非经典光场与原子相互作用的理论研究
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摘要
光与原子的相互作用,一直是量子光学和原子物理研究领域的重要课题之一。随着实验上各种非经典光场的出现,研究原子与非经典光场的作用引起了人们的注意。其中的压缩光场,在实验上已经被广泛研究并且在量子信息处理过程,特别是量子纠缠的产生和连续变量量子信息过程中具有特殊意义,因此它与原子的作用更是备受关注。研究非经典光场与原子的作用,一方面希望探索这种有别于普通相干光的光场与原子作用中所表现的量子行为,揭示原子处在更为特殊的环境(非经典场)中将呈现的各种奇异性质,这对我们理解光与原子相互作用这一基本过程具有重要意义;另一方面,由于大多数非经典态是非常弱的光场,它们与单个原子的作用过程可以获得清晰的物理图像,研究在单光子和单原子水平原子与光子的作用过程对于今天人们广泛关注的量子纠缠、量子退相干过程、单光子源的产生,量子信息处理等具有重要的价值。研究这一课题的另外一个动机是:目前国际上若干研究组以及本人所在的课题组已经可以在单原子水平上对原子进行良好的操控和测量,量子光学与光量子器件国家重点实验室在各种非经典光场的产生、测量和应用方面具有很强的实验基础,从而使我们的研究主要从实验出发,围绕实验开展工作,也使理论研究的某些结果可望直接应用到实验方面。
要使原子与光场发生很好的作用,腔QED实验无疑是最好的手段。光频段腔量子电动力学(Cavity QED)对认识原子与光的作用至关重要。作为目前为数不多的能够在实验室环境下观察单粒子量子行为的系统,腔QED系统不仅可以作为探索量子物理世界若干非经典行为的重要工具,例如薛定谔猫态、量子测量等等,而且在量子计算、量子态的制备以及量子通信等领域也具有重要价值。而对单原子或少数原子的有效操控是实现上述过程的基础。随着技术的进步,现在人们不仅可以将冷原子冷却到绝对零度附近,而且可以通过光学偶极阱实现对少数原子的操控。20世纪90年代,随着量子光学和冷原子技术的发展,高品质微腔和原子冷却与俘获技术的结合使得单原子与光场相互作用的Jaynes-Cummings模型已经可以得到很好的实验检验。
目前我们实验小组已经建立了用于腔QED实验的磁光阱系统,高品质微光学腔系统,实现了原子的光学偶极俘获,获得了单个原子的长时间控制,并在单原子和单光子探测方面取得了重要进展;在非经典光场的产生方面也获得了原子线附近的亚泊松光场并正在开展铯原子线压缩真空态和EPR态的研究。这些实验基础为进一步开展微腔中单个原子与光场,尤其是与非经典光场相互作用的研究奠定了基础,这也是本理论研究的重要出发点:我们希望通过非经典光场与原子相互作用的研究,探索该过程中新的量子现象,对该过程的基本物理过程有深入的理解,同时,以实验中的真实参数为理论计算的依据,以期对实验上可能得到的结果或者已经得到的结果做出预判或者解释。
结合相关的实验内容,我们从原子和光场相互作用的哈密顿量(一般还需要考虑热库)出发,利用基本的量子光学处理方法(如薛定谔方程、主方程、Fokker-Planck方程、Langevin方程等),考虑相关的初始条件,理论推导和数值计算相结合(主要采用mathematica、Matlab、qo-toolbox等),得到了一些有意义的结果。本文完成的主要工作包含以下内容:
1.讨论了在现有的实验条件下,如腔的参数等已知的情况下,要实现能够俘获单个铯原子的光学偶极阱,即深度达到1mK以上,所需的其他参数的最优选择,比如偶极俘获光的波长、功率及腰斑等。
2.提出了利用介质表面的多束倏逝驻波形成的二维光学晶格获得亚半波长偶极阱的一种方案,并对其中偶极阱的特点进行了分析,包括深度和尺度等方面。结果表明,通过选择合适的波长可以获得尺度小于半波长的光学微阱,再配合瓦级功率的FORT光,阱深可达mK量级。为在微尺度上更好地控制原子提供了一种可能的方案。
3.利用原子和光场强耦合的缀饰理论,可以很好的解释一些实验结果。我们在考虑多能级的情况下,仔细计算了原子的精细能级和超精细能级对光频移(阱深)的影响,得到了铯原子D_2线两个能级的magic wavelength,为分析实验中确实存在的复杂能级的影响提供了可靠的方法。
4.研究了原子与各种光场(包括经典光场和非经典光场)相互作用时原子和光场各自特性的变化,包括原子的布居数、能级、吸收谱和荧光谱,以及光场的起伏、光子数统计性质等等。其中,重点研究了压缩真空环境下原子-光场纠缠的演化以及该过程对光场本身的非经典特性的影响,并与相干态进行了比较,结果表明,在相同条件下,压缩真空中原子-光场之间的纠缠要远强于相干光场的情形。
5.研究了将原子放入简并光学参量振荡器(DOPO腔)中时内腔场(输出场)的光子统计性质,以及光学双稳和阈值改变对它的影响,结果表明,当腔内原子很多时,有很强的亚泊松统计性质和很弱的反聚束效应,可用于大数目的数态的制备;而当腔内只有单个原子时,显示出的亚泊松统计和反聚束效应均较强,适合单光子源的制备。
6.研究了腔QED系统中腔长和泵浦光强度对腔的输出场以及原子特性的影响,比如输出场的光子统计性质、原子的布居数等。进一步研究了铯原子腔QED系统产生单光子源的可能方案。
The interaction between light and atom is an important issue in quantum optics and atomic physics.Since several kinds of nonclassical light field were experimentally generated,much interest has been induced about the interaction between atoms and nonclassical states.The interaction between atom and squeezed light,which has been investigated extensively and especially is very important in quantum entanglement generation and quantum information processing,has been more attractive.To investigate the interaction between atom and nonclassical field,on the one hand,we want to explore the new features of the atom locating in a nonclassical environment,which is quite different from the interaction with the coherent light in some