高精细度微光学腔及单原子的控制与测量
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摘要
腔量子电动力学(Cavity QED)主要研究受限系统中量子化电磁场和原子之间的相互作用。该系统不但可以检验量子物理的基本理论，有助于人们从根本上认识光与原子相互作用的过程，而且近年来作为量子信息的一种方案引起了人们的高度关注。在强耦合腔量子电动力学过程中，单个原子与单个光子相互作用的拉比(Rabi)频率远大于腔场的衰减率和原子的自发辐射率，即腔内光与原子的相干相互作用强于整个系统的消相干过程，原子和腔场之间的演化在一定范围内可以看成相干演化过程，腔QED系统也因此成为研究光场与原子纠缠和消相干过程的重要手段。对腔QED过程的研究极大地促进了原子操控、单粒子测量等多方面的发展。
一方面，随着激光冷却和俘获中性原子技术的发展成熟，人们可以将一团原子甚至于单个原子俘获在空间中特定的范围，并冷却到接近绝对零度。但是如何在微腔中确定性地控制单个原子并对其进行测量是光频区腔QED实验面临的一个主要问题。本文系统回顾了腔QED实验中内腔单原子的制备方案，并提出利用微光学偶极阱的单原子隔离效应实现微腔内确定性单原子的俘获方案。在实验上我们采用双级磁光阱，利用原子自由下落的实验方案建立了自己的实验系统，在一定程度上获得了原子的控制。
另一方面，光频区腔QED实验应用腔长极短(几十到几百微米)的超高精细度(几十万到一百万)的光学F-P腔作为光子和原子相互作用的环境。由于光学F-P腔极高的精细度，内腔光场的的衰减率非常小；同时极短的腔长可以增强单个原子的电场强度，增大光子与原子之间的相互作用(即拉比频率)，从而使整个系统达到强耦合。光学微腔的建立、测量和控制是整个实验过程中的另一个重要环节。本文详细介绍了光学微腔的搭建和参数的测量过程，并对微腔锁定和操控系统的实现做了具体的分析，最终实现了微腔的锁定并在实验上观察到原子自由下落穿过微腔的信号。
同时，对于腔QED实验系统这样一个开放系统，只能通过微腔腔镜的透射信号获得腔内的光场与原子相互作用的信息，并通过透射光场获得原子的控制等。对于强耦合的腔QED系统，平均内腔光子数非常小，微腔出射光一般在pW量级。因此建立单粒子(单原子、单光子)水平上的测量系统是实验的另一个重要方面。本文从平衡差拍探测和单光子计数两方面分析了基于腔QED中的测量问题，建立了灵敏的测量系统。
综合上面的几个方面，围绕腔QED系统中的若干问题，本文完成了以下的具体工作：
1．用曲率半径为10 mm的一对腔镜搭建了用于腔QED实验的光学微腔，并严格测量了其有效腔长和几何腔长分别为L_(eff)＝44.627±0.004μm和L＝43.900±0.005μm，线宽为△v＝47.8±1.5MHz，对应的光和原子的最大耦合系数和腔场衰减率分别为2π×39.2MHz和2π×23.9MHz。对比铯原子D2线的能级衰减率2π×2.61MHz，相应的临界光子数和临界原子数分别为m_o＝0.0022和N_o=0.081。该光学微腔满足光场与原子之间强耦合的要求。
2．系统分析了高精细度光学F-P腔的透射和反射，并在实验上通过对微腔两端入射光场的功率透射率和反射率以及相应的模式匹配效率的精确测量，在较高的精度上确定了任意非对称高精细度光学腔的有用和无用损耗，确定了实验所用微光学腔的透射和其他损耗分别为：T_1=5.0(9)ppm，T_2=4.5(8)ppm,l_1=33.2(7)ppm，l_2=45.4(6)ppm。
3．自制了探测带宽为100MHz的射频探测器，并用其搭建了一套测量灵敏度可达3.6fW的差拍探测系统。对于我们建立起来的光学微腔，用其可以探测到的最小内腔平均光子数为0.001。
4．建立了一个基于实际系统的模型，从理论上分析了由两个单光子探测模块(SPCM)组成的HB7探测系统对各种光场二阶相干度和Mandel因子测量时，由于多种因素，包括SPCM不能同时相应多个光子的特性、背景光场和有限的探测效率等，对实际结果的影响，并从实验上通过对相干光和热光场二阶相干度的测量证实了理论分析。
5．系统分析了腔QED系统中微腔腔长的稳定性要求和其锁定环路中的噪声要求，并采用射频边带锁频技术，利用微腔透射光场将微腔锁定到透射峰的0.1，对应的微腔长度起伏小于2pm。
6．在实验上用斩波法实现对微腔的控制，并利用用差拍探测系统观察到铯原子自由下落时在微腔腔模中的渡越信号。
The cavity quantum electrodynamics (Cavity QED) mainly focuses on the interaction between single atoms and quantized electromagnetic field in a confined space. It has been provided a platform to test the principles of quantum electrodynamics and help people to get a deep insight into the fundamentals of atom-photon interaction. As one of the main methods for quantum information process (QIP) the cavity QED system has been a hot research field recently to demonstrate quantum computation based on the manipulation of individual atoms inside a cavity. In the strong-coupling-regime cavity QED, the atom-photon interaction (the Rabi frequency) is much larger than atom's spontaneous decay and cavity field decay, which means that the coherence effect of atom-photon system is overwhelming the decoherence of the system. In this case the evolvement of the atom-photon-cavity system can be seen as a coherent system and it makes the cavity QED system one of the prospects studying quantum entanglements, quantum decoherence process and quantum information science. The research of cavity QED, in the meantime, boosts the research of atom manipulation, single quanta detection etc.
