多色电磁感应透明与量子纠缠态的制备
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摘要
原子相干与量子干涉效应是激光物理和量子光学领域的重要前沿研究课题之一。电磁感应透明是利用原子相干与量子干涉效应消去介质对光的吸收的现象。理论和实验工作都表明电磁感应透明现象可以用来减慢光的群速度甚至使光束完全停下来。在这种原子介质中光子间的相互作用的强度可以比普通介质中的要强几个数量级。因此,电磁感应透明现象在慢光、弱光强下的非线性和量子信息中的光存储和释放过程中有着重要的作用。量子纠缠反映的是两个或多个量子系统之间所存在的非局域的量子关联。量子纠缠涉及实在性、定域性、隐变量以及测量理论等量子力学的基本问题,并在量子计算和量子信息的研究中起着重要的作用。对于纠缠态性质的研究可以用于验证量子力学的基本原理,而纠缠态本身是量子信息处理的基本资源,因此如何制备纠缠态受到人们的广泛关注。另外,由于系统与周围的环境的相互作用而导致的退相干的影响,使得所制备的纠缠态十分脆弱而难以长时间保存。因此,基于现有的实验条件和技术,如何制备出抗环境干扰能力强、稳定的、高纠缠度的纠缠源是人们感兴趣的问题。本文在多色场驱动的电磁感应透明和量子纠缠态的制备方面做了有益的探索。论文的主要创新性结果如下:
1.关于多色电磁感应透明方面的工作:
多色电磁感应透明方面的第一个工作,我们研究了三色场驱动的三能级A型原子系统对单色弱探测场的吸收和色散,考察了吸收和色散谱对驱动场的振幅和相位的依赖性。我们采用数值方法计算吸收和色散谱。除了能够获得多电磁感应透明外,吸收和色散谱还有两个主要特征。第一,通过调节驱动场的振幅或者相位,在与探测场频率共振的频率处是电磁感应透明还是吸收是可以控制的。第二,只要我们固定驱动场的两个边频部分相对于中心频率部分的相对相位的和而改变两个相对相位各自的值,吸收和色散谱保持不变。
多色电磁感应透明方面的第二个工作,我们研究了由一对等频率差的双色场驱动的三能级级联型原子系统中的双光子吸收现象。在我们的计算中,一个双色场的高频部分的频率和另一个双色场的低频部分的频率满足双光子共振条件。我们采用谐振展开和逆矩阵方法计算双光子跃迁几率。主要结果如下:当满足双光子共振的两对场的相对相位的和相等时,双光子吸收被显著地抑制原子系统对双光子吸收透明。产生双光子透明的物理机制是:由于动态斯塔克分裂,由两对满足双光子共振的场所引起的双光子跃迁所经历的两个不同的修饰态之间相差相位π。因此,两个双光子跃迁通道间的相消干涉导致了双光子吸收的抑制。
2.关于量子纠缠态制备方面的工作:
量子纠缠态制备方面的第一个工作,我们分析了有传统非相干泵浦的量子拍激光和有相干场驱动的量子拍激光,发现在这两种激光系统中都可以产生工作在远高于阈值以上的纠缠的亚泊松光。在数值计算和结果分析时,我们采用了组合模方法引入了两个激光模的和模和差模。对有传统非相干泵浦的量子拍激光和有相干场驱动的量子拍激光,差模都是从相互作用中退耦合并且处在各自的真空态,而和模则是工作在远高于阈值以上并具有亚泊松光子统计。量子拍激光与和模强度的噪声抑制的联合导致了两束亮光间的纠缠和各个光束的亚泊松光子统计。
量子纠缠态制备方面的第二个工作,我们提出了在腔电动力学中利用暗态绝热演化方法制备一个两原子纠缠态和一个N原子W态的方案。这个方案的第一个优点是完成这个方案的时间不需要精确地控制。这个方案的第二个优点是来源于腔衰减这部分的退相干可以被抑制掉,因为在整个实施绝热演化和控制原子-腔相互作用的过程中腔模总是没有被激发的。
量子纠缠态制备方面的第三个工作,我们提出了一个腔电动力学中的基于拉曼相互作用的利用纠缠交换实现的未知原子纠缠态的纠缠浓缩方案。在这个方案中我们从一对两原子的部分纠缠态中几率地获得了一个两原子的最大纠缠态。由于两个原子和腔场以及一个外加驱动场的拉曼相互作用,我们消去了原子自发辐射的影响。同时,由于在相互作用过程中腔模是虚激发的,我们可以忽略源于腔模的衰减和热场的退相干的影响。
Atomic coherence and quantum interference is one of the most important research subjects in the field of laser physics and quantum optics.Electromagnetically induced transparency makes an otherwise opaque medium almost transparent.Theoretical and experimental work has demonstrated that this phenomenon can be used to slow down light pulses dramatically,or even bring them to a complete halt.Interactions between photons in such an atomic medium can be many orders of magnitude stronger than in conventional optical materials.Thus,electromagnetically induced transparency plays an important role in slow light,nonlinearity at low light level,light storing and retrieving in quantum information processing.Quantum entanglement reflects the nonclassical quantum correlation between two or more quantum systems.The problems related to quantum entanglement are basic theories in quantum mechanics such as reality,locality,hidden variables and measurement. Quantum entanglement also lies in the key of quantum computation and quantum information. The research about the properties of entangled states can be used to test the basic rules in quantum mechanics,while entangled states themselves are basic resources in quantum information processing.Thus entanglement preparation has received extensively research.Otherwise,due to decoherence came from the interaction between the system with the environment,the entangled states prepared are fragile and can not be kept for a long time.Thus,the preparation of robust,steady and bright entangled states has been paid more attention.In this thesis,we have studied the amplitude and phase control of electromagnetically induced transparency with polychromatic driven fields and presented several schemes to prepare entangled states in different systems.The main initiative results are presented as follows.
