom trapped on different nodes of the blue trap along Z is in good agreement with the prediction (yellow solid line) of Eq. (2).$

图 5 通过扫描单原子在腔中的位置实现原子与腔耦合强度的精确调节　(a)与腔耦合的单个原子分别沿X (红色圆点)和Y (蓝色圆点)方向扫描时, 耦合强度大小随位置的变化 (红色和蓝色实线分别表示高斯函数拟合的结果); (b)单原子沿Z轴(黄色圆点)方向扫描, 原子处于腔内晶格不同节点时, 耦合强度的大小变化趋势(黄色实线表示与(2)式的预期一致)

Fig. 5. Manipulation of the atom-cavity coupling by scanning the position of a single atom in cavity: (a) The position is scanned along X (red circles) and Y (blue circles) axis (Red and blue solid curves are the data fitting by Gaussian functions); (b) position is scanned along cavity axis (Z-axis), the coupling strength with atom trapped on different nodes of the blue trap along Z is in good agreement with the prediction (yellow solid line) of Eq. (2).

下载: 全尺寸图片幻灯片

4. 总　结

实验上实现了微光学腔内单原子的俘获和耦合强度的精密操控. 通过在长度为336 µm的光学F-P腔内构建单个微尺度 (2.1 μm) 光学偶极阱, 实现了腔内单个原子的俘获, 俘获寿命为(2.60 ± 0.18) s, 从而获得了稳定的单原子与光学腔强耦合的腔QED系统. 通过在三维方向上精确调节原子的位置, 实现了原子与光学腔耦合强度的精确控制, 测量了不同耦合强度下的单原子真空拉比分裂谱. 该系统能够用于研究耦合强度可调的单原子与光子相互作用的动力学特性^[33,34]. 此外, 该系统克服了受限狭小空间中确定数目原子装载的困难, 具有腔内确定性原子阵列的扩展并开展多原子量子纠缠^[39,40]、量子模拟^[41]等研究的潜力.

References

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[11]	王婧, 何军, 张天才, 王军民 2008 物理 37 103 Wang J, He J, Zhang T C, Wang J M 2008 Physics 37 103
[12]	Maunz P, Puppe T, Schuster I, Syassen N, Pinkse P W H, Rempe G 2004 Nature 428 50 Google Scholar
[13]	Horak P, Hechenblaikner G, Gheri K M, Stecher H, Ritsch H 1997 Phys. Rev. Lett. 79 4974 Google Scholar
[14]	Vuletic V, Chu S 2000 Phys. Rev. Lett. 84 3787 Google Scholar
[15]	Chan H W, Black A T, Vuletic V 2003 Phys. Rev. Lett. 90 063003 Google Scholar
[16]	Murr K, Nussmann S, Puppe T, Hijlkema M, Weber B, Webster S C, Kuhn A, Rempe G 2006 Phys. Rev. A 73 063415 Google Scholar
[17]	Thompson J D, Tiecke T G, Zibrov A S, Vuletic V, Lukin M D 2013 Phys. Rev. Lett. 110 133001 Google Scholar
[18]	Lester B J, Kaufman A M, Regal C A 2014 Phys. Rev. A 90 011804 Google Scholar
[19]	Lee H J, Adams C S, Kasevich M, Chu S 1996 Phys. Rev. Lett. 76 2658 Google Scholar
[20]	Nussmann S, Murr K, Hijlkema M, Weber B, Kuhn A, Rempe G 2005 Nat. Phys. 1 122 Google Scholar
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[22]	Hood C J, Chapman M S, Lynn T W, Kimble H J 1998 Phys. Rev. Lett. 80 4157 Google Scholar
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图 1 (a)实验装置示意图. 微光学F-P腔水平放置, 磁光阱(MOT)位于左侧约8 mm处, MOT释放后的铯原子团经光学“传送阱”(蓝色光束, transfer beam)传输至腔模内. 垂直于腔轴的四束对射光(紫色光束, PGC)用于腔内原子冷却, 单个光镊(红色光束, trap beam)用于俘获单个原子. (b)原子传输过程中的光学“传送阱”(36 μm ODT, transfer beam)和光镊(2 μm ODT, trap beam)引起的MOT与腔模之间势能的空间分布, 其阱深分别为–229 μK和–800 μK

Figure 1. (a) Schematic experimental setup. The micro-sized optical F-P cavity is located horizontally, magneto-optical trap (MOT) is about 8 mm to the left. The cesium atoms released from the MOT are transferred into the cavity mode by an optical “conveyor trap” (blue beam, transfer beam) and an optical tweezer (red beam, trap beam) counter-propagating with the belt is used to trap a single atom. Four beams perpendicular to the cavity axis (purple beams, PGC) are for intra-cavity atom cooling. (b) The potential associated with the optical “conveyor trap” (36 μm ODT, transfer beam) and the optical tweezer (2 μm ODT, trap beam) between the MOT and the cavity mode. The corresponding well depths are –229 and –800 μK, respectively.

