1.State Key Laboratory of Quantum Optics and Quantum Optics Devices, and Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China 2.Collaborative Innovation Center of Extreme Optics, the Ministry of Education and Shanxi Province, Shanxi University, Taiyuan 030006, China
Fund Project:Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304502), the National Natural Science Foundation of China (Grant Nos. 11774210, 61875111, 61475091), and the Shanxi Provincial 1331 Projects for Key Subjects Construction.
Received Date:27 December 2018
Accepted Date:29 January 2019
Available Online:23 March 2019
Published Online:05 April 2019
Abstract:A narrow-linewidth continuous-wave single-frequency tunable 318.6-nm ultraviolet laser system with watt-level output power is developed in our experiment based on well-developed fiber lasers, fiber amplifiers, and efficient laser frequency conversion technique. Cesium 6S1/2—nP3/2 (n = 70—94) single-photon Rydberg excitation in a room-temperature cesium atomic vapor cell is realized by using our ultraviolet laser system. The single-photon Rydberg excitation signal is obtained via the V-type three-level atomic system which contains 6S1/2 (F = 4) ground state, 6P3/2 (F = 5) excited state and one of nP3/2 (n = 70—94) Rydberg states. When cesium atoms populated on the ground state are partially excited to Rydberg state by the ultraviolet laser, absorption of 852.3-nm probe beam which is locked to 6S1/2 (F = 4)—6P3/2 (F ′ = 5) hyperfine transition will decrease. In this way, the cesium Rydberg states are detected. The quantum defects for cesium nP3/2 (n = 70—94) Rydberg states are experimentally measured with a high-precision wavemeter. The variation trend of experimentally measured data deviates from that of calculated values. Due to the fact that the cesium vapor cell is positioned in a magnetic shielding tank, the Zeeman effect can be ignored. Considering that the polarizability of Rydberg atoms is proportional to (n*)7, in which n* is the effective principal quantum number, the Rydberg screen effect of cesium atomic vapor cell cannot completely protect cesium atoms from being perturbed by an external DC electric field. Therefore the residual DC electric field existing inside the cesium vapor cell will have a significant influence on quantum defect measurement of Rydberg atoms. Using the theoretical model of Stark effect and the relationship between polarizability of Rydberg atoms and the effective principal quantum number n*, the corrected experimental value of quantum defect for cesium nP3/2 (n = 70—94) Rydberg states is found to be ~(3.5591 ± 0.0007). The corrected experimental value of quantum defect is consistent with the calculation. Keywords:cesium Rydberg atoms/ single-photon excitation/ quantum defect/ Rydberg screen effect
