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As an important candidate for quantum simulation and quantum computation, a microscopic array of single atoms confined in optical dipole traps is advantageous in controlled interaction, long coherence time, and scalability of providing thousands of qubits in a small footprint of less than 1 mm2. Recently, several breakthroughs have greatly advanced the applications of neutral atom system in quantum simulation and quantum computation, such as atom-by-atom assembling of defect-free arbitrary atomic arrays, single qubit addressing and manipulating in two-dimensional and three-dimensional arrays, extending coherence time of atomic qubits, controlled-NOT (C-NOT) gate based on Rydberg interactions, high fidelity readout, etc.In this paper, the experimental progress of quantum computation based on trapped single neutral atoms is reviewed, along with two contributions done by single atom group in Wuhan Institute of Physics and Mathematics of Chinese Academy of Sciences. First, a magic-intensity trapping technique is developed and used to mitigate the detrimental decoherence effects which are induced by light shift and substantially enhance the coherence time to 225 ms which is 100 times as large as our previous coherence time thus amplifying the ratio between coherence time and single qubit operation time to 105. Second, the difference in resonant frequency between the two atoms of different isotopes is used to avoid crosstalking between individually addressing and manipulating nearby atoms. Based on this heteronuclear single atom system, the heteronuclear C-NOT quantum gate and entanglement of an Rb-85 atom and an Rb-87 atom are demonstrated via Rydberg blockade for the first time. These results will trigger the quests for new protocols and schemes to use the double species for quantum computation with neutral atoms. In the end, the challenge and outlook for further developing the neutral atom system in quantum simulation and quantum computation are also reviewed.
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Keywords:
- Rydberg state /
- single neutral atom /
- quantum entanglement /
- coherence time
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图 1 中性单原子量子计算的概念架构
Figure 1. Conceptual architecture for a neutral atom quantum computer.
图 2 远红失谐光聚焦形成的偶极阱和偶极阱中收集的单原子荧光信号
Figure 2. The optical dipole trap formed by strongly focusing far red-detuned laser. The fluorescence of single atoms trapped by the dipole trap.
图 3
$ ^{87}{\rm Rb} $ 原子能级和相关的冷却光$ I_{\rm cool} $ 、回泵光$ I_{\rm rep} $ 、态制备光$ I_{\rm pum} $ 和态探测光$ I_{\rm prob} $ 对应的跃迁(量子比特的$ |0\rangle $ 态和$ |1\rangle $ 态编码在$ F=1 $ ,$ m_F $ = 0和$ F=2 $ ,$ m_F=0 $ 上)Figure 3. The energy levels and lasers used for cooling, repumpiup ng, optical pumpiup ng, and state detection of
$ ^{87}{\rm Rb} $ . The ground hyperfine states of$ F=1 $ ,$ m_F=0 $ and$ F=2 $ ,$ m_F=0 $ are used for encoding the qubit.
图 4 (a)超极化率不可忽略情况下, 原子量子比特的微分光频移在不同磁场下随偶极阱势深的变化; (b)原子量子比特相干时间在不同偶极阱势深下的实验值, 蓝色实线为理论值; 内插图显示了阱深为
$ U_{\rm M} $ 时, 通过拟合Ramsey条纹的对比度得到相干时间为$ \tau= (225 \pm 21) $ ms[17]Figure 4. (a) In the presence of hyperpolarizability, the differential light shift (DLS) of a qubit in the circularly polarized trap is measured as a function of trap depths at various magnetic field strengths; (b) coherence time
$ \tau $ and its dependence on normalized ratios$ U/U_{\rm M} $ obtained from experiment. The solid blue line is the theoretical curve. A coherence time is extracted from a decay time of the envelope of Ramsey visibility, as shown as in the inset. At$ U_a= U_{\rm M} $ ,$ \tau= (225 \pm 21) $ ms[17].
图 5 (a)原子量子比特相干转移的实验装置示意图(Trap 1是可移动阱, 其在焦平面上的位置由2D声光偏转器控制; Trap 2是静止阱; 两阱的偏振可以通过液晶相位片(Thorlabs LCR-1-NIR)实时控制); (b) 原子量子比特在两阱中不转移(黑色方块)和转移(红色圆点)时的Ramsey条纹(实验数据中每个点是100多次实验的平均值; 通过衰减的正弦函数拟合(实线部分), 可以得到静止量子比特和转移量子比特的相干时间分别是(206
$ \pm $ 69) ms和(205$ \pm $ 74) ms[17]Figure 5. (a) Experimental setup for coherent transfer of atomic qubit. Trap 1 is a movable trap which can be shiftted in two orthogonal diretions by an AOD. Trap 2 is a static one. Both of their polarizations can be actively controlled by a liquid crystal retarder (LCR). (b) Measured Ramsey signals for single static qubits (black squares) and single mobile qubits (red dots) at
$ B = 3.115 $ G. Every point is an average over 100 experimental runs. The solid curves are fits to the damped sinusoidal function, with coherence times of static qubits and mobile qubits are (206$ \pm $ 69) ms and (205$ \pm $ 74) ms, respectively[17].
