摘要
量子信息处理过程中,信息的载体是量子态,关键技术之一是操控量子态,制备尽可能多的非经典光场量子态是量子信息研究的重要基础和先决条件,对光场量子态的制备及其性质(反聚束效应、亚泊松分布、压缩效应和负的Wigner函数)研究尤为重要。
由于制备光场量子态是量子信息研究的先决条件。在本论文第三章,利用典型的光场量子态,首次在理论上通过玻色湮灭和产生算符的逆算符分别作用在平移Fock态上制备了增、减光子平移Fock态。又利用玻色产生算符作用于压缩真空态上得到了增光子压缩真空态,同时阐述了在实验上如何制备增光子压缩真空态。
量子信息研究的光场量子态应为非经典光场量子态,非经典光场量子态可通过其非经典性质来反映。在本论文的第四章,根据二阶关联函数、Q因子、压缩效应和Wigner函数首次对所制备的光场量子态(增、减光子平移Fock态,单光子增压缩真空态)和Fock态及其叠加态的性质进行了数值计算和分析讨论。结果显示增、减光子平移福克态在｜α｜2较小区域展现出反聚束效应和亚泊松分布;单光子增压缩真空态展现出明显的反聚束效应和压缩效应,这表示这些光场量子态为非经典光场量子态。这些光场量子态的Wigner函数在相空间都有明显的负值分布。福克态｜1〉、｜2〉和｜3〉的Wigner函数波包为非高斯波包,且随着光子数的增加,Wigner函数变化也越复杂。在相空间中心区域,Wigner函数的峰值与福克态数n的奇偶性存在一定的联系：n为奇数时,Wigner函数的尖峰向下,n为偶数时尖峰向上。Fock态叠加态的Wigner函数有明显的向下负值尖峰和向上尖峰,这反应出两量子态的叠加性质。单光子增压缩真空态的Wigner函数与福克态｜1〉的Wigner函数相似,只是取负值的相空间被压缩了。总之,这些光场量子态都具有明显的非经典特性,为非经典光场量子态。
量子信息的处理不可避免地受到环境的影响,因此量子退相干和量子态非经典性质消失的研究对量子信息处理具有重要意义。Fock态、福克态叠加态和增光子压缩真空态在量子信启、中具有重要的价值,然而未见对其耗散研究的报道。在本论文的第五章,根据Wigner函数的定义和密度算符主方程理论,利用纠缠态表象和拉盖尔多项式与厄米多项式的性质,首次解析推导了福克态、福克态叠加态和单光子增压缩真空态的Wigner函数随时间的演化,并对各参数如何影响这种演化进行了数值计算和分析讨论。在仅耗散情况,初始这些光场量子态的Wigner函数具有明显的非经典性质,且Wigner函数的负值在相空间中有明显的投影区域：｜1〉的Wigner函数负值投影区域为一圆面；｜2〉的Wigner函数负值投影区域为一空实心圆环；｜3〉的Wigner函数负值投影区域为一中心区域的圆面和一实心圆环；｜1〉和｜2〉叠加态的Wigner函数负值投影区域为两个半月形；单光子增压缩真空态的Wigner函数负值投影区域为一圆面。随着时间的演化,这些光场量子态Wigner函数的负值向正的方向收缩,Wigner函数负值的相空间投影区域也减小。若演化时间足够长,这些光场量子态的Wigner函数负值将消失,Wigner函数负值所对应的相空间投影也消失,最终原来的非经典光场量子态将演化为真空的纯态。在有驱动的耗散情况下,当耗散系数L和(?)时间t给定时,随着驱动系数g的增大,这些光场量子态的Wigner函数负值将向正的方向收缩直至负值消失,Wigner函数负值所对应的相空间投影将减小直至消失,非经典的光场量子态将演化为经典量子态。当驱动系数g取不同值(大于或小于耗散系数k)时,对于同一光场量子态,Wigner函数的负值演化至负值消失所需时间不同。当耗散系数k大于驱动系数g时,光场量子态的Wigner函数由非经典性质演化至其消失所用时间相对较长,反之所用时间相对较短。因此通过控制g-k的大小,理论上就可以控制这些光场量子态的时间演化。这些结果为量子信息实际应用这些光场量子态的非经典性质提供了理论基础。
In the process of quantum information, the carrier of quantum information is quantum state. The operating of quantum state is one of the key technologies. Therefore, the quantum state preparation of nonclassical optical field is the important basis and prerequisite condition for quantum information research. The preparation of quantum state and its property research (antibunching effect, subpossion distribution, squeezed effect and negative of Wigner function) are important.