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2.原理及实验方案与铯原子的低激发态不同, 高激发里德伯态的跃迁概率低, 用常规光学探测方法获得的吸收信号非常弱. 我们采用共振于铯原子6S1/2 (F = 4)—6P3/2 (F' = 5)超精细跃迁线的852.3 nm探测光的吸收减弱信号来获得单光子跃迁里德伯激发的信息[18]. 考虑如图1(a)所示的铯原子V型三能级系统, 852.3 nm探测光共振于6S1/2 (F = 4)—6P3/2 (F' = 5)跃迁, 318.6 nm激发光频率扫过6S1/2 (F = 4)—nP3/2 (n = 70—94)单光子里德伯跃迁. 部分基态原子被紫外光激发到里德伯态, 导致基态原子布居数减少, 因而对852.3 nm探测光的吸收减弱, 从而可间接获得单光子跃迁里德伯激发信号. 图 1 (a) 铯原子V型三能级系统, 318.6 nm紫外光将原子从6S1/2 (F = 4)基态激发到nP3/2 (n = 70—94)里德伯态, ${\varDelta_c}$为激发光相对跃迁频率的失谐量; 852.3 nm探测光频率锁定在6S1/2 (F = 4)—6P3/2 (F' = 5)超精细跃迁; (b)实验装置示意图; OI, 光隔离器; EOM, 带输入和输出尾纤的集成光波导型电光位相调制器; PBS, 偏振分束棱镜; BS, 分束片; DM, 双色片; DPD, 差分探测器; $\Omega $, EOM所加的射频调制信号 Figure1. (a) The V-type cesium three-level system; a 318.6 nm ultraviolet laser excited partial cesium atoms from 6S1/2 (F = 4) ground state to nP3/2 (n = 70–94) Rydberg state, where ${\varDelta_c}$ is the frequency detuning of pump laser; a 852.3 nm probe laser is locked to 6S1/2 (F = 4) –6P3/2 (F' = 5) hyperfine transition. (b) Schematic diagram of experimental setup. OI, optical isolator; EOM, fiber-pigtailed integration optical waveguide phase-type electro-optic modulator; PBS, polarization beam spliter cube; BS, beam spliter plate; DM, dichroic mirror; DPD, differential photo-diode; Ω, the radio-frequency modulated signal applied on EOM
图1(b)为实验装置示意图, 852.3 nm探测光由分布式布拉格反射式(DBR)半导体激光器产生, 光斑大小扩束至1.3 mm (1/e2), 输出通过光隔离器后, 经偏振分光棱镜分为两路: 一路注入偏振光谱装置中将激光频率锁定在铯原子6S1/2 (F = 4)—6P3/2 (F' = 5)跃迁; 另一路耦合进带输入和输出尾纤的集成光波导型电光位相调制器(EOM), 通过改变施加在EOM上的射频调制信号频率$\varOmega $对谱线频率间隔进行标定; 随后经过分束镜将功率等分为两路用于后续实验. 激发光方面, 我们利用两中心波长分别为1560.5 nm和1076.9 nm的红外光单次穿过周期极化的掺氧化镁铌酸锂晶体和频获得637.2 nm红光[15], 后经偏振分光棱镜分为两路: 一路耦合入高精度波长计(HighFinesse WS-7, Toptica-Amstrong, 绝对精度120 MHz)用于校准激发光的波长, 并记录基态到里德伯态的单光子跃迁频率; 另一路进入四镜环形倍频腔利用谐振倍频方案得到单光子激发所需要的318.6 nm紫外光[15], 其光斑扩束至1.6 mm (1/e2). 整个系统中1560.5 nm激光通过射频调制边带技术将运转频率锁定在一个超低膨胀系数的双波长(1560.5 nm、637.2 nm) 高精细度光学腔上, 扫描1076.9 nm激光频率即可间接实现318.6 nm激光的连续调谐, 进而实现不同里德伯态的激发. 利用对318.6 nm紫外光高反、852.3 nm近红外光高透的双色片使激发光与一路探测光合束后穿过10 cm长的处于室温的熔融石英玻璃圆柱状铯原子气室. 铯原子气室置于磁屏蔽筒内, 以屏蔽外界杂散磁场的影响. 与318.6 nm紫外激发光合束的852.3 nm探测光束穿过铯原子气室后, 经双色片滤掉紫外激发光成分, 与另一路直接穿过铯原子气室的852.3 nm参考探测光束一起入射到差分探测器(Model 2107 DPD, New Focus), 得到高信噪比的里德伯激发光谱. 以铯原子71P3/2里德伯态的光谱为例, 852.3 nm探测光频率通过偏振光谱技术锁定于6S1/2 (F = 4)—6P3/2 (F' = 5)超精细跃迁线, 同时在6S1/2 (F = 4)—71P3/2跃迁线附近扫描318.6 nm泵浦光频率, 可得到如图2所示的单光子里德伯激发光谱. 由于室温铯原子气室中的多普勒效应, 所以在对应${v_z} = 0$速度组分的零失谐透射峰的蓝失谐一定频率处出现一个小透射峰, 表示另一速度组分的原子也被激发到71P3/2里德伯态. 为了确定另一速度组分原子的信息, 我们利用EOM对探测光进行调制来标定谱线间隔, EOM上加的调制频率为$\varOmega $, 如图1(b), 透射峰左右将出现对应频率为${f_{\rm{p}}} \pm \varOmega $的 ± 1级射频调制边带成分. 增加调制频率$\varOmega $, 零失谐透射峰的+1级边带向蓝失谐方向移动. 考虑室温铯原子速度分布服从玻尔兹曼分布, 在激光传播方向上与不同速度组分的原子作用的光的频率为 图 2 速度选择单光子跃迁铯原子71P3/2里德伯态的激发光谱. 