1.The work about electromagnetically induced transparency with polychromatic driven fields:
The first work about electromagnetically induced transparency with polychromatic driven fields is to study the absorption and dispersion properties of the three-level A atomic system when a trichromatic driven field and a monochromatic probe field couple two different transitions,respectively.The dependence of the absorption and the dispersion on the amplitude and phase of the driven field is checked.Numerical method is adopted to calculate the spectra.Multiple electromagnetically induced transparency is obtained.Two characteristic features are found.First,the central transparency can be made to appear or disappear by utilizing the amplitudes and phases of the components of the driven field. Secondly,so long as we fix the sum of two relative phases of two sideband excitation components to the central component,the absorption and dispersion spectra keep their own lineshapes unchanged no matter how we vary the respective relative phases.
The second work about electromagnetically induced transparency with polychromatic driven fields is to study the two-photon absorption in a three-level cascade atomic system driven by a pair of bichromatic fields with equal frequency difference.The high-frequency component of one bichromatic field and the low-frequency component of the other are on two-photon resonance.We adopt the method of harmonic expansion and matrix inversion. The main result is that when the sums of the phases of the different pairs of field components on the two-photon resonance are equal to each other,two-photon absorption is dramatically suppressed and the atomic system becomes transparent against two-photon absorption. Due to dynamic Stark splitting,the two-photon transitions induced by the different pairs of field components experience different dressed states with phase difference ofπ.As a result,destructive interference occurs between the two pathways and leads to the inhibition of two-photon absorption.
2.The work about preparation of entangled states:
In the first scheme of entanglement preparation,we show that a quantum-beat system with incoherent pump or coherent driving produces an entangled sub-shot-noise laser that operates well above threshold.We adopt the combination modes of the lasing fields to present the numerical results and physical analysis.The relative mode is decoupled from the active medium and stays in its vacuum state,while the sum mode operates well above threshold and has sub-shot-noise.The quantum beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of the respective beams.
