多量子比特与光场强耦合系统“类似暗态”的研究

There exist “dark states" in the strong coupling system between multi-qubit and photon field, which are exceptional solutions to the even qubit Dicke model, formed by the products of the two-qubit singlets. Their eigenenergies are constant in the whole qubit-photon coupling regime, and can be used to store quantum correlations since they preserve entanglement even under dissipation. We have obtained a novel kind of exceptional solution– “dark-like states” for the n-qubit (n=2,3,4) Rabi models recently, whose eigenenergies are also constant for arbitrary single qubit-photon coupling strength. But they are entanglement states, and the photon number is bounded from above at 1. At the same time, their existence condition are simple. To find out novel “dark-like states” in more general systems and their application is in urgent need. In this project, we aim to generalize the researches on the “dark-like states” to the case of arbitrary qubit number N, and consider arbitrary K-photon interaction, searching for these novel “dark-like states” and their universal existence conditions. At the same time, we will try to find out if there are some similar properties and application for the dark-like states as the “dark states”, under the influence of environment. The prospective results would reveal the universal existence condition of these “dark-like states” in the strong coupling system between multi-qubit and photon field, their peculiarity and possible application.

多量子比特与光场强耦合系统中存在“暗态”，它是偶数全同比特Dicke模型的特殊解，由两比特自旋单态直乘构成，对于任意比特-光场耦合强度它的能量为常数，在腔场存在耗散等情况下可以用来存储量子关联。最近我们在研究非全同n比特（n=2,3,4）Rabi模型时发现一种新奇的特殊解-“类似暗态”，它同样在单比特与光场任意耦合强度下能量为常数，但它是比特与光场的纠缠态，并且光子数上限为1。同时，存在条件比较简单。更普遍系统中“类似暗态”的寻找及其应用是亟待解决的问题。本项目拟将“类似暗态”的研究推广到任意比特数N的情况，并考虑比特与光场任意K光子相互作用，寻找新奇的N比特“类似暗态”解及其存在的普适条件。同时，我们将研究在环境影响下“类似暗态”是否具有与“暗态”类似的性质和应用。预期成果将精确揭示光场与多比特耦合系统中“类似暗态”的存在条件、特性和可能的应用。

量子信息中众多应用都离不开量子光场与原子的相互作用，而量子Rabi 模型描述的是最简单又最基本的二能级原子（量子比特）与单模光场的相互作用，对该模型及其扩展的研究能够为该系统的性质、演化和应用研究提供理论基础。Rabi模型的相互作用可以耦合任意光子数态，因此系统的本征态都包含有无穷多个光子数态，动力学演化过程比较复杂，这也导致人们无法直接利用Rabi模型获得单一的光子数态。我们将其推广到任意多比特与多模光场相互作用系统，发现对应的Rabi模型都存在光子数上限为1的本征态，这是因为部分基矢以特定系数相干叠加使得光子数布居局限在0和1上，我们称之为“特殊暗态”解。该解对于任意单比特与光场耦合强度都存在，且能量为常数，但同时也是比特与光场的纠缠态。“特殊暗态”丰富了人们对于含反旋波项的扩展Rabi 模型解析解的认识，并且我们发现利用该态的特殊结构，通过绝热演化，可以快速同时生成一个单光子态（或者多模单光子W态）和双比特Bell态，其演化时间理论上可以和最近的最快两比特量子门相比拟。同时我们根据Circuit QED设计了一个试验方案，能够可控的产生、存储与释放单光子态或者W态。另一方面，超辐射是量子光学研究中心十分重要的研究课题，我们通过一个相同的配分函数统一研究了一些扩展的Rabi模型在零温和有限温，热力学极限和经典谐振子极限下的超辐射相变，发现它们具有相同的性质。同时我们发现了比特与光场偶极相互作用情况下超辐射相变的一般规律，能够为各种相应模型的超辐射相变研究提供理论基础，也为它们在量子信息中的应用提供一定的帮助。