锶光钟的原子冷却及互组跃迁谱线测量
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摘要
时间频率作为表征物质运动的最基本物理量，在日常生活、国民经济和基础科学研究中起着重要作用。锶原子光钟是目前性能参数最好的原子钟，其不确定度和稳定度指标都已进入10-18量级，较现有铯原子喷泉钟基准钟高出2~3个数量级，且有望成为下一代国际秒的定义。锶原子的冷却与俘获是整个光钟研究中最基础的一步，它为光钟提供具有高品质因子钟跃迁谱线的原子参考源。本实验研究工作主要是围绕着锶冷原子样品的制备而逐步进行展开，本论文介绍的内容主要有：锶原子的两级冷却与俘获、二级冷却689nm激光线宽压窄、窄线宽互组跃迁谱线探测和锶原子四种同位素跃迁绝对频率的测量几部分：
（1）实验完成锶原子的461nm一级宽带冷却及冷原子相关参数的详细测量，初步实现了689nm二级窄线宽冷却与俘获。实验测得88Sr原子一级冷却温度为5mK，在加入两再抽运707nm和679nm激光后俘获冷原子数目为3.1×108，蓝色MOT的冷原子俘获率为2.8×109s-1，同时在理论和实验上研究了再抽运激光频率失谐和光强波动对俘获冷原子数目的影响，提出了一种可将两再抽运光的频率直接锁定在三重态原子跃迁吸收谱线上的技术方法。初步实现二级红色MOT，利用释放再捕获的方法测得二级窄线宽冷却原子的转载效率大于20％。理论计算了可消除钟跃迁两能级a. c. Stark频移差的“魔术”光波长值，得出蓝色光晶格“魔术”光波长值（389.9nm、359.8nm、345.2nm和335.8nm）及红色“魔术”光波长值813.4nm。
（2）研制了689nm窄线宽激光系统。为了能够满足二级窄线宽冷却对冷却激光线宽的要求，实验利用PDH稳频技术将半导体激光器频率锁定在精细度为12000的高稳ULE参考腔上，激光线宽被压窄至150Hz以下。利用飞秒光频梳对窄线宽激光器的性能进行测试评估，在1秒处的频率稳定度为2.8×10-13，16秒平坦处的稳定度约为4.4×10-14。同时在实验上测试了不同阶次横模匹配情况下ULE腔的精细度，并结合腔内损耗理论分析了精细度与横模阶次的关系。
（3）实验首次全面完成了对锶原子四种同位素互组跃迁线绝对光频率值的测量，其中对于87Sr（F=9/2→F’=7/2）和84Sr两跃迁的频率值是首次通过实验测量给出的数据结果。光纤飞秒光频梳（Menlo FC1500）的重复频率和偏置频率锁定在外参考氢钟（sigma-Tau）的10MHz射频频率源上，利用光频梳对窄线宽锶原子互组跃迁谱的绝对频率进行了测量，分别给出了锶原子四种同位素（88Sr、87Sr、86Sr和84Sr）六组互组跃迁线的绝对光频值。
（4）首次提出并完成了一种可精确测量锶原子束横向速度分布的实验方法。利用两束独立但可同相位扫描的探测光和泵浦光，在锶原子束中观测到具有速度选择的高分辨锶原子互组跃迁谱。实验获得了测量精度为0.13m/s（对应的热学温度90μK），测得原子束的速度分布线型为一特殊“伞”形状，无法用常用的Maxwell-Boltzmann线型分布或是Lorentzian线型分布进行分析，我们在理论上进行了模拟计算并与实验结果取得了很好的吻合。相比较常用的激光诱导荧光测速方法，选择Lamb-dip测速方法可消除探测激光线宽、谱线功率增宽、同位素远失谐共振等其它谱线加宽的影响。实验对原子速度分布的精确测量能为原子钟钟频误差分析提供可靠的实验参数依据。
（5）实验获得线宽为55kHz的高信噪比窄线宽锶原子互组跃迁谱线。在此高分辨光谱基础上对原子谱线加宽的各个因素进行了详细分析，实验上观测窄线宽原子塞曼分裂谱，并利用改变极化角度的方法来消除其中的交叉峰。同时观测了锶原子互组跃迁原子相干谱线，利用窄线宽激光探测V型三能级Zeeman子能级中EIT谱线，并获得了在单光子失谐但双光子共振情况下的EIT谱线。实验测得透明窗口线宽约为450kHz，为探索将原子相干技术应用到锶原子钟跃迁探测提供实验研究基础。
The measurement of time and frequency has always been fundamental in themankind’s everyday life, the foundation of the national economy, even an importantrole in scientific research. New kinds of clocks are revolutionizing time keeping withenormous consequences for science and technology, they are called optical clocks andas a new generation of atomic clocks based on optical transitions. Now, optical clocksbased on strontium neutral atoms are the new generation of frequency standards withstability and accuracy at the10-18level. Accuracy for the SI (International System ofUnits) second is currently defined by the Cs primary standard. However, strontiumoptical clocks have now achieved a lower systematic uncertainty. This systematicuncertainty will become accuracy once the SI second has been redefined. The coolingand trapping of strontium is the basis of the entire optical clock, it provides highquality factor Q of strontium atomic transition reference. This thesis mainly describesthe laser cooling and trapping of strontium: the first-stage broadband Doppler coolingusing the strong dipole allowed1S0→1P1transition at461nm with a natural width of32MHz, strontium atoms in this so called “Blue MOT” are Doppler cooled to a finaltemperature at~5mK level; the second-stage narrow-line cooling using theintercombination transition1S0→3P1which has a natural linewidth of7.6kHz, atomsin this so called “Red MOT” are cooled to a final temperature at~μK level. Thecontents of this thesis can be summarized as following:
(1) The detailed experimental measurement of broadband cooling in the “Blue MOT”,radiation at461nm resonant with the dipole allowed transition1S0→1P1which isindeed very robust and for a typical choice of laser, the atoms are cooled reaching afinal temperature at about5mK. The first cooling transition is not perfectly closed,due to a small leakage towards the4d1D2state. In order to recycle the atoms stored inthe metastable states two repumping lasers, respectively at707nm and679nm can beused to pump these atoms. The experimental and theoretical investigations of thefrequency and power fluctuation of repumping lasers, impact on the cooling andtrapping of strontium atoms. More than3.1×108atoms have been trapped with the capture rate2.8×109s-1when the two repumping lasers added. An optical latticeconfinement can be employed to load atoms in so as to cancel Doppler、recoilfrequency shift and broadening resulting from thermal motional effects. However, theconservative force of optical dipole traps is much weaker than dissipative force ofDoppler cooling. The optical dipole trap depth of lattice is about only tens of μK.Owing to the singlet-triplet spin-forbidden narrow transition1S30P1at689nm(27.6kHz), it has a low Doppler cooling limit of180nK, which can be used assecond-stage cooling transition to cool mK atoms down to a few μK. The preliminaryexperimental results of second-stage narrow-line cooling of “Red MOT” have beenimplemented. About20%strontium atoms in the blue MOT are transferred to the redMOT using the release and recapture method. The theoretical calculation of "magic"wavelength with a.c. Stark shift cancellation has been introduced, the blue-detunedlattice “magic” wavelengths values (389.9nm,359.8nm,345.2nm and335.8nm) whilered-detuned lattice “magic” wavelength value813.4nm.
(2) A linewidth reduction of the689nm laser from MHz to sub-kHz level is necessary,as a result of its nature linewidth of only7.6kHz. The laser linewidth is reduced lessthan150Hz by locking to the resonance of a high finesse cut-out ULE cavity withstandard Pound–Drever–Hall technique. The finesse of ULE cavity is12000measured in experiment using the cavity ring down technique. Combining afiber-based optical frequency comb, the Allan deviation for beat signal of stablenarrow689nm laser with fiber optical frequency comb is obtained, with a stability of2.8×1013at1s averaging time. The floor of the Allan deviation is about4.4×1014atan averaging time of16s. The finesse was measured using cavity ring downtechniques in different transverse modes of the cavity.