On one hand, the technique of laser cooling and trapping for neutral atoms comprehensively enhanced the ability of manipulating large number atoms, even single atom, in the free space. In the cavity QED experiment, however, a single atom needs to be captured inside a tiny space formed by a microcavity and this is still the main challenge. We retrospect in this dissertation some methods of getting single atoms trapped in optical domain cavity QED experiment, including optical lattices and tiny single optical trap with which single atom can be trapped by the blockade effect. We propose a new method, combined the single atom optical trap and microcavity, to capture deterministic single atoms inside microcavity. At present time, based on the free-falling configuration, we have designed and built our double MOT system and realized atom transportation from up-MOT to down-MOT and demonstrated the atom falling to the cavity.
On the other hand, the cavity used in the optical domain cavity QED experiments usually has a length of tens micrometers and the cavity finesse is very high (usually from 10~4 to 10~6). High quality cavity implies long pthoton life time inside the cavity, which dramatically decreases the dissipation of the intracacity fields. And the short cavity means small cavity volume with high amplitude of a single-photon field, consequently, strong atom-photon interaction (Rabi frequency). All these efforts can bring the whole photon-atom system to the strong coupling regime. Clearly the microcavity plays a critical role in the whole experiment, including the cavity building, the parameter measurement and the cavity control. As one of the main part of this dissertation, we will introduce in detail our microcavity building procedure, parameters measuring methods, microcavity locking and control schemes. And eventually by chopping the cavity locking beam we observed the atom transits based on the microcavity and atom control.
Moreover, cavity QED is an open quantum system and the intracavity atom-photon dynamic process can be known only by the leakage of the field through the cavity mirrors. By measuring the output field one can not only know what happened inside the cavity, but also prepare certain quantum states and control the atoms by quantum feedback. However, in the strong coupling regime the intracavity mean-photon-number is so small that the leakage power is usually at the level of pW. So a very sensitive detection system on single quanta level is needed and it is another important issue for the cavity QED experiment. We have theoretically analyzed and experimentally investigated the ultra-sensitive detection based on the balanced heterodyne detection as well as the single photon counting detection.
The main works of this dissertation are as follows:
1. We have built a microcavity by means of two super-mirrors with 100 mm of radius and measured the effective and physical lengths as L_(eff)= 44.627±0.004μm and L = 43.900±0.005μm , respectively. We also measured cavity linewidth asΔv = 47.8±1.5MHz , the corresponding maximum atom-cavity coupling factor and the cavity field decay rate are 2π×39.2MHz and 2π×23.9MHz, respectively. Since the decay rates of the Cesium atom D2 line is 2π×2.61MHz, the corresponding critical photon number and critical atom number are m_0=0.0022 and N_0=0.081 , respectively. This implies that our microcavity fulfill the requirements of strong coupling.
2. We theoretically analyzed the reflectivities and transmissions of an arbitary F-P cavity with incident beams on both sides. And by measuring the TEM_(00) mode matching efficiency we have accomplished the measurement experimentally with high precision and determined the transmission losses and other unwanted losses of an asymmetric microcavity. The measured results for mirror 1 and mirror 2 are: T_1 = 5.0(9) ppm , T_2 = 4.5(8)ppm, l_1 = 33.2(7)ppm,l_2 = 45.4(6)ppm, respectively.
3. We built a balanced heterodyne detection system with two home-made RF detectors. The minimum detected power can be achieved as 3.7 fW, which corresponds to a mean intracavity photon number of 0.001 for our microcavity.
4. We established a detection model based on the HBT scheme and modern single photon count module (SPCM) which is not photon number resolvable. The real experimental situations have been taken into account, including total detection efficiency, background noise and the property of SPCM. The detected second order degree of coherence, g~((2)), has been comprehensively analyzed. We also finished the experiment measurement of g~((2)) with coherent light and thermal light and confirmed our theoretical analyses.