aspects,and this is also important to understand the fundamentals of the atom-field interaction.On the other hand,most generated nonclassical light are very weak,so their interaction with single atom can bring us a clear physical picture.Investigating atom-photon interaction at the single-atom and single-photon level is playing an important role in quantum entanglement,quantum decoherence,generation of single-photon resource and quantum information processing.One more motivation is probably more convincing:several groups in the world, including our group,has already realized the single atom manipulation,and our institute,state key laboratory of quantum optics and quantum optics devices,has strong experimental background of the generation, measurement and application of various nonclassical fields,therefore the theoretical works in this thesis are fundamentally based on the experiments or closely related to the experiments.
Cavity Quantum Electrodynamics(Cavity QED) is the best way to demonstrate the interaction between atom and light field.As a special system that can experimentally observe the quantum behavior of single particle,Cavity QED is not only an important tool to explore the nonclassical properties in the quantum physical world,such as the Schr(o|¨)dinger cat state,quantum measurement,etc.,but also can play an important role in quantum computation,quantum state preparation and quantum communication.Yet,the effective control of single or few atoms is a precondition of realizing the above-mentioned process.With the development of the technologies,cold atoms with ultra-low temperature and single atom manipulation with micro-optical dipole trap have already been realized.From 1990s to the beginning of 21 century,the combination of high quality micro-cavity and atom cooling and trapping technology eventually provided a good experimental test of the Jaynes-Cummings model in the strong interaction regime at the single atom and single photon level.
Our experimental group has already established a high quality micro-cavity system and a double Magnetic Optical Trap(double MOT) system for Cavity QED experiment,we have realized optical dipole trap of atoms and long-time control of single atom.We also have a group involving the generation of nonclassical light.We have obtained the sub-Poissonian light field near atomic line,and are trying to generate the squeezed vacuum state and the EPR state at exact transitions of Cs atom.All these experiments constitute the basis of investigating the interaction of single atom and field, especially nonclassical field,in the micro-cavity.It should be pointed out that,through the study of the interaction between the atom and the nonclassical field,we want to explore the new quantum phenomenon in this process and to understand more fundamentals.Meanwhile by using the real experimental parameters,we also want to predict or explain some experimental results.