852.3 nm探测光共振于6S1/2 (F = 4)—6P3/2 (F' = 5)跃迁线, 探测光功率为159 $\;{\text{μW}}$; 318.6 nm紫外激发光频率在6S1/2 (F = 4)—71P3/2态跃迁扫描, 功率为1.6 W; 激发光频率相对71P3/2态零失谐和蓝失谐671 MHz时, 出现两个透射信号, 分别对应速度组分为vz=0 (对应852.3 nm探测光的载频)和vz=213.94 m/s (对应852.3 nm探测光的 + 1级251 MHz射频调制边带)的铯原子被激发到71P3/2态 Figure2. Velocity-selective spectra. The frequency of 852.3 nm probe beam is locked on the 6S1/2 (F = 4)—6P3/2 (F' = 5) transition and the light power is 159 $\;{\text{μW}}$; the 318.6 nm coupling beam is scanned over the transition of 6S1/2 (F = 4)—71P3/2 and the light power is 1.6 W. Two transmission peaks appeared when the frequency of the coupling beam resonated with the 6S1/2 (F = 4)—71P3/2 transition line or blue detuning of 671 MHz, corresponding to atoms which have velocity of vz = 0 (corresponding to the carrier of 852.3 nm probe beam) and vz = 213.94 m/s (corresponding to the +1 order 251 MHz radio-frequency modulation component of 852.3 nm probe beam) are excited to 71P3/2 Rydberg state, respectively.
在原子处于主量子数n较大的高激发里德伯态时, 上式仅需考虑前两项, 铯原子nP3/2态对应的参数${\delta _0}$和${\delta _2}$可通过查阅文献[1]得到, 代入(4)式即可计算得到对应能态的量子亏损值. 图3 为理论计算得到的铯原子nP3/2 (n = 50—100)态的量子亏损值随主量子数n的变化, 随着主量子数n的增加, 量子亏损值缓慢减小. 图 3 铯原子nP3/2 (n = 50—100)里德伯态量子亏损随主量子数n的变化. 量子亏损随着主量子数n增加而缓慢减小 Figure3. The theory values of quantum defects for cesium nP3/2 (n = 50–100) Rydberg states. Quantum defect is decreasing with increasing of the principal quantum number n.
其中${E_{{\rm{IP}}}}$为铯原子的电离阈值, ${R_{{\rm{akali}}}}=$10973686.274 m–1为铯原子的里德伯常数, ${E_{h,f}}$=13.41520205 m–1为铯原子6S1/2 (F = 4)态相对于6S1/2基态精细结构的超精细分裂值, 为了计算方便, 此处的能量单位均以波数单位表示. 基于里德伯原子的速度选择光谱, 我们利用高精度波长计测量了不同铯原子里德伯态nP3/2 (n = 70—94)的单光子跃迁频率, 利用(5)式拟合得到nP3/2 (n = 70—94)各态量子亏损随n的变化趋势如图4. 其中, 量子亏损的理论值与实验数据的整体差异是由于在波长计120 MHz的绝对精度范围内存在一个约100 MHz的固定测量误差, 这可能是由于校准波长计使用的852.3 nm近红外光频率与波长计实际测量的637.2 nm红光频率相差较远导致的, 因此量子亏损的实验数据整体与理论值存在固定的偏差. 考虑固定频率差影响后, 实验数据显示出明显的离散性. 这是由于实验中虽然1560.5 nm和1076.9 nm红外光已分别进行了频率锁定, 但是经过非线性过程产生的紫外光依然存在频率起伏, 导致测量结果存在误差, 使得整体变化趋势呈现明显的离散性. 考虑了这些影响后, 在理论计算值近似不变的情况下, 量子亏损的实验数据呈现随n增加而增加的趋势. 图 4 铯原子nP3/2 (n = 70—94)态的量子亏损计算值与实验直接测量值的对比. 其中红色圆点为计算值, 黑色方块为实验直接测量值; 随着主量子数n的增加, 计算值近乎不变, 而实验直接测量值却是增加的. 这一趋势表明有一些影响因素必须要考虑, 去修正直接实验测量得到的铯原子nP3/2 (n = 70—94)里德伯态的量子亏损值 Figure4. Comparison of direct experimentally measured data with calculated values of quantum defects for cesium nP3/2 (n = 70—94) Rydberg states. The red dots are calculated values and the black cubes are direct experimentally measured data. When the principal quantum number n increasing, the calculated values are almost constant, but the direct experimentally measured data are increasing obviously. This variation trend indicate that some influence factors should be took into account to correct the direct experimentally measured data.