5. We analyzed the stability of the microcavity length and the requirement of feedback loop for the cavity locking. By using the Pound-Drever-Hall method the microcavity has been controlled with length stability of 2 pm.
6. Atom transits were observed with heterodyne detection when carefully controlling the atom falling and the microcavity with a chopped auxiliary locking beam.
一方面，随着激光冷却和俘获中性原子技术的发展成熟，人们可以将一团原子甚至于单个原子俘获在空间中特定的范围，并冷却到接近绝对零度。但是如何在微腔中确定性地控制单个原子并对其进行测量是光频区腔QED实验面临的一个主要问题。本文系统回顾了腔QED实验中内腔单原子的制备方案，并提出利用微光学偶极阱的单原子隔离效应实现微腔内确定性单原子的俘获方案。在实验上我们采用双级磁光阱，利用原子自由下落的实验方案建立了自己的实验系统，在一定程度上获得了原子的控制。
另一方面，光频区腔QED实验应用腔长极短(几十到几百微米)的超高精细度(几十万到一百万)的光学F-P腔作为光子和原子相互作用的环境。由于光学F-P腔极高的精细度，内腔光场的的衰减率非常小；同时极短的腔长可以增强单个原子的电场强度，增大光子与原子之间的相互作用(即拉比频率)，从而使整个系统达到强耦合。光学微腔的建立、测量和控制是整个实验过程中的另一个重要环节。本文详细介绍了光学微腔的搭建和参数的测量过程，并对微腔锁定和操控系统的实现做了具体的分析，最终实现了微腔的锁定并在实验上观察到原子自由下落穿过微腔的信号。
同时，对于腔QED实验系统这样一个开放系统，只能通过微腔腔镜的透射信号获得腔内的光场与原子相互作用的信息，并通过透射光场获得原子的控制等。对于强耦合的腔QED系统，平均内腔光子数非常小，微腔出射光一般在pW量级。因此建立单粒子(单原子、单光子)水平上的测量系统是实验的另一个重要方面。本文从平衡差拍探测和单光子计数两方面分析了基于腔QED中的测量问题，建立了灵敏的测量系统。
综合上面的几个方面，围绕腔QED系统中的若干问题，本文完成了以下的具体工作：
1．用曲率半径为10 mm的一对腔镜搭建了用于腔QED实验的光学微腔，并严格测量了其有效腔长和几何腔长分别为L_(eff)＝44.627±0.004μm和L＝43.900±0.005μm，线宽为△v＝47.8±1.5MHz，对应的光和原子的最大耦合系数和腔场衰减率分别为2π×39.2MHz和2π×23.9MHz。对比铯原子D2线的能级衰减率2π×2.61MHz，相应的临界光子数和临界原子数分别为m_o＝0.0022和N_o=0.081。该光学微腔满足光场与原子之间强耦合的要求。
2．系统分析了高精细度光学F-P腔的透射和反射，并在实验上通过对微腔两端入射光场的功率透射率和反射率以及相应的模式匹配效率的精确测量，在较高的精度上确定了任意非对称高精细度光学腔的有用和无用损耗，确定了实验所用微光学腔的透射和其他损耗分别为：T_1=5.0(9)ppm，T_2=4.5(8)ppm,l_1=33.2(7)ppm，l_2=45.4(6)ppm。
3．自制了探测带宽为100MHz的射频探测器，并用其搭建了一套测量灵敏度可达3.6fW的差拍探测系统。对于我们建立起来的光学微腔，用其可以探测到的最小内腔平均光子数为0.001。
4．建立了一个基于实际系统的模型，从理论上分析了由两个单光子探测模块(SPCM)组成的HB7探测系统对各种光场二阶相干度和Mandel因子测量时，由于多种因素，包括SPCM不能同时相应多个光子的特性、背景光场和有限的探测效率等，对实际结果的影响，并从实验上通过对相干光和热光场二阶相干度的测量证实了理论分析。
5．系统分析了腔QED系统中微腔腔长的稳定性要求和其锁定环路中的噪声要求，并采用射频边带锁频技术，利用微腔透射光场将微腔锁定到透射峰的0.1，对应的微腔长度起伏小于2pm。
6．在实验上用斩波法实现对微腔的控制，并利用用差拍探测系统观察到铯原子自由下落时在微腔腔模中的渡越信号。
The cavity quantum electrodynamics (Cavity QED) mainly focuses on the interaction between single atoms and quantized electromagnetic field in a confined space. It has been provided a platform to test the principles of quantum electrodynamics and help people to get a deep insight into the fundamentals of atom-photon interaction. As one of the main methods for quantum information process (QIP) the cavity QED system has been a hot research field recently to demonstrate quantum computation based on the manipulation of individual atoms inside a cavity. In the strong-coupling-regime cavity QED, the atom-photon interaction (the Rabi frequency) is much larger than atom's spontaneous decay and cavity field decay, which means that the coherence effect of atom-photon system is overwhelming the decoherence of the system. In this case the evolvement of the atom-photon-cavity system can be seen as a coherent system and it makes the cavity QED system one of the prospects studying quantum entanglements, quantum decoherence process and quantum information science. The research of cavity QED, in the meantime, boosts the research of atom manipulation, single quanta detection etc.
