开放量子系统的非马尔科夫动力学和弱测量反馈控制
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摘要
任何一个真实的量子体系不可避免地会与外部环境发生相互作用,从而导致量子体系退相干。研究开放量子系统的退相干性质及其动力学行为,必然要考虑其所处环境的特点,不同类型的环境可能会导致完全不同的动力学结果。处理开放量子体系的传统方法往往只考虑系统与环境的弱耦合情况,把环境看成没有记忆的马尔科夫环境。但是,在系统与环境强耦合条件下,环境的记忆反馈作用产生的非马尔科夫效应必须考虑。最近几年来,实验技术的发展使得制备适合量子信息处理的强耦合系统成为现实。因此,研究开放量子系统的非马尔科夫动力学和相关反馈控制有着重要的理论和应用意义。本文运用开放量子系统理论和量子信息理论研究开放量子系统的非马尔科夫动力学和弱测量反馈控制,取得了一系列创新性成果：
1.从阻尼Jaynes-Cummings模型出发,研究了开放二能级系统的非马尔科夫熵压缩动力学,考察了非马尔科夫效应和失谐量对熵压缩的影响。结果表明：非马尔科夫效应和失谐的共同作用可以使系统的熵压缩保持相当长的时间。原因在于：在非马尔科夫环境中,失谐能够更有效地抑制系统相干性的衰减。这些结果为利用压缩性质进行高精密测量提供了更有利的条件。
2.研究了一个与非马尔科夫库耦合的三能级Λ系统的动力学。针对洛伦兹形式的谱线,详细讨论了在弱耦合和强耦合两种情形下的非马尔科夫含时衰减系数和激发态布居的动力学行为。结果表明：非马尔科夫效应不仅存在于强耦合情形,也存在于弱耦合情况,只不过其非马尔科夫效应非常弱,在很多时侯可以忽略不计。最后,从信息流动的角度对这些结果进行了解释。
3.提出了两种非马尔科夫环境下使量子体系间的量子纠缠和量子discord长时间保持的理论方案：一是通过失谐调控技术来保持纠缠和量子discord;二是通过外加经典驱动场来保持纠缠。最后利用准模理论,唯象地解释了这两种情况下纠缠能够长时间保持的物理原因。这为实际量子信息处理中利用非马尔科夫效应抑制退相干提供了新的途径。
4.研究了基于弱测量方式的反馈控制策略对抑制开放二能级系统噪声的作用。研究表明：对于某些合适的系统初态,针对不同的噪声,基于弱测量方式的反馈控制方案总是要比基于投影测量的方案更能有效地抑制噪声对系统状态的干扰。这一方案很好地平衡了量子测量过程对系统的信息提取和扰动之间的矛盾,为实现最优量子反馈控制提供了新的思路。
Any realistic physical system will suffer from unwanted interactions with the out-side environments, causing decoherence and destroying entanglement. In order to in-vestigate the quantum decoherence and the entanglement dynamics of open quantum systems, we must take account of the characteristics of the environments coupled to the system. Usually, in the standard theory of the open quantum systems, environments are treated as the Markovian environments without memory. However, in the strong cou-pling regime, non-Markovian effects induced by the memory and feedback interactions of environments should be considered carefully. Recently, the strong coupling systems for quantum information processing has been realized with the development of science and technology. Thus, investigating the non-Markovian dynamics and related quantum feedback control of open quantum systems have important theoretical and partical sig-nificance. In this thesis, non-Markovian dynamics and weak measurement feedback control of open quantum systems have been studied by using the theories of open quan-tum systems and quantum information, and a series of significant results are obtained. The concrete contents are listed as follows:
1. Based on the damped Jaynes-Cummings model, the entropy squeezing dynamics of a two-level atom off-resonantly coupled to a non-Markovian reservoir has been inves-tigated. The influences of non-Markovian effects and detunings on the atomic squeezing have been examined. It is interesting to note that atomic squeezing can be protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the decay rate is suppressed much more by detuning in the non-Markovian regime than in the Markovian case. These results provide a poten-tial method to extend the possible usage time of squeezing, which would be useful in high-precision applications.
2. We have studied the excited-state population dynamics of a three-level A-atom coupled to a non-Markovian reservoir. Comparing the Lorentzian time-dependent decay rate and population dynamics for the weak coupling regime with those for the strong coupling regime, we have noted that non-Markovian features exist in both regimes, but population dynamics shows fairly different behaviors since the non-Markovian effect can be neglected safely in weak coupling regime. The results have been interpreted from the perspective of information flow.
3. We have presented two theoretical methods to protect the entanglement and quantum discord in non-Markovian regime:One is based on the technology of detuning control; the other is based on the classical driving fields acted upon the systems. The physical mechanism behind our results has been explained via the quasimode theory. Our schemes would be helpful for suppressing the decoherence and dis-entanglement by non-Markovian effect in practical quantum information processing.