对于铯原子nP3/2 (n = 70—94)里德伯态, A = 2.74 × 10–9[24], B = 8.13 × 10–10[24]. 利用有效主量子数n*求得铯原子nP3/2 (n = 70—94)里德伯态的极化率如表1所列. 为计算方便, 极化率的单位已转换为MHz/(V/cm)2.
Principal quantum number
Polarizability/MHz/(V/cm)2
Principal quantum number
Polarizability/MHz/(V/cm)2
70
15730.1
83
54913.3
71
17463.0
84
59935.9
72
19356.9
85
65347.2
73
21424.3
86
71172.0
74
23678.2
87
77436.3
75
26132.3
88
84167.3
76
28801.2
89
91393.7
77
31700.5
90
99145.6
78
34846.4
91
107454.3
79
38256.2
92
116352.9
80
41948.1
93
125875.7
81
45941.3
94
136058.9
82
50255.9
-
-
表1铯原子高激发nP3/2 (n = 70—94)里德伯态的极化率 Table1.Polarizability of highly-excited Cs nP3/2 (n = 70—94) Rydberg states.
考虑到造成系统误差的主要原因应当是未被完全屏蔽的残余直流电场, nP3/2 (n = 70—94)态的跃迁频率计算值与实验数据的频率差即为Stark效应造成的铯原子里德伯态能级的移动. 将nP3/2 (n = 70—94)里德伯态的极化率与相应的Stark频移代入(6)式进行拟合, 得到作用于铯原子气室内的残余直流电场约(31 ± 2) mV/cm, 如图5(a)所示. 利用(6)式计算该残余直流电场造成的nP3/2 (n = 70—94)态的Stark频移值, 并在跃迁频率的直接测量值中补偿该频移后, 利用(5)式重新拟合量子亏损值, 得到修正后的结果如图5(b)所示. 由于随着主量子数n增加, 基态到里德伯态跃迁概率减小, 高激发态里德伯原子的单光子跃迁里德伯激发信号的信噪比变差, 使得图5(b)中的几组实验数据与理论值存在较大偏差. 考虑此因素, 修正后的nP3/2 (n = 70—94)量子亏损平均值为3.5591 ± 0.0007, 与理论计算结果吻合. 图 5 (a) 利用估算的残余直流电场对量子亏损直接实验测量值进行修正, 根据Stark频移量和有效主量子数n*的关系, 拟合得到了作用于铯原子气室中的残余直流电场约为 (31 ± 2) mV/cm; (b) 修正Stark效应及波长计测量误差的影响后, 铯原子nP3/2(n = 70—94)态量子亏损的实验测量修正值约3.5591 ± 0.0007; 实验数据与计算值相吻合 Figure5. (a) Using the estimated residual DC electric field to correct the direct experimentally measured data, according to the relationship between Stark shift and effective principal quantum number n*, the magnitude of the residual DC electric field acting on the cesium atomic vapor cell is ~(31 ± 2) mV/cm; (b) after correction of the impact of Stark effect and the measurement error of wavemeter, the corrected experimentally measured quantum defect value of cesium nP3/2 (n = 70—94) states is ~(3.5591 ±0.0007). This corrected result is consistent with the theoretically calculated value.