Because the quantum state preparation of optical field is the prerequisite condition for quantum information research. In the third chapte, according to the classical optical field quantum state, the photon-added and photon-subtracted displaced Fork states are generated theoretically for the first time by applying the inverse operator of annihilation and generator operators on the displaced Fork states. In addition, the photon-added squeezed vacuum state is generated by using generator operator on the squeezed vacuum state and the preparation in experiment is described as well.
The optical field quantum state of quantum information research is the nonclassical optical field quantum. the nonclassical optical field quantum can be responsed by their nonclassical properties. According to the second-order correlation function, Q factor, squeezed effect and Wigner function, the theoretical research of of properties are carried on for the photon-added and photon-subtracted displaced Fork states, signle photon-added squeezed vacuum state, and Fock state and its superposition states in the fourth chapter. The results are shown that the photon-added and photon-subtracted displaced Fork states have antibunching effect and subpoisson distribution in the small region of |α|2; Single photon-added squeezed vacuum state has clearly antibunching effect and squeezed effect, which denote that these optical field quantum states are the non-classical quantum states. The Wigner functions of these optical field quantum states all have clearly distribution of negative value in the phase space. The wave packages of |1>、|2> and |3> are non-gaussian package and these Wigner functions change to be more complexity with the increment of photon. In the center of phase space, the peak value of Wigner function is related to the parity of n:the peak value of Wigner function is downward with the odd of n, the peak value of Wigner function is upward with the even of n. The Wigner function of the superposition of Fock states have obviously the negative value peak and the upward peak, which show the superposition property of two quantum states. The Wigner function of signle photon-added squeezed vacuum state is similar to the Wigner function of |1>, but the phase space of negative value is shrink. In conclusion, these quantum states have obviously nonclassical property, and are the nonclassical optical field quantum state..
The influence between the disposal of quantum information and the environment can not be prevented completely. Thus, the research of the decoherent and the disappearance of the nonclassical property of quantum state has very important significance in the process of quantum information. The Fock state, the superposition of Fock states and photon-added squeezed vacuum states have important practical value in the quamtum information research. However, there is rarely no report about the research of their dissipation. In the fifth chapter, according to the definition of Wigner function and the master equation theory, and the entangled state representation and the relation of Laguerre polynomials and Hermite polynomials, taking the Fock states and their superposition states, the photon-added squeezed vacuum state, the analytical expression of the time evolution Wigner function of these quantum states are obtained. The time evolution characteristics of Wigner functions of these quantum states with different parameters is systematically calculated and discussed. In initial stage, the Wigner functions of these quamtum states have obvious nonclassical property, and the negative value of their Wigner function has apparent and different projective region in the phase space on the condition of dissipation. For the Wigner function of |1>, the projective region of the negative value is a circular surface. For the Wigner function of |2>, it is a solid annulus surface. For the Wigner function of |3>, it is a combination of a centered circular surface and a solid annulus surface. For the Wigner function of |1> and |2>, the projective region of the negative value are two half-moon surfaces. As for the Wigner function of the single photon-added squeezed vacuum states, it is a circular surface. The negative values of the Wigner function of these optical field quantum states will shrink to the positive direction with the time evolution. The projective region of its negative value will decrease simultaneously. If the evolution time is long enough, the negative value of their Wigner function will disappear and the corresponding projective region will also disappear in the phase space. Finally, the original nonclassical optical field quantum states change into the pure state of vacuum. On the condition of the dissipation and the driving, the negative value will approach to positive value until the negative value disappear with the increment of driving coefficient when the dissipation coefficient and dissipation time are determined. The corresponding projective region will shrink and vanish at last. Then the nonclassical optical field quantum states change into the classical quantum states. When the dissipation coefficient and the driving coefficient are given different values, the evolution time is also different for the same optical field quantum states. When the dissipation coefficient is larger than the driving coefficient, it needs relative more time in the process which the nonclassical property of Wigner function of optical field quantum states change to be disappeared. On the contrary, the evolution time is relative short. Therefore, the evolution of these quantum states can be control by the value of g-k in terms of theory. For using the nonclassical property of these quantum states in quantum information, these results offer the foundation of theory.
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