698nm超窄线宽激光器研制以及飞秒光频流相关理论研究
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摘要
光钟被认为是精度最高的原子钟,在未来很有可能代替铯时间频率基准而复现新的秒定义。光钟主要由三大部分组成：基于激光冷却与俘获技术获得的温度为mK甚至μK量级的原子或离子,用于实现高谱纯度钟跃迁探测的超窄线宽激光,以及基于锁模飞秒脉冲激光器的飞秒光频梳。目前研制的光钟稳定性指标比理论预期值尚差一个数量级,其主要原因是,光钟的稳定性受限于其本地振荡器(超窄线宽激光器)输出的参考光频率稳定性。因此,研制具有更高频率稳定度的超窄线宽激光器是进一步提高光钟性能指标的关键途径。此外,飞秒光频梳是基于锁模飞秒脉冲技术的现代光频率链,其主要用途是测量光钟输出的光频率以及获得原子的高精密光谱。在频域,飞秒光频梳因其频率带宽扩展需要用到许多频率转换技术,例如和频产生(SFG)技术等。在时域,飞秒光频梳作为飞秒激光可以应用于近来非常活跃的“相干控制”领域。因此,研究飞秒光频梳的原理、特性及其在时域、频域的相关应用具有重要的科学意义和应用价值。
本论文工作主要分为实验和理论研究两部分。实验部分主要工作是研制一套波长为698nm的超窄线宽激光器。实验方案是,采用Pound-Drever-hall (PDH)隐频技术,通过两级稳频实现具有Hz量级线宽的激光器。相对于初级频率参考第一级稳频目标是实现线宽为1kHz的激光,而相对于高级频率参考第二级稳频目标则是实现线宽为1Hz的激光。理论研究部分包括：设计了一种新放置方式的振动不敏感Fabry-Perot (F-P)腔;研究了飞秒光频梳频带扩展技术—SFG；研究了飞秒激光在与原子相互作用过程中的相干控制问题；研究了利用飞秒光频梳实现超高分辨光谱问题。具体内容包括：
1.698nm超窄线宽激光器的研制。
(1)设计制作了一套精细度约为1000的F-P腔,作为初级频率参考(初稳腔)；设计并建立了一套精细度约为500000的ULE(ultra low expansion)F-P腔,作为高级频率参考(高稳腔)。将初稳腔与高稳腔置于真空度在10-6Pa量级的真空系统中,以减弱空气流动对腔长稳定度的影响。
(2)由于超窄线宽激光频率稳定度主要取决于高稳腔腔长的稳定度,而高稳腔腔长的稳定度主要受环境温度及机械振动影响,为了减小上述因素对腔稳定性的影响,我们采取以下四个措施：(i)采用了超低热膨胀系数的ULE玻璃高稳腔,设计并制作了多层隔热、隔音的控温箱；(ii)设计并研制了高稳腔温控系统以降低环境温度变化对高稳腔腔长稳定度的影响；(iii)利用主动隔振平台减弱了高频振动噪声对高稳腔腔长稳定度的影响；(iv)设计并优化了高稳腔的支撑方式,以减弱低频振动对腔长稳定性的影响。
(3)通过模式匹配透镜组实现了激光与初稳腔以及高稳腔的模式匹配以获得高信噪比的误差信号,以便实现较好的激光频率锁定。
(4)利用初稳腔锁频后,激光相对于初稳腔线宽为1.1kHz,因此第一级稳频已经达到预期目标；利用高稳腔直接锁频后,实现激光相对于高稳腔的线宽约为680Hz。
(5)在上述初稳腔和高稳腔的基础上,正在进行利用两级稳频技术实现Hz量级窄线宽激光输出的实验研究。目前已经初步实现了两级稳频锁定,且在进一步优化锁频参数及降低锁频环路噪声,以实现更好的锁定结果。
2.根据泊松效应及腔几何对称性,利用有限元方法设计了一种新放置方式的F-P腔,通过数值模拟获得了这种F-P腔最佳的支撑位置。该结果接近目前国际上理论计算的最佳结果。此外,正在设计一套可搬运、小型化F-P腔用于空间光钟计划。
3.利用缀饰态理论及数值计算研究了飞秒脉冲在三波混频时发生的SFG过程；揭示出SFG绝热过程的物理实质；证明了绝热和透热在SFG过程中的重要作用；得出了所产生光场响应带宽的另一种计算方法；并展示了SFG过程中发生的类似于单缝衍射或双缝衍射的物理现象。该研究对于宽频带飞秒光频梳的SFG绝热技术具有重要的参考价值。
4.理论研究了整形(裁剪)飞秒脉冲驱动原子跃迁时发生的干涉、衍射效应,实现了激发态波函数的量子相干控制。以一个已知的波函数作为参考,然后使得第二个波函数与之干涉；通过调制第二个波函数驱动光场的相位,实现了干涉结果的人为控制；根据全息思想,提出了一种可以在实验中测量波函数的新方法。该研究对于飞秒光频梳在量子相干控制领域的应用具有重要的指导意义。
5.从时域和频域的角度,研究了飞秒光频梳驱动下87Rb原子的双光子跃迁过程。结果表明,通过独立改变飞秒光频梳的两个参量在理论上可以实现87Rb超高分辨光谱。
Among the atomic clocks, optical clock is considered as the most accurate one. Today optical clocks based on optical transitions have been widely accepted as the most important candidate to replace Cs microwave Frequency standards for a more accurate definition of SI second. To realize an optical clock, three techniques are mainly involved, i.e., the laser cooling and trapping technique which can drop the temperature of the atoms or ions system to mK even μK, the ultra-narrow linewidth laser (ULL) stabilization technique which is used to detect the optical transitions