Basically,we started from the Hamiltonian of the atom-field interacting system(generally,the reservoir is considered),using the usual method of quantum optics(such as the Schr(o|¨)dinger Equation,Master Equation, Fokker-Planck Equation and Langevin Equation) and the initial condition, to discuss the system either by some theoretical deducing pocess or numerical simulations(Mathematica,Matlab and qotoolbox,etc.),and we obtained some significative results.The main works accomplished in this thesis are the following:
1.We discussed the optimized parameter of optical dipole trap,such as the wavelength,the power and the waist of the trapping light for obtaining optical dipole traps with 1mK in depth,based on the existing experimental conditions.
2.We proposed a scheme of generating bi-dimentional optical lattices formed by sub-half-wavelength traps by using several sets of laser evanescent standing waves propagating at the surface of a dielectric prism.The characteristics of the optical traps including their depths and the sizes are analyzed.It is shown that the micro-optical lattice with sub-half-wavelength size can be achieved by the interference of the selected evanescent waves.With a few Watts of the trapping laser beams in power,an optical lattice with a potential depth around 1 mK can be achieved.This provides a possible way of controlling single atom in a sub-micron range.
3.Using the dressed atom theory about strong atom-field coupling,one can explain some experimental results well.Further considering the multilevels of the atom Cs,we obtained the magic wavelength of its D_2 line by calculating the influence of trapping light on the atomic fine-structure.This work provides a reliable method for analyzing the complicated energy level of the atom in the real experiments.
4.We investigated the interaction of atoms and light field(including classical and nonclassical field) and the evolution of the properties of atom and field,including the inversion,decay,absorption and fluorescence spectrum of the atom,and the fluctuations and photon statistics of the light field.We focused on the entanglement and nonclassicality evolution of an atom in a squeezed vacuum—a typical nonclassical field,and compared it with that of the coherent state.It shows that the atom-field entanglement in squeezed vacuum is much stronger and stable than that of coherent state,whereas the nonclassicality of the light field depends on its initial status.This investigation is trying to find a new insight into the relation between entanglement and nonclassicality of light fields and the result shows that nonclassical field may provide helps for getting strong quantum entanglement,and the strong entanglement implies the better control of the atom and photon mutually in a nonclassical environment.
5.By putting the atoms directly into a squeezed light generator—a degenerate optical parametric oscillator(DOPO),we investigated the photon statistics of the intracavity field and analyzed the influence of the optical bistability and the modified threshold of the systen.The result is that when there are many atoms in the cavity it shows strong sub-Poinssonian and weak anti-bunching effects,which may be used for the generation of Fock state with arbitrary photon numbers and when there is only one atom in the cavity,the system shows both strong sub-Poissonian and anti-bunching,as is expected.This feature is supposing for the generation of single photon source.