In the second work about preparation of entangled states,we propose a scheme for generating a two-atom entangled state and an N-atom W state using adiabatic evolution of dark eigenstates in cavity QED.This scheme has two advantages.Firstly,the time required to complete the process does not need precise control.Secondly,since the cavity modes are never excited during the operations by engineering adiabatic evolution and controlling the atom-cavity couplings,the decoherence due to the cavity decay can be suppressed.
The last work about preparation entangled states is a concentration scheme for unknown atomic states through the Laman interaction of two atoms with a cavity mode and an external laser field.We obtain a two-atom maximally entangled sate from a pair of unknown partially entangled atomic states.In the concentration process,as the cavity mode is virtually excited and the atomic excited states are eliminated,our scheme is robust against the cavity decay,the thermal field and the atomic spontaneous emission.
1.关于多色电磁感应透明方面的工作:
多色电磁感应透明方面的第一个工作,我们研究了三色场驱动的三能级A型原子系统对单色弱探测场的吸收和色散,考察了吸收和色散谱对驱动场的振幅和相位的依赖性。我们采用数值方法计算吸收和色散谱。除了能够获得多电磁感应透明外,吸收和色散谱还有两个主要特征。第一,通过调节驱动场的振幅或者相位,在与探测场频率共振的频率处是电磁感应透明还是吸收是可以控制的。第二,只要我们固定驱动场的两个边频部分相对于中心频率部分的相对相位的和而改变两个相对相位各自的值,吸收和色散谱保持不变。
多色电磁感应透明方面的第二个工作,我们研究了由一对等频率差的双色场驱动的三能级级联型原子系统中的双光子吸收现象。在我们的计算中,一个双色场的高频部分的频率和另一个双色场的低频部分的频率满足双光子共振条件。我们采用谐振展开和逆矩阵方法计算双光子跃迁几率。主要结果如下:当满足双光子共振的两对场的相对相位的和相等时,双光子吸收被显著地抑制原子系统对双光子吸收透明。产生双光子透明的物理机制是:由于动态斯塔克分裂,由两对满足双光子共振的场所引起的双光子跃迁所经历的两个不同的修饰态之间相差相位π。因此,两个双光子跃迁通道间的相消干涉导致了双光子吸收的抑制。
2.关于量子纠缠态制备方面的工作:
量子纠缠态制备方面的第一个工作,我们分析了有传统非相干泵浦的量子拍激光和有相干场驱动的量子拍激光,发现在这两种激光系统中都可以产生工作在远高于阈值以上的纠缠的亚泊松光。在数值计算和结果分析时,我们采用了组合模方法引入了两个激光模的和模和差模。对有传统非相干泵浦的量子拍激光和有相干场驱动的量子拍激光,差模都是从相互作用中退耦合并且处在各自的真空态,而和模则是工作在远高于阈值以上并具有亚泊松光子统计。量子拍激光与和模强度的噪声抑制的联合导致了两束亮光间的纠缠和各个光束的亚泊松光子统计。
量子纠缠态制备方面的第二个工作,我们提出了在腔电动力学中利用暗态绝热演化方法制备一个两原子纠缠态和一个N原子W态的方案。这个方案的第一个优点是完成这个方案的时间不需要精确地控制。这个方案的第二个优点是来源于腔衰减这部分的退相干可以被抑制掉,因为在整个实施绝热演化和控制原子-腔相互作用的过程中腔模总是没有被激发的。
量子纠缠态制备方面的第三个工作,我们提出了一个腔电动力学中的基于拉曼相互作用的利用纠缠交换实现的未知原子纠缠态的纠缠浓缩方案。在这个方案中我们从一对两原子的部分纠缠态中几率地获得了一个两原子的最大纠缠态。由于两个原子和腔场以及一个外加驱动场的拉曼相互作用,我们消去了原子自发辐射的影响。同时,由于在相互作用过程中腔模是虚激发的,我们可以忽略源于腔模的衰减和热场的退相干的影响。
Atomic coherence and quantum interference is one of the most important research subjects in the field of laser physics and quantum optics.Electromagnetically induced transparency makes an otherwise opaque medium almost transparent.Theoretical and experimental work has demonstrated that this phenomenon can be used to slow down light pulses dramatically,or even bring them to a complete halt.Interactions between photons in such an atomic medium can be many orders of magnitude stronger than in conventional optical materials.Thus,electromagnetically induced transparency plays an important role in slow light,nonlinearity at low light level,light storing and retrieving in quantum information processing.Quantum entanglement reflects the nonclassical quantum correlation between two or more quantum systems.The problems related to quantum entanglement are basic theories in quantum mechanics such as reality,locality,hidden variables and measurement. Quantum entanglement also lies in the key of quantum computation and quantum information. The research about the properties of entangled states can be used to test the basic rules in quantum mechanics,while entangled states themselves are basic resources in quantum information processing.Thus entanglement preparation has received extensively research.Otherwise,due to decoherence came from the interaction between the system with the environment,the entangled states prepared are fragile and can not be kept for a long time.Thus,the preparation of robust,steady and bright entangled states has been paid more attention.In this thesis,we have studied the amplitude and phase control of electromagnetically induced transparency with polychromatic driven fields and presented several schemes to prepare entangled states in different systems.The main initiative results are presented as follows.
