光机械系统中非马尔科夫效应的理论研究

With the coupling between optical and mechanical degrees of freedom, optomechanical systems have applications in many areas, such as precision detection, quantum memory and quantum information processing. It is a hot research field in quantum information science. In recent works, we have successfully generalized the research scope of optomechanical systems, which is from Markovian environment to non-Markovian environment including memory effects, meanwhile, the value of this research area is also confirmed by new experimental evidence. The project is build on this general background, and we will study the non-Markovian effects intensely from the following three aspects, namely, experimental realization, theoretical perfection and application fields extending. The project is based on the following objectives: (1) we will detect the environmental spectral density of the mechanical resonator in wide-band range, and put forward a detectable measurement of non-Markovianity; (2) we will develop a fully quantum approach beyond linearization and study the effect of initial system-reservoir correlation, and we will also clarify the transition between non-Markovian and Markovian dynamics; (3) we will enhance the optomechanically induced transparency effect and increase the signal to noise ratio by utilizing memory effects.

光机械系统有效地实现了光学和机械自由度之间的直接耦合，其在精密探测、量子存储、量子信息处理等领域都有应用，是目前量子信息学研究领域的热门方向。在近期的工作中，申请人已经成功地将光机械系统的研究范围从Markov环境推广到了包含记忆效应的non-Markov环境，同时新的实验证据的出现也进一步确认了该方向的研究价值。本项目正是构建在此背景之下，我们将从实验实现、理论完善、应用拓展这三个方面深入研究光机械系统中的non-Markov效应。相应的，本立项将确立如下目标：（1）提出全频带的机械振子环境谱密度的探测方案并给出可被探测的non-Markovianity的度量方法；（2）发展一套超越线性化近似的全量子的处理方法；描述初始关联对系统退相干动力学的影响；阐明non-Markov到Markov的动力学过渡问题；（3）利用环境的记忆效应增强光机械诱导透明并提高探测信号的信噪比。

光机械系统是一种理想的展现光与物质相互作用的系统。它有效地实现了光学和机械自由度之间的直接耦合，其在精密探测、量子存储、量子信息处理等领域都有应用，是目前量子信息学研究领域的热门方向。最近新的实验证据表明，振子的环境可以是高度非马尔科夫的，而目前该领域绝大多数的理论研究都停留在马尔科夫环境的假设之下。对于记忆环境的研究目前还在起步阶段，很多问题有待回答。本项目深入研究了光机械系统中的非马尔科夫效应。得到如下研究结果：（1）提出了全频带的机械振子环境谱密度的探测方案；（2）提出了利用光机械系统初始关联实现对振子边带冷却的进一步优化的方案；（3）提出了在光机械系统中利用量子关联增强弱场探测的信噪比以打破标准量子极限的方案；（4）提出了利用环境记忆效应提高量子态传输保真度的方案；（5）初步研究了非马尔科夫到马尔科夫的动力学转变问题。我们的研究从实验验证、理论完善、应用拓展这三个方面展开，较为系统的回答了非马尔科夫效应的验证问题、理论刻画问题以及现实的应用问题。随着实验技术和新材料制造工艺的不断完善，人们对于量子系统的操控能力正日趋提高，我们相信对于光机械系统中非马尔科夫效应的理论研究将在不远的将来为记忆环境下光机械系统的实验发展提供理论基础。