On one hand, the technique of laser cooling and trapping for neutral atoms comprehensively enhanced the ability of manipulating large number atoms, even single atom, in the free space. In the cavity QED experiment, however, a single atom needs to be captured inside a tiny space formed by a microcavity and this is still the main challenge. We retrospect in this dissertation some methods of getting single atoms trapped in optical domain cavity QED experiment, including optical lattices and tiny single optical trap with which single atom can be trapped by the blockade effect. We propose a new method, combined the single atom optical trap and microcavity, to capture deterministic single atoms inside microcavity. At present time, based on the free-falling configuration, we have designed and built our double MOT system and realized atom transportation from up-MOT to down-MOT and demonstrated the atom falling to the cavity.
On the other hand, the cavity used in the optical domain cavity QED experiments usually has a length of tens micrometers and the cavity finesse is very high (usually from 10~4 to 10~6). High quality cavity implies long pthoton life time inside the cavity, which dramatically decreases the dissipation of the intracacity fields. And the short cavity means small cavity volume with high amplitude of a single-photon field, consequently, strong atom-photon interaction (Rabi frequency). All these efforts can bring the whole photon-atom system to the strong coupling regime. Clearly the microcavity plays a critical role in the whole experiment, including the cavity building, the parameter measurement and the cavity control. As one of the main part of this dissertation, we will introduce in detail our microcavity building procedure, parameters measuring methods, microcavity locking and control schemes. And eventually by chopping the cavity locking beam we observed the atom transits based on the microcavity and atom control.
Moreover, cavity QED is an open quantum system and the intracavity atom-photon dynamic process can be known only by the leakage of the field through the cavity mirrors. By measuring the output field one can not only know what happened inside the cavity, but also prepare certain quantum states and control the atoms by quantum feedback. However, in the strong coupling regime the intracavity mean-photon-number is so small that the leakage power is usually at the level of pW. So a very sensitive detection system on single quanta level is needed and it is another important issue for the cavity QED experiment. We have theoretically analyzed and experimentally investigated the ultra-sensitive detection based on the balanced heterodyne detection as well as the single photon counting detection.
The main works of this dissertation are as follows:
1. We have built a microcavity by means of two super-mirrors with 100 mm of radius and measured the effective and physical lengths as L_(eff)= 44.627±0.004μm and L = 43.900±0.005μm , respectively. We also measured cavity linewidth asΔv = 47.8±1.5MHz , the corresponding maximum atom-cavity coupling factor and the cavity field decay rate are 2π×39.2MHz and 2π×23.9MHz, respectively. Since the decay rates of the Cesium atom D2 line is 2π×2.61MHz, the corresponding critical photon number and critical atom number are m_0=0.0022 and N_0=0.081 , respectively. This implies that our microcavity fulfill the requirements of strong coupling.
2. We theoretically analyzed the reflectivities and transmissions of an arbitary F-P cavity with incident beams on both sides. And by measuring the TEM_(00) mode matching efficiency we have accomplished the measurement experimentally with high precision and determined the transmission losses and other unwanted losses of an asymmetric microcavity. The measured results for mirror 1 and mirror 2 are: T_1 = 5.0(9) ppm , T_2 = 4.5(8)ppm, l_1 = 33.2(7)ppm,l_2 = 45.4(6)ppm, respectively.
3. We built a balanced heterodyne detection system with two home-made RF detectors. The minimum detected power can be achieved as 3.7 fW, which corresponds to a mean intracavity photon number of 0.001 for our microcavity.
4. We established a detection model based on the HBT scheme and modern single photon count module (SPCM) which is not photon number resolvable. The real experimental situations have been taken into account, including total detection efficiency, background noise and the property of SPCM. The detected second order degree of coherence, g~((2)), has been comprehensively analyzed. We also finished the experiment measurement of g~((2)) with coherent light and thermal light and confirmed our theoretical analyses.
5. We analyzed the stability of the microcavity length and the requirement of feedback loop for the cavity locking. By using the Pound-Drever-Hall method the microcavity has been controlled with length stability of 2 pm.
6. Atom transits were observed with heterodyne detection when carefully controlling the atom falling and the microcavity with a chopped auxiliary locking beam.
引文
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