6.We also discussed the influence of the cavity and light parameter of the Cavity QED system on the properties of the output field,such as the photon statistics and the power spectrum,etc.This discussion is helpful for our experiment of generating single-photon source with proper parameters,such as the cavity length,and the pumping power,etc.
要使原子与光场发生很好的作用,腔QED实验无疑是最好的手段。光频段腔量子电动力学(Cavity QED)对认识原子与光的作用至关重要。作为目前为数不多的能够在实验室环境下观察单粒子量子行为的系统,腔QED系统不仅可以作为探索量子物理世界若干非经典行为的重要工具,例如薛定谔猫态、量子测量等等,而且在量子计算、量子态的制备以及量子通信等领域也具有重要价值。而对单原子或少数原子的有效操控是实现上述过程的基础。随着技术的进步,现在人们不仅可以将冷原子冷却到绝对零度附近,而且可以通过光学偶极阱实现对少数原子的操控。20世纪90年代,随着量子光学和冷原子技术的发展,高品质微腔和原子冷却与俘获技术的结合使得单原子与光场相互作用的Jaynes-Cummings模型已经可以得到很好的实验检验。
目前我们实验小组已经建立了用于腔QED实验的磁光阱系统,高品质微光学腔系统,实现了原子的光学偶极俘获,获得了单个原子的长时间控制,并在单原子和单光子探测方面取得了重要进展;在非经典光场的产生方面也获得了原子线附近的亚泊松光场并正在开展铯原子线压缩真空态和EPR态的研究。这些实验基础为进一步开展微腔中单个原子与光场,尤其是与非经典光场相互作用的研究奠定了基础,这也是本理论研究的重要出发点:我们希望通过非经典光场与原子相互作用的研究,探索该过程中新的量子现象,对该过程的基本物理过程有深入的理解,同时,以实验中的真实参数为理论计算的依据,以期对实验上可能得到的结果或者已经得到的结果做出预判或者解释。
结合相关的实验内容,我们从原子和光场相互作用的哈密顿量(一般还需要考虑热库)出发,利用基本的量子光学处理方法(如薛定谔方程、主方程、Fokker-Planck方程、Langevin方程等),考虑相关的初始条件,理论推导和数值计算相结合(主要采用mathematica、Matlab、qo-toolbox等),得到了一些有意义的结果。本文完成的主要工作包含以下内容:
1.讨论了在现有的实验条件下,如腔的参数等已知的情况下,要实现能够俘获单个铯原子的光学偶极阱,即深度达到1mK以上,所需的其他参数的最优选择,比如偶极俘获光的波长、功率及腰斑等。
2.提出了利用介质表面的多束倏逝驻波形成的二维光学晶格获得亚半波长偶极阱的一种方案,并对其中偶极阱的特点进行了分析,包括深度和尺度等方面。结果表明,通过选择合适的波长可以获得尺度小于半波长的光学微阱,再配合瓦级功率的FORT光,阱深可达mK量级。为在微尺度上更好地控制原子提供了一种可能的方案。
3.利用原子和光场强耦合的缀饰理论,可以很好的解释一些实验结果。我们在考虑多能级的情况下,仔细计算了原子的精细能级和超精细能级对光频移(阱深)的影响,得到了铯原子D_2线两个能级的magic wavelength,为分析实验中确实存在的复杂能级的影响提供了可靠的方法。
4.研究了原子与各种光场(包括经典光场和非经典光场)相互作用时原子和光场各自特性的变化,包括原子的布居数、能级、吸收谱和荧光谱,以及光场的起伏、光子数统计性质等等。其中,重点研究了压缩真空环境下原子-光场纠缠的演化以及该过程对光场本身的非经典特性的影响,并与相干态进行了比较,结果表明,在相同条件下,压缩真空中原子-光场之间的纠缠要远强于相干光场的情形。
5.研究了将原子放入简并光学参量振荡器(DOPO腔)中时内腔场(输出场)的光子统计性质,以及光学双稳和阈值改变对它的影响,结果表明,当腔内原子很多时,有很强的亚泊松统计性质和很弱的反聚束效应,可用于大数目的数态的制备;而当腔内只有单个原子时,显示出的亚泊松统计和反聚束效应均较强,适合单光子源的制备。
6.研究了腔QED系统中腔长和泵浦光强度对腔的输出场以及原子特性的影响,比如输出场的光子统计性质、原子的布居数等。进一步研究了铯原子腔QED系统产生单光子源的可能方案。
The interaction between light and atom is an important issue in quantum optics and atomic physics.Since several kinds of nonclassical light field were experimentally generated,much interest has been induced about the interaction between atoms and nonclassical states.The interaction between atom and squeezed light,which has been investigated extensively and especially is very important in quantum entanglement generation and quantum information processing,has been more attractive.To investigate the interaction between atom and nonclassical field,on the one hand,we want to explore the new features of the atom locating in a nonclassical environment,which is quite different from the interaction with the coherent light in some aspects,and this is also important to understand the fundamentals of the atom-field interaction.On the other hand,most generated nonclassical light are very weak,so their interaction with single atom can bring us a clear physical picture.Investigating atom-photon interaction at the single-atom and single-photon level is playing an important role in quantum entanglement,quantum decoherence,generation of single-photon resource and quantum information processing.One more motivation is probably more convincing:several groups in the world, including our group,has already realized the single atom manipulation,and our institute,state key laboratory of quantum optics and quantum optics devices,has strong experimental background of the generation, measurement and application of various nonclassical fields,therefore the theoretical works in this thesis are fundamentally based on the experiments or closely related to the experiments.