with high spectrum purity, and the optical frequency comb (OFC) technique based on femtosecond mode-locked laser. Presently, the instability of the state-of-the-art optical clock is about an order larger than that desired by theory. One of the main limititations is due to the frequency instability of its local oscillator, that is, the ULL. Thus, developing an ULL with more stable frequency is a critical route to improve the stability of the optical clock. Furthermore, optical frequency comb based on a mode-locked femtosecond laser, working as an optical frequency synthesizer chain, can be used to measure the output frequency of optical clock and obtain high precision spectroscopy. In the frequency-domain, in order to extend the frequency bandwidth of the OFC, one should investigate many kinds of frequency conversions, such as sum frequency generation (SFG), etc. In the time-domain, the OFC can be lately applied to the active "coherent control" area. Therefore, it is very important and valuable to investigate the working principle, character, and application of the OFC in both the time-and frequency-domain.
This work can be mainly divided into two parts, i.e., experimental and theoretical parts. In experiment, we develop an ULL at698nm. Pound-Drever-hall (PDH) method is utilized to achieve a Hz level linewidth laser with two-steps frequency stabilization. With the first frequency stabilization we achieved a1.1kHz linewidth laser relative to the primary frequency reference (pre-stable Fabry-Perot cavity or PFC in abbreviation) as planned. While for the second frequency stabilization, the setup was built and is now under optimization to achieve the expected1Hz linewidth laser relative to the advanced frequency reference (ultra-stable Fabry-Perot cavity or UFC). In theory, we presented a novel vibration-insensitive Fabry-Perot (F-P) cavity design; we studied the bandwidith extension technique of OFC i.e., SFG method; we also investigated the coherent control method during the interaction between a femtosecond laser pulse and an atom. At last, we reported how to achieve ultrahigh resolution spectroscopy using an OFC. Specified contents are shown as follows,
1. Development of an ULL at698nm
(1) A finesse of-1000F-P cavity is designed and prepared as the PFC, while a finesse of-560000F-P cavity is used as the UFC. Then, these two F-P cavities are placed in two vacuum systems with pressure of-10-6Pa to reduce the influence of air fluxion on the stability of cavities's length.