(3) The optical frequency measurements are performed for four natural isotopes88Sr,86Sr,87Sr and84Sr, using a fiber frequency comb (Menlo FC1500) generatorreferenced to H maser（sigma-Tau）with the repetition rate and the carrier offsetenvelope frequency are locked to the H maser. The absolute optical frequencymeasurement values of84Sr and87S（rF=9/2→F’=7/2）was also given for the first time.
(4) We have demonstrated that Lamb dip holes with velocity selection can be used forvelocimetry. We report measurements of the transverse velocity distribution ofalkaline-earth strontium atoms in a collimated atomic beam, using the stable narrow689nm laser corresponding to1S30P1intercombination transition. The use of anultrastable laser system and the narrow intercombination transition line of Sr atomswith the resolution of the measured velocity can reach0.13m/s, corresponding to90μK in energy units. The velocity or momentum distribution of the thermal atomicbeam is most likely to be Maxwell-Boltmann distribution or Lorentzian distribution.The experimental result of the distribution shape is in agreement well with thetheoretical predictions. The atomic beams have been widely used in the determinationof atomic structures, measurement of physical constants, studies of chemical reactionsand atomic frequency standards. Especially, for the second order Doppler effect andatomic clock frequency error analysis. In all these applications, measurement of thevelocity distribution of the atomic beams is both necessary and highly important.
(5) We observe the intercombination transition spectroscopy of alkaline-earthstrontium, the saturation spectroscopy has been conducted with the minimumsub-Doppler width is55kHz, using a stable narrow689nm laser which is locked to ahigh fineness ultralow expansion (ULE) reference cavity. Experimental results andtheoretical explanations of spectra broadening factors have been introduced, such aspower broadening and collisional broadening. In the presence of external magneticfield, we observed a single, triplet or quintuplet spectral line with the differentpolarization angle. A new technique for elimination of crossover resonance is alsodemonstrated by changing the polarization pattern. The EIT effect is also investigatedexperimentally in the strontium atomic beam, using the V-type Zeeman three sublevelssystem of intercombination transition line with the linewidth of transparent window450kHz. It has provided a proposed EIT-based clock scheme using coherent couplingbetween the two states of optical clock transition.
（1）实验完成锶原子的461nm一级宽带冷却及冷原子相关参数的详细测量，初步实现了689nm二级窄线宽冷却与俘获。实验测得88Sr原子一级冷却温度为5mK，在加入两再抽运707nm和679nm激光后俘获冷原子数目为3.1×108，蓝色MOT的冷原子俘获率为2.8×109s-1，同时在理论和实验上研究了再抽运激光频率失谐和光强波动对俘获冷原子数目的影响，提出了一种可将两再抽运光的频率直接锁定在三重态原子跃迁吸收谱线上的技术方法。初步实现二级红色MOT，利用释放再捕获的方法测得二级窄线宽冷却原子的转载效率大于20％。理论计算了可消除钟跃迁两能级a. c. Stark频移差的“魔术”光波长值，得出蓝色光晶格“魔术”光波长值（389.9nm、359.8nm、345.2nm和335.8nm）及红色“魔术”光波长值813.4nm。
（2）研制了689nm窄线宽激光系统。为了能够满足二级窄线宽冷却对冷却激光线宽的要求，实验利用PDH稳频技术将半导体激光器频率锁定在精细度为12000的高稳ULE参考腔上，激光线宽被压窄至150Hz以下。利用飞秒光频梳对窄线宽激光器的性能进行测试评估，在1秒处的频率稳定度为2.8×10-13，16秒平坦处的稳定度约为4.4×10-14。同时在实验上测试了不同阶次横模匹配情况下ULE腔的精细度，并结合腔内损耗理论分析了精细度与横模阶次的关系。
（3）实验首次全面完成了对锶原子四种同位素互组跃迁线绝对光频率值的测量，其中对于87Sr（F=9/2→F’=7/2）和84Sr两跃迁的频率值是首次通过实验测量给出的数据结果。光纤飞秒光频梳（Menlo FC1500）的重复频率和偏置频率锁定在外参考氢钟（sigma-Tau）的10MHz射频频率源上，利用光频梳对窄线宽锶原子互组跃迁谱的绝对频率进行了测量，分别给出了锶原子四种同位素（88Sr、87Sr、86Sr和84Sr）六组互组跃迁线的绝对光频值。
（4）首次提出并完成了一种可精确测量锶原子束横向速度分布的实验方法。利用两束独立但可同相位扫描的探测光和泵浦光，在锶原子束中观测到具有速度选择的高分辨锶原子互组跃迁谱。实验获得了测量精度为0.13m/s（对应的热学温度90μK），测得原子束的速度分布线型为一特殊“伞”形状，无法用常用的Maxwell-Boltzmann线型分布或是Lorentzian线型分布进行分析，我们在理论上进行了模拟计算并与实验结果取得了很好的吻合。相比较常用的激光诱导荧光测速方法，选择Lamb-dip测速方法可消除探测激光线宽、谱线功率增宽、同位素远失谐共振等其它谱线加宽的影响。实验对原子速度分布的精确测量能为原子钟钟频误差分析提供可靠的实验参数依据。