Cavity Quantum Electrodynamics(Cavity QED) is the best way to demonstrate the interaction between atom and light field.As a special system that can experimentally observe the quantum behavior of single particle,Cavity QED is not only an important tool to explore the nonclassical properties in the quantum physical world,such as the Schr(o|¨)dinger cat state,quantum measurement,etc.,but also can play an important role in quantum computation,quantum state preparation and quantum communication.Yet,the effective control of single or few atoms is a precondition of realizing the above-mentioned process.With the development of the technologies,cold atoms with ultra-low temperature and single atom manipulation with micro-optical dipole trap have already been realized.From 1990s to the beginning of 21 century,the combination of high quality micro-cavity and atom cooling and trapping technology eventually provided a good experimental test of the Jaynes-Cummings model in the strong interaction regime at the single atom and single photon level.
Our experimental group has already established a high quality micro-cavity system and a double Magnetic Optical Trap(double MOT) system for Cavity QED experiment,we have realized optical dipole trap of atoms and long-time control of single atom.We also have a group involving the generation of nonclassical light.We have obtained the sub-Poissonian light field near atomic line,and are trying to generate the squeezed vacuum state and the EPR state at exact transitions of Cs atom.All these experiments constitute the basis of investigating the interaction of single atom and field, especially nonclassical field,in the micro-cavity.It should be pointed out that,through the study of the interaction between the atom and the nonclassical field,we want to explore the new quantum phenomenon in this process and to understand more fundamentals.Meanwhile by using the real experimental parameters,we also want to predict or explain some experimental results.
Basically,we started from the Hamiltonian of the atom-field interacting system(generally,the reservoir is considered),using the usual method of quantum optics(such as the Schr(o|¨)dinger Equation,Master Equation, Fokker-Planck Equation and Langevin Equation) and the initial condition, to discuss the system either by some theoretical deducing pocess or numerical simulations(Mathematica,Matlab and qotoolbox,etc.),and we obtained some significative results.The main works accomplished in this thesis are the following:
1.We discussed the optimized parameter of optical dipole trap,such as the wavelength,the power and the waist of the trapping light for obtaining optical dipole traps with 1mK in depth,based on the existing experimental conditions.
2.We proposed a scheme of generating bi-dimentional optical lattices formed by sub-half-wavelength traps by using several sets of laser evanescent standing waves propagating at the surface of a dielectric prism.The characteristics of the optical traps including their depths and the sizes are analyzed.It is shown that the micro-optical lattice with sub-half-wavelength size can be achieved by the interference of the selected evanescent waves.With a few Watts of the trapping laser beams in power,an optical lattice with a potential depth around 1 mK can be achieved.This provides a possible way of controlling single atom in a sub-micron range.
3.Using the dressed atom theory about strong atom-field coupling,one can explain some experimental results well.Further considering the multilevels of the atom Cs,we obtained the magic wavelength of its D_2 line by calculating the influence of trapping light on the atomic fine-structure.This work provides a reliable method for analyzing the complicated energy level of the atom in the real experiments.
4.We investigated the interaction of atoms and light field(including classical and nonclassical field) and the evolution of the properties of atom and field,including the inversion,decay,absorption and fluorescence spectrum of the atom,and the fluctuations and photon statistics of the light field.We focused on the entanglement and nonclassicality evolution of an atom in a squeezed vacuum—a typical nonclassical field,and compared it with that of the coherent state.It shows that the atom-field entanglement in squeezed vacuum is much stronger and stable than that of coherent state,whereas the nonclassicality of the light field depends on its initial status.This investigation is trying to find a new insight into the relation between entanglement and nonclassicality of light fields and the result shows that nonclassical field may provide helps for getting strong quantum entanglement,and the strong entanglement implies the better control of the atom and photon mutually in a nonclassical environment.
5.By putting the atoms directly into a squeezed light generator—a degenerate optical parametric oscillator(DOPO),we investigated the photon statistics of the intracavity field and analyzed the influence of the optical bistability and the modified threshold of the systen.The result is that when there are many atoms in the cavity it shows strong sub-Poinssonian and weak anti-bunching effects,which may be used for the generation of Fock state with arbitrary photon numbers and when there is only one atom in the cavity,the system shows both strong sub-Poissonian and anti-bunching,as is expected.This feature is supposing for the generation of single photon source.
6.We also discussed the influence of the cavity and light parameter of the Cavity QED system on the properties of the output field,such as the photon statistics and the power spectrum,etc.This discussion is helpful for our experiment of generating single-photon source with proper parameters,such as the cavity length,and the pumping power,etc.
引文
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