(2) The frequency stability of the ULL mainly depends on the length stability of the UFC, while the length stability of the UFC is mainly influenced by environmental temperature and mechanic vibration. In this thesis, we adopt four steps to weaken the influence of these two factors, which are sketched as follows,
i. The UFC is made of ULE (ultra low expansion), and a temperature-controlled box is prepared with multi-layer thermal-and voice-isolations.
ii. Temperature-controlled system for the UFC is developed to reduce the impact of the environmental temperature change on the length stability of the UFC.
iii. Active vibration isolator is used to weaken the high frequency vibration.
iv. Low frequency vibration is reduced by simply optimizing the supports of UFC.
(3) Mode-matching between the coupled laser mode and the PFC cavity mode as well as the UFC cavity mode are investigated and performed by using a set of mode-matching lens, to obtain the error signal of high signal-to-noise ratio for frequency stabilazation.
(4) With respect to the PFC1.1kHz linewidth laser has been achieved, while680Hz linewidth laser relative to the UFC has been obtained by direct frequency stabilazation with UFC.
(5) Based on PFC and UFC, two-steps frequency stabilazation are used to experimentally achieve Hz level ULL output. At present, two-steps frequency stabilazation are preliminarily achieved, and many efforts such as optimizing locking parameters and reducing the servo loop noises are to be made to obtain better result.
2. Based on Poisson effect and geometry symmetry, a F-P cavity with new placement is designed using finite element method. Through extensive simulations the optimal supports were obtained. The results are close to the best results achieved in the world. Furthermore, a portable F-P cavity is being designed for application in the space optical clock project.
3. Based on the dressed state formalism and numerical calculation, we investigated the SFG method when mixing three femtosecond lasers. We also showed the physical essence of adiabatic SFG. We demonstrated that the adiabatic and non-adiabatic processes play important roles in SFG. We presented another method to calculate the frequency response bandwidth of the generated light pulse. At last, we described the physical processes of SFG in the frequency-domain, which resembles the diffraction phenomena induced by the single slim or double slims. This study has valuable reference for broad bandwidth SFG technique of OFC.
4. We investigated the interference and diffraction effect when using a tailored femtosecond laser pulse drives an atom. By modulating the phase and amplitude of a femtosecond laser pulse, we theoretically achieved the quantum coherent control for a wave function related to the atom transition. Furthermore, using a given wave function as a reference one, the interference can occur when another wave function is generated by exciting the same atom with another femtosecond laser pulse. It is shown that the interference can be controlled by modulating the phase of the second laser pulse. Based on the holography we presented a new method to measure an unknown wave function. This work provides guidelines for application of OFC in quantum coherent control.