（5）实验获得线宽为55kHz的高信噪比窄线宽锶原子互组跃迁谱线。在此高分辨光谱基础上对原子谱线加宽的各个因素进行了详细分析，实验上观测窄线宽原子塞曼分裂谱，并利用改变极化角度的方法来消除其中的交叉峰。同时观测了锶原子互组跃迁原子相干谱线，利用窄线宽激光探测V型三能级Zeeman子能级中EIT谱线，并获得了在单光子失谐但双光子共振情况下的EIT谱线。实验测得透明窗口线宽约为450kHz，为探索将原子相干技术应用到锶原子钟跃迁探测提供实验研究基础。
The measurement of time and frequency has always been fundamental in themankind’s everyday life, the foundation of the national economy, even an importantrole in scientific research. New kinds of clocks are revolutionizing time keeping withenormous consequences for science and technology, they are called optical clocks andas a new generation of atomic clocks based on optical transitions. Now, optical clocksbased on strontium neutral atoms are the new generation of frequency standards withstability and accuracy at the10-18level. Accuracy for the SI (International System ofUnits) second is currently defined by the Cs primary standard. However, strontiumoptical clocks have now achieved a lower systematic uncertainty. This systematicuncertainty will become accuracy once the SI second has been redefined. The coolingand trapping of strontium is the basis of the entire optical clock, it provides highquality factor Q of strontium atomic transition reference. This thesis mainly describesthe laser cooling and trapping of strontium: the first-stage broadband Doppler coolingusing the strong dipole allowed1S0→1P1transition at461nm with a natural width of32MHz, strontium atoms in this so called “Blue MOT” are Doppler cooled to a finaltemperature at~5mK level; the second-stage narrow-line cooling using theintercombination transition1S0→3P1which has a natural linewidth of7.6kHz, atomsin this so called “Red MOT” are cooled to a final temperature at~μK level. Thecontents of this thesis can be summarized as following:
(1) The detailed experimental measurement of broadband cooling in the “Blue MOT”,radiation at461nm resonant with the dipole allowed transition1S0→1P1which isindeed very robust and for a typical choice of laser, the atoms are cooled reaching afinal temperature at about5mK. The first cooling transition is not perfectly closed,due to a small leakage towards the4d1D2state. In order to recycle the atoms stored inthe metastable states two repumping lasers, respectively at707nm and679nm can beused to pump these atoms. The experimental and theoretical investigations of thefrequency and power fluctuation of repumping lasers, impact on the cooling andtrapping of strontium atoms. More than3.1×108atoms have been trapped with the capture rate2.8×109s-1when the two repumping lasers added. An optical latticeconfinement can be employed to load atoms in so as to cancel Doppler、recoilfrequency shift and broadening resulting from thermal motional effects. However, theconservative force of optical dipole traps is much weaker than dissipative force ofDoppler cooling. The optical dipole trap depth of lattice is about only tens of μK.Owing to the singlet-triplet spin-forbidden narrow transition1S30P1at689nm(27.6kHz), it has a low Doppler cooling limit of180nK, which can be used assecond-stage cooling transition to cool mK atoms down to a few μK. The preliminaryexperimental results of second-stage narrow-line cooling of “Red MOT” have beenimplemented. About20%strontium atoms in the blue MOT are transferred to the redMOT using the release and recapture method. The theoretical calculation of "magic"wavelength with a.c. Stark shift cancellation has been introduced, the blue-detunedlattice “magic” wavelengths values (389.9nm,359.8nm,345.2nm and335.8nm) whilered-detuned lattice “magic” wavelength value813.4nm.