1.The work about electromagnetically induced transparency with polychromatic driven fields:
The first work about electromagnetically induced transparency with polychromatic driven fields is to study the absorption and dispersion properties of the three-level A atomic system when a trichromatic driven field and a monochromatic probe field couple two different transitions,respectively.The dependence of the absorption and the dispersion on the amplitude and phase of the driven field is checked.Numerical method is adopted to calculate the spectra.Multiple electromagnetically induced transparency is obtained.Two characteristic features are found.First,the central transparency can be made to appear or disappear by utilizing the amplitudes and phases of the components of the driven field. Secondly,so long as we fix the sum of two relative phases of two sideband excitation components to the central component,the absorption and dispersion spectra keep their own lineshapes unchanged no matter how we vary the respective relative phases.
The second work about electromagnetically induced transparency with polychromatic driven fields is to study the two-photon absorption in a three-level cascade atomic system driven by a pair of bichromatic fields with equal frequency difference.The high-frequency component of one bichromatic field and the low-frequency component of the other are on two-photon resonance.We adopt the method of harmonic expansion and matrix inversion. The main result is that when the sums of the phases of the different pairs of field components on the two-photon resonance are equal to each other,two-photon absorption is dramatically suppressed and the atomic system becomes transparent against two-photon absorption. Due to dynamic Stark splitting,the two-photon transitions induced by the different pairs of field components experience different dressed states with phase difference ofπ.As a result,destructive interference occurs between the two pathways and leads to the inhibition of two-photon absorption.
2.The work about preparation of entangled states:
In the first scheme of entanglement preparation,we show that a quantum-beat system with incoherent pump or coherent driving produces an entangled sub-shot-noise laser that operates well above threshold.We adopt the combination modes of the lasing fields to present the numerical results and physical analysis.The relative mode is decoupled from the active medium and stays in its vacuum state,while the sum mode operates well above threshold and has sub-shot-noise.The quantum beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of the respective beams.
In the second work about preparation of entangled states,we propose a scheme for generating a two-atom entangled state and an N-atom W state using adiabatic evolution of dark eigenstates in cavity QED.This scheme has two advantages.Firstly,the time required to complete the process does not need precise control.Secondly,since the cavity modes are never excited during the operations by engineering adiabatic evolution and controlling the atom-cavity couplings,the decoherence due to the cavity decay can be suppressed.
The last work about preparation entangled states is a concentration scheme for unknown atomic states through the Laman interaction of two atoms with a cavity mode and an external laser field.We obtain a two-atom maximally entangled sate from a pair of unknown partially entangled atomic states.In the concentration process,as the cavity mode is virtually excited and the atomic excited states are eliminated,our scheme is robust against the cavity decay,the thermal field and the atomic spontaneous emission.
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