5. In the time-and frequency-domain, we investigated the physical mechanism to achieve ultrahigh resolution spectroscopy, theoretically demonstrated the two-photon transition by driving a87Rb atom with an OFC. It is shown that the ultra-high resolution spectroscopy of87Rb atom can be achieved by independently changing the two parameters of OFC.
本论文工作主要分为实验和理论研究两部分。实验部分主要工作是研制一套波长为698nm的超窄线宽激光器。实验方案是,采用Pound-Drever-hall (PDH)隐频技术,通过两级稳频实现具有Hz量级线宽的激光器。相对于初级频率参考第一级稳频目标是实现线宽为1kHz的激光,而相对于高级频率参考第二级稳频目标则是实现线宽为1Hz的激光。理论研究部分包括：设计了一种新放置方式的振动不敏感Fabry-Perot (F-P)腔;研究了飞秒光频梳频带扩展技术—SFG；研究了飞秒激光在与原子相互作用过程中的相干控制问题；研究了利用飞秒光频梳实现超高分辨光谱问题。具体内容包括：
1.698nm超窄线宽激光器的研制。
(1)设计制作了一套精细度约为1000的F-P腔,作为初级频率参考(初稳腔)；设计并建立了一套精细度约为500000的ULE(ultra low expansion)F-P腔,作为高级频率参考(高稳腔)。将初稳腔与高稳腔置于真空度在10-6Pa量级的真空系统中,以减弱空气流动对腔长稳定度的影响。
(2)由于超窄线宽激光频率稳定度主要取决于高稳腔腔长的稳定度,而高稳腔腔长的稳定度主要受环境温度及机械振动影响,为了减小上述因素对腔稳定性的影响,我们采取以下四个措施：(i)采用了超低热膨胀系数的ULE玻璃高稳腔,设计并制作了多层隔热、隔音的控温箱；(ii)设计并研制了高稳腔温控系统以降低环境温度变化对高稳腔腔长稳定度的影响；(iii)利用主动隔振平台减弱了高频振动噪声对高稳腔腔长稳定度的影响；(iv)设计并优化了高稳腔的支撑方式,以减弱低频振动对腔长稳定性的影响。
(3)通过模式匹配透镜组实现了激光与初稳腔以及高稳腔的模式匹配以获得高信噪比的误差信号,以便实现较好的激光频率锁定。
(4)利用初稳腔锁频后,激光相对于初稳腔线宽为1.1kHz,因此第一级稳频已经达到预期目标；利用高稳腔直接锁频后,实现激光相对于高稳腔的线宽约为680Hz。
(5)在上述初稳腔和高稳腔的基础上,正在进行利用两级稳频技术实现Hz量级窄线宽激光输出的实验研究。目前已经初步实现了两级稳频锁定,且在进一步优化锁频参数及降低锁频环路噪声,以实现更好的锁定结果。
2.根据泊松效应及腔几何对称性,利用有限元方法设计了一种新放置方式的F-P腔,通过数值模拟获得了这种F-P腔最佳的支撑位置。该结果接近目前国际上理论计算的最佳结果。此外,正在设计一套可搬运、小型化F-P腔用于空间光钟计划。
3.利用缀饰态理论及数值计算研究了飞秒脉冲在三波混频时发生的SFG过程；揭示出SFG绝热过程的物理实质；证明了绝热和透热在SFG过程中的重要作用；得出了所产生光场响应带宽的另一种计算方法；并展示了SFG过程中发生的类似于单缝衍射或双缝衍射的物理现象。该研究对于宽频带飞秒光频梳的SFG绝热技术具有重要的参考价值。
4.理论研究了整形(裁剪)飞秒脉冲驱动原子跃迁时发生的干涉、衍射效应,实现了激发态波函数的量子相干控制。以一个已知的波函数作为参考,然后使得第二个波函数与之干涉；通过调制第二个波函数驱动光场的相位,实现了干涉结果的人为控制；根据全息思想,提出了一种可以在实验中测量波函数的新方法。该研究对于飞秒光频梳在量子相干控制领域的应用具有重要的指导意义。
5.从时域和频域的角度,研究了飞秒光频梳驱动下87Rb原子的双光子跃迁过程。结果表明,通过独立改变飞秒光频梳的两个参量在理论上可以实现87Rb超高分辨光谱。
Among the atomic clocks, optical clock is considered as the most accurate one. Today optical clocks based on optical transitions have been widely accepted as the most important candidate to replace Cs microwave Frequency standards for a more accurate definition of SI second. To realize an optical clock, three techniques are mainly involved, i.e., the laser cooling and trapping technique which can drop the temperature of the atoms or ions system to mK even μK, the ultra-narrow linewidth laser (ULL) stabilization technique which is used to detect the optical transitions with high spectrum purity, and the optical frequency comb (OFC) technique based on femtosecond mode-locked laser. Presently, the instability of the state-of-the-art optical clock is about an order larger than that desired by theory. One of the main limititations is due to the frequency instability of its local oscillator, that is, the ULL. Thus, developing an ULL with more stable frequency is a critical route to improve the stability of the optical clock. Furthermore, optical frequency comb based on a mode-locked femtosecond laser, working as an optical frequency synthesizer chain, can be used to measure the output frequency of optical clock and obtain high precision spectroscopy. In the frequency-domain, in order to extend the frequency bandwidth of the OFC, one should investigate many kinds of frequency conversions, such as sum frequency generation (SFG), etc. In the time-domain, the OFC can be lately applied to the active "coherent control" area. Therefore, it is very important and valuable to investigate the working principle, character, and application of the OFC in both the time-and frequency-domain.