(2) A linewidth reduction of the689nm laser from MHz to sub-kHz level is necessary,as a result of its nature linewidth of only7.6kHz. The laser linewidth is reduced lessthan150Hz by locking to the resonance of a high finesse cut-out ULE cavity withstandard Pound–Drever–Hall technique. The finesse of ULE cavity is12000measured in experiment using the cavity ring down technique. Combining afiber-based optical frequency comb, the Allan deviation for beat signal of stablenarrow689nm laser with fiber optical frequency comb is obtained, with a stability of2.8×1013at1s averaging time. The floor of the Allan deviation is about4.4×1014atan averaging time of16s. The finesse was measured using cavity ring downtechniques in different transverse modes of the cavity.
(3) The optical frequency measurements are performed for four natural isotopes88Sr,86Sr,87Sr and84Sr, using a fiber frequency comb (Menlo FC1500) generatorreferenced to H maser（sigma-Tau）with the repetition rate and the carrier offsetenvelope frequency are locked to the H maser. The absolute optical frequencymeasurement values of84Sr and87S（rF=9/2→F’=7/2）was also given for the first time.
(4) We have demonstrated that Lamb dip holes with velocity selection can be used forvelocimetry. We report measurements of the transverse velocity distribution ofalkaline-earth strontium atoms in a collimated atomic beam, using the stable narrow689nm laser corresponding to1S30P1intercombination transition. The use of anultrastable laser system and the narrow intercombination transition line of Sr atomswith the resolution of the measured velocity can reach0.13m/s, corresponding to90μK in energy units. The velocity or momentum distribution of the thermal atomicbeam is most likely to be Maxwell-Boltmann distribution or Lorentzian distribution.The experimental result of the distribution shape is in agreement well with thetheoretical predictions. The atomic beams have been widely used in the determinationof atomic structures, measurement of physical constants, studies of chemical reactionsand atomic frequency standards. Especially, for the second order Doppler effect andatomic clock frequency error analysis. In all these applications, measurement of thevelocity distribution of the atomic beams is both necessary and highly important.
(5) We observe the intercombination transition spectroscopy of alkaline-earthstrontium, the saturation spectroscopy has been conducted with the minimumsub-Doppler width is55kHz, using a stable narrow689nm laser which is locked to ahigh fineness ultralow expansion (ULE) reference cavity. Experimental results andtheoretical explanations of spectra broadening factors have been introduced, such aspower broadening and collisional broadening. In the presence of external magneticfield, we observed a single, triplet or quintuplet spectral line with the differentpolarization angle. A new technique for elimination of crossover resonance is alsodemonstrated by changing the polarization pattern. The EIT effect is also investigatedexperimentally in the strontium atomic beam, using the V-type Zeeman three sublevelssystem of intercombination transition line with the linewidth of transparent window450kHz. It has provided a proposed EIT-based clock scheme using coherent couplingbetween the two states of optical clock transition.
引文
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