隐形传态和耗散量子位的几何相位研究
摘要
本文主要包括两个部分的内容。在第一部分我们主要研究利用强量子电动力学系统中的光子极化法拉第旋转来实现任意多粒子态的量子隐形传态。在第二部分我们主要研究与一个具有洛伦兹谱密度的环境相互作用的耗散二能级原子所产生的退相干对几何相位的修正。首先,我们基于腔量子电动力学系统提出一个实际的量子隐形传态的方案。量子隐形传态指的是利用EPR纠缠对建立成的量子通道,发送者通过向接收者传递两位经典信息来实现一个粒子的量子信息传送的协议。我们可以通过腔场单光子脉冲的输入输出过程来实现这个传送过程。通过光子对腔的输入输出过程,光子和禁锢在腔场中原子的相互作用会使得反射光子的极化方向相对入射光子的极化方向发生角度的偏转,我们称这个旋转为法拉第旋转。利用法拉第旋转,我们就可以在发送者和接收者之间建立由光子和原子之间的纠缠形成的量子通道。利用这条纠缠通道,一个利用低品质腔和适中腔与原子耦合强度的量子隐形传态就可以实现。我们的方案完全可以推广为实现一个任意多体态的传输。
相比于以前提出的利用衰变腔实现量子隐形传态的方案,我们的方案具有以下几个优点。首先,在我们的方案中腔与原子的耦合强度适中即可,无需像以往方案中的强耦合条件,这极大的降低了实验难度。其次,我们的方案是基于低品质腔的单光子脉冲的输入输出过程,而且只考虑了原子的虚激发,因此不同于以往方案是概率性的,我们的方案不受腔衰变及原子自激辐射影响的确定性隐形传态。此外,我们的方案不涉及利用CNOT门操作来实现Bell态测量,也大大降低了实验难度。
在第二部分,我们研究由二能级原子组成的量子系统受到具有洛伦兹谱密度的环境影响所导致的退相干对几何相位的修正。通过解析推导与数值计算,我们主要集中研究了环境的非马尔科夫效应对几何相位的影响。文中推导并得到了在弱耦合极限下几何相位的最低阶修正的解析解及一般情况下的数值解。我们发现当谱宽很小的时候退相干效应对几何相位的修正将非常大的,此时退相干的非马尔科夫效应比较显著。但是,随着环境谱宽的增加,马尔科夫效应越来越弱,环境对几何相位的修正液变得越来越小,以至于在白噪声极限下,该几何相位的修正几乎可以忽略不计。上述结果表明几何相位不仅对由系统参数变化所引起的经典噪声具有抗干扰性,同样对量子白噪声也具有抗干扰性。该结果对基于几何相位的容错量子信息处理具有非常重要的意义。
This thesis is contributed to the study of two parts. In the first part, we propose a practical scheme for deterministically teleporting an arbitrary multipartite pure state, either product or entangled, using Faraday rotation of the photonic polarization in cavity QED system. In the second part, we study the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density.
Firstly, we propose a practical scheme for quantum teleportation in cavity QED system. In quantum teleportation, using an EPR entangled pair as quantum channel, one can transfer one qubit quantum information via delivering two classical bits classical information from the sender to the receiver. Here we can accomplish this protocol by the single-photon input-output process regarding cavities. The interaction between the photons and optical cavities with atoms trapped in leads to the polarization direction of the reflected photon rotating an angle with respect to the input one, named Faraday rotation. Making use of the Faraday rotation, we could establish the entangled channel between photon pulse and the atom in the sender's hands. Based on the channel, a practical teleportation scheme using low-Q cavities and moderate atom-cavity couplings can be realized. The scalability of our scheme to realize the teleportation of an arbitrary multipartite pure state is also proved.
Compared with previous proposals for teleportation with decaying cavities, there are some advantageous in ours. Firstly, our scheme could work very well even in the case of moderate Rabi frequencies, and achieve the teleportation perfectly and deter-ministically. Secondly, our scheme, based on the input-output process of single-photon pulses regarding cavities, works in low-Q cavities and only involves virtual excitation of the atoms, which is insensitive to both cavity decay and atomic spontaneous emis-sion. Besides, the Bell-state measurement is accomplished by the Faraday rotation plus product-state measurements, which could much relax the experimental difficulty to realize the Bell-state measurement by the CNOT operation. Finally, our scheme us-ing bipartite entangledment as quantum channels is more robust to decoherence than others based on multipartite entanglement.