This work can be mainly divided into two parts, i.e., experimental and theoretical parts. In experiment, we develop an ULL at698nm. Pound-Drever-hall (PDH) method is utilized to achieve a Hz level linewidth laser with two-steps frequency stabilization. With the first frequency stabilization we achieved a1.1kHz linewidth laser relative to the primary frequency reference (pre-stable Fabry-Perot cavity or PFC in abbreviation) as planned. While for the second frequency stabilization, the setup was built and is now under optimization to achieve the expected1Hz linewidth laser relative to the advanced frequency reference (ultra-stable Fabry-Perot cavity or UFC). In theory, we presented a novel vibration-insensitive Fabry-Perot (F-P) cavity design; we studied the bandwidith extension technique of OFC i.e., SFG method; we also investigated the coherent control method during the interaction between a femtosecond laser pulse and an atom. At last, we reported how to achieve ultrahigh resolution spectroscopy using an OFC. Specified contents are shown as follows,
1. Development of an ULL at698nm
(1) A finesse of-1000F-P cavity is designed and prepared as the PFC, while a finesse of-560000F-P cavity is used as the UFC. Then, these two F-P cavities are placed in two vacuum systems with pressure of-10-6Pa to reduce the influence of air fluxion on the stability of cavities's length.
(2) The frequency stability of the ULL mainly depends on the length stability of the UFC, while the length stability of the UFC is mainly influenced by environmental temperature and mechanic vibration. In this thesis, we adopt four steps to weaken the influence of these two factors, which are sketched as follows,
i. The UFC is made of ULE (ultra low expansion), and a temperature-controlled box is prepared with multi-layer thermal-and voice-isolations.
ii. Temperature-controlled system for the UFC is developed to reduce the impact of the environmental temperature change on the length stability of the UFC.
iii. Active vibration isolator is used to weaken the high frequency vibration.
iv. Low frequency vibration is reduced by simply optimizing the supports of UFC.
(3) Mode-matching between the coupled laser mode and the PFC cavity mode as well as the UFC cavity mode are investigated and performed by using a set of mode-matching lens, to obtain the error signal of high signal-to-noise ratio for frequency stabilazation.
(4) With respect to the PFC1.1kHz linewidth laser has been achieved, while680Hz linewidth laser relative to the UFC has been obtained by direct frequency stabilazation with UFC.
(5) Based on PFC and UFC, two-steps frequency stabilazation are used to experimentally achieve Hz level ULL output. At present, two-steps frequency stabilazation are preliminarily achieved, and many efforts such as optimizing locking parameters and reducing the servo loop noises are to be made to obtain better result.
2. Based on Poisson effect and geometry symmetry, a F-P cavity with new placement is designed using finite element method. Through extensive simulations the optimal supports were obtained. The results are close to the best results achieved in the world. Furthermore, a portable F-P cavity is being designed for application in the space optical clock project.
3. Based on the dressed state formalism and numerical calculation, we investigated the SFG method when mixing three femtosecond lasers. We also showed the physical essence of adiabatic SFG. We demonstrated that the adiabatic and non-adiabatic processes play important roles in SFG. We presented another method to calculate the frequency response bandwidth of the generated light pulse. At last, we described the physical processes of SFG in the frequency-domain, which resembles the diffraction phenomena induced by the single slim or double slims. This study has valuable reference for broad bandwidth SFG technique of OFC.
4. We investigated the interference and diffraction effect when using a tailored femtosecond laser pulse drives an atom. By modulating the phase and amplitude of a femtosecond laser pulse, we theoretically achieved the quantum coherent control for a wave function related to the atom transition. Furthermore, using a given wave function as a reference one, the interference can occur when another wave function is generated by exciting the same atom with another femtosecond laser pulse. It is shown that the interference can be controlled by modulating the phase of the second laser pulse. Based on the holography we presented a new method to measure an unknown wave function. This work provides guidelines for application of OFC in quantum coherent control.
5. In the time-and frequency-domain, we investigated the physical mechanism to achieve ultrahigh resolution spectroscopy, theoretically demonstrated the two-photon transition by driving a87Rb atom with an OFC. It is shown that the ultra-high resolution spectroscopy of87Rb atom can be achieved by independently changing the two parameters of OFC.
引文
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