DownLoad: Full-Size Img PowerPoint

图 2 (a)腔内单原子信号; (b)腔透射计数分布直方图, 分别展示了空腔透射(蓝色)和俘获单原子后的腔透射(红色)计数分布及相应的泊松分布函数拟合(实线), 取阈值计数40作为鉴别俘获单个原子成功与否的判断标准

Figure 2. (a) Transmission counts of cavity with one atom being trapped. (b) Histogram of cavity transmission counts. Histogram of the empty-cavity transmission (blue) and the cavity with a single atom trapped inside (red). The solid cures are the corresponding fittings by Poisson distribution. Photon count of 40 is taken as threshold to discriminate the trapping of single atom.

DownLoad: Full-Size Img PowerPoint

图 3 (a)实验时序示意图 (阴影填充部分表示实验中所控制光功率随时序的变化, 坐标轴未按比例绘制); (b)腔内单原子俘获概率随时间的变化 (蓝色圆点表示在t₀时刻成功俘获单原子100次, 不同t时刻SPCM计数平均值低于阈值的概率; 蓝色实线为实验数据的e指数拟合, 拟合得到原子寿命为(2.60 ± 0.18) s)

Figure 3. (a) Experimental time sequence (Shaded parts indicate the changes of the optical power in the experiment, and the scale of the time axis is distorted for clarity); (b) the dependence of the survival probability of single atom in the cavity on storage time (The blue dots represent the averaged probability at different storage time t at the case of successfully trapping of one atom at time t₀. The probability is obtained with 100 times of experiment trial. The blue solid line indicates data fitting with an exponential function and the fitted lifetime is (2.60 ± 0.18) s).

DownLoad: Full-Size Img PowerPoint

图 4 原子与光学腔耦合最大时的真空拉比分裂谱, 拟合得到其最大的光与原子耦合强度为 ${{{g_0}} / {(2}}{\text{π}}) =( 8.10 \pm$ $0.16 ){\text{ MHz}}$

Figure 4. Experimental vacuum rabi splitting corresponds to the maximum atom-cavity coupling. The coupling strength between atom and cavity is ${{{g_0}} \mathord{\left/ {\vphantom {{{g_0}} {(2}}} \right. } {(2}}{\text{π)}} = \left( {8.10 \pm 0.16} \right){\text{ MHz}}$ .

DownLoad: Full-Size Img PowerPoint

图 5 通过扫描单原子在腔中的位置实现原子与腔耦合强度的精确调节　(a)与腔耦合的单个原子分别沿X (红色圆点)和Y (蓝色圆点)方向扫描时, 耦合强度大小随位置的变化 (红色和蓝色实线分别表示高斯函数拟合的结果); (b)单原子沿Z轴(黄色圆点)方向扫描, 原子处于腔内晶格不同节点时, 耦合强度的大小变化趋势(黄色实线表示与(2)式的预期一致)

Figure 5. Manipulation of the atom-cavity coupling by scanning the position of a single atom in cavity: (a) The position is scanned along X (red circles) and Y (blue circles) axis (Red and blue solid curves are the data fitting by Gaussian functions); (b) position is scanned along cavity axis (Z-axis), the coupling strength with atom trapped on different nodes of the blue trap along Z is in good agreement with the prediction (yellow solid line) of Eq. (2).