Secondly, we study the geometric phase of an open two-level atom interacting with an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit the lowest-order correction to the geometric phase is derived analytically and the general case is calculated numerically. It is found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact to the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result shows that the geometric phase in this cavity QED system is fault-tolerant not only against the classical noise induced by the parameter fluctuation but also against the quantum noise. It is significant to the quantum information processing based on the geometric phase.
相比于以前提出的利用衰变腔实现量子隐形传态的方案,我们的方案具有以下几个优点。首先,在我们的方案中腔与原子的耦合强度适中即可,无需像以往方案中的强耦合条件,这极大的降低了实验难度。其次,我们的方案是基于低品质腔的单光子脉冲的输入输出过程,而且只考虑了原子的虚激发,因此不同于以往方案是概率性的,我们的方案不受腔衰变及原子自激辐射影响的确定性隐形传态。此外,我们的方案不涉及利用CNOT门操作来实现Bell态测量,也大大降低了实验难度。
在第二部分,我们研究由二能级原子组成的量子系统受到具有洛伦兹谱密度的环境影响所导致的退相干对几何相位的修正。通过解析推导与数值计算,我们主要集中研究了环境的非马尔科夫效应对几何相位的影响。文中推导并得到了在弱耦合极限下几何相位的最低阶修正的解析解及一般情况下的数值解。我们发现当谱宽很小的时候退相干效应对几何相位的修正将非常大的,此时退相干的非马尔科夫效应比较显著。但是,随着环境谱宽的增加,马尔科夫效应越来越弱,环境对几何相位的修正液变得越来越小,以至于在白噪声极限下,该几何相位的修正几乎可以忽略不计。上述结果表明几何相位不仅对由系统参数变化所引起的经典噪声具有抗干扰性,同样对量子白噪声也具有抗干扰性。该结果对基于几何相位的容错量子信息处理具有非常重要的意义。
This thesis is contributed to the study of two parts. In the first part, we propose a practical scheme for deterministically teleporting an arbitrary multipartite pure state, either product or entangled, using Faraday rotation of the photonic polarization in cavity QED system. In the second part, we study the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density.
Firstly, we propose a practical scheme for quantum teleportation in cavity QED system. In quantum teleportation, using an EPR entangled pair as quantum channel, one can transfer one qubit quantum information via delivering two classical bits classical information from the sender to the receiver. Here we can accomplish this protocol by the single-photon input-output process regarding cavities. The interaction between the photons and optical cavities with atoms trapped in leads to the polarization direction of the reflected photon rotating an angle with respect to the input one, named Faraday rotation. Making use of the Faraday rotation, we could establish the entangled channel between photon pulse and the atom in the sender's hands. Based on the channel, a practical teleportation scheme using low-Q cavities and moderate atom-cavity couplings can be realized. The scalability of our scheme to realize the teleportation of an arbitrary multipartite pure state is also proved.
Compared with previous proposals for teleportation with decaying cavities, there are some advantageous in ours. Firstly, our scheme could work very well even in the case of moderate Rabi frequencies, and achieve the teleportation perfectly and deter-ministically. Secondly, our scheme, based on the input-output process of single-photon pulses regarding cavities, works in low-Q cavities and only involves virtual excitation of the atoms, which is insensitive to both cavity decay and atomic spontaneous emis-sion. Besides, the Bell-state measurement is accomplished by the Faraday rotation plus product-state measurements, which could much relax the experimental difficulty to realize the Bell-state measurement by the CNOT operation. Finally, our scheme us-ing bipartite entangledment as quantum channels is more robust to decoherence than others based on multipartite entanglement.
Secondly, we study the geometric phase of an open two-level atom interacting with an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit the lowest-order correction to the geometric phase is derived analytically and the general case is calculated numerically. It is found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact to the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result shows that the geometric phase in this cavity QED system is fault-tolerant not only against the classical noise induced by the parameter fluctuation but also against the quantum noise. It is significant to the quantum information processing based on the geometric phase.
引文
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