图 6 (a)
$ ^{85}{\rm Rb} $ 和$ ^{87}{\rm Rb} $ 的能级及相应的激光; (b) 实验光路示意图; (c)$ ^{87}{\rm Rb} $ 原子在$ |\!\!\uparrow\rangle $ 和$ |r\rangle $ 态间的相干Rabi振荡; 里德伯态激发光同时作用到$ ^{85} {\rm Rb}$ , 由于频率的差别,$ ^{85}{\rm Rb} $ 没有任何激发, 两原子间操作的串扰可忽略[20]Figure 6. (a) Energy levels and lasers of
$ ^{85}{\rm Rb} $ and$ ^{87}{\rm Rb} $ ; (b) experimental setup; (c) the coherent Rabi oscillation between$ |\!\!\uparrow\rangle $ and$ |r\rangle $ of$ ^{87}{\rm Rb} $ , there is no excitation of$ ^{85}{\rm Rb} $ although the Rydberg excitation lasers also act on it which shows negligible crosstalk between two atoms[20].
图 7 (a) 异核里德伯阻塞的时序; (b) 异核里德伯阻塞. 没有
$ ^{87}{\rm Rb} $ 时,$ ^{85}{\rm Rb} $ 展示了很好的基态到里德伯态的相干Rabi振荡, 当$ ^{87}{\rm Rb} $ 激发到里德伯态时, 由于异核里德伯阻塞,$ ^{85}{\rm Rb} $ 几乎没有Rabi振荡[20]Figure 7. (a) Time sequence for heteronuclear Rydberg blockade; (b) Rabi oscillations between the
$ ^{85}{\rm Rb} $ $ {\rm 5S_{1/2}}, F=3, m_F=0 $ and$ {\rm 79D_{5/2}}, m_j=5/2 $ states with and without$ ^{87}{\rm Rb} $ in Rydberg state[20].
图 8 (a) 异核C-NOT门的时序; (b) 不同输入态
$ |\!\!\downarrow\Uparrow\rangle $ (黑色方块)和$ |\!\!\uparrow\Uparrow\rangle $ (红色圆点)时, 输出态的布居随两个Raman$ {\text{π}}/2 $ 脉冲的振荡; 用正弦函数拟合后, 两个振荡间的相位差为$ (0.94 \pm 0.01) {\text{π}} $ ; (c) 初态制备的真值表; (d) 两个Raman$ {\text{π}}/2 $ 脉冲的相对相位设为0时, 测得的H-Cz型的C-NOT门的真值表[20]Figure 8. (a) Experimental time sequence of H-Cz C-NOT gate; (b) output states as a function of the relative phase between the Raman
$ {\text{π}}/2 $ pulses, for the initial states$ |\!\!\downarrow\Uparrow\rangle $ (black squares) and$ |\!\!\uparrow\Uparrow\rangle $ (red circles). The solid curves are sinusoidal fits yielding the phase difference of$ (0.94 \pm 0.01){\text{π}}$ between the two signals; (c) truth table matrix for the initial state preparation; (d) set the relative phase to be 0, the measured truth table matrix for H-Cz C-NOT gate[20]..
图 9 (a) 制备和测量异核两原子纠缠的时序; (b) 纠缠态的布居; (c) 宇称信号随测量脉冲相对相位的振荡, 拟合得到
$ |C_{1}|= 0.16 \pm 0.01 $ [20]Figure 9. (a) Time sequence for generating and verifying entanglement of two heteronuclear atoms; (b) measured probabilities for the entangled state; (c) the parity signal
$ P $ ; the solid curve is a sinusoidal fit with$ |C_{1}|= 0.16 \pm 0.01 $ [20].表 1 魔幻光强偶极阱中的退相干机制
Table 1. The mechanisms of decoherence in magic intensity optical trap.
87Rb 退相干机制 参数 无转移时$T_2 $ 转移后$T_2 $ 均匀退相时间$T'_{2} $
(Homogeneous dephasing time)磁场起伏 $ \sigma_B=0.019 $% 300 ms 300 ms 偶极光功率起伏 $ \sigma_I=0.0015 $ 200 s 200 s 偶极光重合及指向抖动 $ \sigma_{\rm{point}}=0.06 $ — 30 s 微波频率起伏 $ \sigma_{\rm MW} < 1 $ mHz $ > 300 $ s $ > 300 $ s 原子加热 2 μK/s 34 s 34 s 非均匀退相时间$T^{*}_{2} $
(Inhomogeneous dephasing time)原子热运动 约8 μK 2 s — 转移引起的加热 $ < 10\;{\text{μ}}{\rm K} $ — $ > 1.2 $ s 自旋翻转时间$T_{1} $ 偶极光引起的自旋翻转 0.66 $ {\rm s}\cdot {\rm mK}$ 4 s 4 s 总的退相干时间T $ T=1/(1/T_{1}+1/T^{*}_{2}+1/T^{'}_{2}) $ — 约242 ms 约222 ms 实验值 约200 ms 约200 ms 
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