DownLoad: Full-Size Img PowerPoint

[1]	Ritter S, Nolleke C, Hahn C, Reiserer A, Neuzner A, Uphoff M, Mucke M, Figueroa E, Bochmann J, Rempe G 2012 Nature 484 195 Google Scholar
[2]	Reiserer A, Rempe G 2015 Rev. Mod. Phys. 87 1379 Google Scholar
[3]	Yang C P, Chu S I, Han S 2004 Phys. Rev. A 70 022329 Google Scholar
[4]	Daiss S, Langenfeld S, Welte S, Distante E, Thomas P, Hartung L, Morin O, Rempe G 2021 Science 371 614 Google Scholar
[5]	Hartmann M J 2016 J. Opt. 18 104005 Google Scholar
[6]	Kaufman A M, Lester B J, Foss Feig M, Wall M L, Rey A M, Regal C A 2015 Nature 527 208 Google Scholar
[7]	Pellizzari T, Gardiner S A, Cirac J I, Zoller P 1995 Phys. Rev. Lett. 75 3788 Google Scholar
[8]	Li J F, Wang Y F, Su K Y, Liao K Y, Zhang S C, Yan H, Zhu S L 2019 Chin. Phys. Lett. 36 074202 Google Scholar
[9]	Cho J Y, Lee H W 2004 Phys. Rev. A 70 034305 Google Scholar
[10]	Strobel H, Muessel W, Linnemann D, Zibold T, Hume D B, Pezze L, Smerzi A, Oberthaler M K 2014 Science 345 424 Google Scholar
[11]	王婧, 何军, 张天才, 王军民 2008 物理 37 103 Wang J, He J, Zhang T C, Wang J M 2008 Physics 37 103
[12]	Maunz P, Puppe T, Schuster I, Syassen N, Pinkse P W H, Rempe G 2004 Nature 428 50 Google Scholar
[13]	Horak P, Hechenblaikner G, Gheri K M, Stecher H, Ritsch H 1997 Phys. Rev. Lett. 79 4974 Google Scholar
[14]	Vuletic V, Chu S 2000 Phys. Rev. Lett. 84 3787 Google Scholar
[15]	Chan H W, Black A T, Vuletic V 2003 Phys. Rev. Lett. 90 063003 Google Scholar
[16]	Murr K, Nussmann S, Puppe T, Hijlkema M, Weber B, Webster S C, Kuhn A, Rempe G 2006 Phys. Rev. A 73 063415 Google Scholar
[17]	Thompson J D, Tiecke T G, Zibrov A S, Vuletic V, Lukin M D 2013 Phys. Rev. Lett. 110 133001 Google Scholar
[18]	Lester B J, Kaufman A M, Regal C A 2014 Phys. Rev. A 90 011804 Google Scholar
[19]	Lee H J, Adams C S, Kasevich M, Chu S 1996 Phys. Rev. Lett. 76 2658 Google Scholar
[20]	Nussmann S, Murr K, Hijlkema M, Weber B, Kuhn A, Rempe G 2005 Nat. Phys. 1 122 Google Scholar
[21]	Turchette Q A, Hood C J, Lange W, Mabuchi H, Kimble H J 1995 Phys. Rev. Lett. 75 4710 Google Scholar
[22]	Hood C J, Chapman M S, Lynn T W, Kimble H J 1998 Phys. Rev. Lett. 80 4157 Google Scholar
[23]	Mabuchi H, Turchette Q A, Chapman M S, Kimble H J 1996 Opt. Lett. 21 1393 Google Scholar
[24]	Munstermann P, Fischer T, Maunz P, Pinkse P W H, Rempe G 1999 Phys. Rev. Lett. 82 3791 Google Scholar
[25]	Munstermann P, Fischer T, Pinkse P W H, Rempe G 1999 Opt. Commun. 159 63 Google Scholar
[26]	Kuhr S, Alt W, Schrader D, Muller M, Gomer V, Meschede D 2001 Science 293 278 Google Scholar
[27]	Dotsenko I, Alt W, Khudaverdyan M, Kuhr S, Meschede D, Miroshnychenko Y, Schrader D, Rauschenbeutel A 2005 Phys. Rev. Lett. 95 033002 Google Scholar
[28]	Reiserer A, Nolleke C, Ritter S, Rempe G 2013 Phys. Rev. Lett. 110 223003 Google Scholar
[29]	Koch M, Sames C, Kubanek A, Apel M, Balbach M, Ourjoumtsev A, Pinkse P W H, Rempe G 2010 Phys. Rev. Lett. 105 173003 Google Scholar
[30]	Doherty A C, Lynn T W, Hood C J, Kimble H J 2000 Phys. Rev. A 63 013401 Google Scholar
[31]	Ye J, Vernooy D W, Kimble H J 1999 Phys. Rev. Lett. 83 4987 Google Scholar
[32]	McKeever J, Buck J R, Boozer A D, Kuzmich A, Nagerl H C, Stamper Kurn D M, Kimble H J 2003 Phys. Rev. Lett. 90 133602 Google Scholar
[33]	Madsen K H, Ates S, Lund-Hansen T, Loffler A, Reitzenstein S, Forchel A, Lodahl P 2011 Phys. Rev. Lett. 106 233601 Google Scholar
[34]	Cimmarusti A D, Yan Z, Patterson B D, Corcos L P, Orozco L A, Deffner S 2015 Phys. Rev. Lett. 114 233602 Google Scholar
[35]	Schlosser N, Reymond G, Grangier P 2002 Phys. Rev. Lett. 89 023005 Google Scholar
[36]	Kuppens S J M, Corwin K L, Miller K W, Chupp T E, Wieman C E 2000 Phys. Rev. A 62 013406 Google Scholar
[37]	Kampschulte T, Alt W, Brakhane S, Eckstein M, Reimann R, Widera A, Meschede D 2010 Phys. Rev. Lett. 105 153603 Google Scholar
[38]	Thompson R J, Rempe G, Kimble H J 1992 Phys. Rev. Lett. 68 1132 Google Scholar
[39]	Zhang Z J, Liu Y, Man Z X 2005 Commun. Theor. Phys. 44 847 Google Scholar
[40]	Lucke B, Scherer M, Kruse J, Pezze L, Deuretzbacher F, Hyllus P, Topic O, Peise J, Ertmer W, Arlt J, Santos L, Smerzi A, Klempt C 2011 Science 334 773 Google Scholar
[41]	赵旭, 赵兴东, 景辉 2013 物理学报 62 060302 Google Scholar Zhao X, Zhao X D, Jing H 2013 Acta Phys. Sin. 62 060302 Google Scholar

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Vol. 72, Issue 11 - 2023-06-05

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