4. We have examined the use of weak measurement-based feedback control for stabilizing quantum states in the presence of different noise sources and with respect to different system states. We have found that the approach is sensitive to the system state, but for some suitable states, it works well for all typical types of noise sources. This scheme fairly balanced the trade-off between information gain and disturbance in quantum measurement, which might shed some new light on the achievement of optimal quantum feedback control.
1.从阻尼Jaynes-Cummings模型出发,研究了开放二能级系统的非马尔科夫熵压缩动力学,考察了非马尔科夫效应和失谐量对熵压缩的影响。结果表明：非马尔科夫效应和失谐的共同作用可以使系统的熵压缩保持相当长的时间。原因在于：在非马尔科夫环境中,失谐能够更有效地抑制系统相干性的衰减。这些结果为利用压缩性质进行高精密测量提供了更有利的条件。
2.研究了一个与非马尔科夫库耦合的三能级Λ系统的动力学。针对洛伦兹形式的谱线,详细讨论了在弱耦合和强耦合两种情形下的非马尔科夫含时衰减系数和激发态布居的动力学行为。结果表明：非马尔科夫效应不仅存在于强耦合情形,也存在于弱耦合情况,只不过其非马尔科夫效应非常弱,在很多时侯可以忽略不计。最后,从信息流动的角度对这些结果进行了解释。
3.提出了两种非马尔科夫环境下使量子体系间的量子纠缠和量子discord长时间保持的理论方案：一是通过失谐调控技术来保持纠缠和量子discord;二是通过外加经典驱动场来保持纠缠。最后利用准模理论,唯象地解释了这两种情况下纠缠能够长时间保持的物理原因。这为实际量子信息处理中利用非马尔科夫效应抑制退相干提供了新的途径。
4.研究了基于弱测量方式的反馈控制策略对抑制开放二能级系统噪声的作用。研究表明：对于某些合适的系统初态,针对不同的噪声,基于弱测量方式的反馈控制方案总是要比基于投影测量的方案更能有效地抑制噪声对系统状态的干扰。这一方案很好地平衡了量子测量过程对系统的信息提取和扰动之间的矛盾,为实现最优量子反馈控制提供了新的思路。
Any realistic physical system will suffer from unwanted interactions with the out-side environments, causing decoherence and destroying entanglement. In order to in-vestigate the quantum decoherence and the entanglement dynamics of open quantum systems, we must take account of the characteristics of the environments coupled to the system. Usually, in the standard theory of the open quantum systems, environments are treated as the Markovian environments without memory. However, in the strong cou-pling regime, non-Markovian effects induced by the memory and feedback interactions of environments should be considered carefully. Recently, the strong coupling systems for quantum information processing has been realized with the development of science and technology. Thus, investigating the non-Markovian dynamics and related quantum feedback control of open quantum systems have important theoretical and partical sig-nificance. In this thesis, non-Markovian dynamics and weak measurement feedback control of open quantum systems have been studied by using the theories of open quan-tum systems and quantum information, and a series of significant results are obtained. The concrete contents are listed as follows:
1. Based on the damped Jaynes-Cummings model, the entropy squeezing dynamics of a two-level atom off-resonantly coupled to a non-Markovian reservoir has been inves-tigated. The influences of non-Markovian effects and detunings on the atomic squeezing have been examined. It is interesting to note that atomic squeezing can be protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the decay rate is suppressed much more by detuning in the non-Markovian regime than in the Markovian case. These results provide a poten-tial method to extend the possible usage time of squeezing, which would be useful in high-precision applications.
2. We have studied the excited-state population dynamics of a three-level A-atom coupled to a non-Markovian reservoir. Comparing the Lorentzian time-dependent decay rate and population dynamics for the weak coupling regime with those for the strong coupling regime, we have noted that non-Markovian features exist in both regimes, but population dynamics shows fairly different behaviors since the non-Markovian effect can be neglected safely in weak coupling regime. The results have been interpreted from the perspective of information flow.
3. We have presented two theoretical methods to protect the entanglement and quantum discord in non-Markovian regime:One is based on the technology of detuning control; the other is based on the classical driving fields acted upon the systems. The physical mechanism behind our results has been explained via the quasimode theory. Our schemes would be helpful for suppressing the decoherence and dis-entanglement by non-Markovian effect in practical quantum information processing.
4. We have examined the use of weak measurement-based feedback control for stabilizing quantum states in the presence of different noise sources and with respect to different system states. We have found that the approach is sensitive to the system state, but for some suitable states, it works well for all typical types of noise sources. This scheme fairly balanced the trade-off between information gain and disturbance in quantum measurement, which might shed some new light on the achievement of optimal quantum feedback control.
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