简并完全未消除情形下的二级微扰公式

本文修改了在一级近似下简并完全未消除情形下的二级修正公式，并以平面转子在外电场中微扰为例说明其应用。     

微扰法求解铅玻璃中的涡旋空间光孤子

在量子力学的微扰理论框架下,利用微扰法求解得到了1+2维强非局域非线性介质——铅玻璃中二阶微扰修正的"类拉盖尔高斯型"涡旋孤子的近似解析解。从非局域非线性薛定谔方程(NNLSE)出发,以铅玻璃中的真实折射率与Snyder-Mitchell(SM)模型中描述的抛物线型折射率的差值为微扰,以SM模型中的拉盖尔高斯孤子解为基态解,求得了铅玻璃材料中二阶微扰修正的"类拉盖尔高斯型"涡旋孤子的解析解。拓扑荷值分别为1、2、3、4的微扰修正的"类拉盖尔高斯型"光孤子比未加微扰的拉盖尔高斯型光孤子更稳定,非常接近孤子真解的传输行为。     

微扰模型分析长周期光纤光栅薄膜传感器

提出了一种新的基于三层阶跃折射率光纤的微扰模型,分析长周期光纤光栅（Long Period Fiber Grating,LPFG）薄膜传感器,并从β2稳定性定理出发推导出适用于薄膜传感器的微扰公式.该模型不仅能够清晰反映薄膜参量与包层模传播常量变化量之间的关系,而且在计算量和计算难度远低于四层波导模型情况下获得与严格求解结果相当的计算准确度.考虑数值计算本身引入的计算误差,该模型能够满足定性和半定量理论分析需要.最后通过长周期光纤光栅液态水膜的挥发实验对该模型进行了初步验证.     

简并谱的涨落统计特征分析

通过引入权重的方式,使简并谱的积累函数形式上连续递增,并用带权重的多元线性拟合提取涨落谱,由此建立了一套适用于分析简并谱的ＮＮＳ分布、谱刚度、能谱分维函数等涨落统计特征的方法,并具体分析了Ｈ２Ｏ、ＮＨ３及ＣＨ４分子的振动能谱进行涨统计特征分析：发现它们的规则谱和约化非简并谱的涨落统计特征均已非Ｐｏｉｓｓｏｎ化;而且约化非简并谱的非Ｐｏｉｓｓｏｎ化程度较规则谱明显,即前者的能级斥力较后者大;此外,随     

多模简并多光子Tavis-Cummings模型中的量子纠缠特性

利用冯·纽曼约化熵理论研究了多模相干态光场与两等同二能级原子简并多光子相互作用系统量子纠缠演化特性,得到了多模光场量子纠缠的解析表达式,并给出了双模光场与两原子相互作用时量子纠缠的数值计算结果.结果表明:量子纠缠随着光子简并度的增大而增强;随着初始平均光子数的增加,量子纠缠演化的周期性变得越来越明显;当场与原子远离共振时,量子纠缠随着频率失谐量的增大而减弱;当失谐量足够大时,场与原子几乎总是处于纠缠状态.这些结论对于纠缠态或纯态的制备及获取光学系统中的量子信息研究中有一定参考价值.     

微扰法求解非线性驻波问题

在历史上,用微扰法求解非线性驻波是不成功的。本文对此进行了分析,认为微扰法给出的一次解是基本解,决定了驻波的基本波形。二次以上的解是由于非线性对波形的影响,使驻波波形上各点随时间运动稍加变动,因此对二次以上的微量只应保留其时间微商。这样所得解不但是稳定的,并且与根据波动方程的严格解基本相同。 关键词：     

DWDM系统非简并四波混频串扰的分析

考虑到DWDM系统中的比特序列的随机性、信道间脉冲走离效应等多种因素的影响,完善了归零调制格式下的四波混频效率的计算方法,给出了相应的非简并四波混频噪声标准差的计算公式,并利用该公式进行实例分析,计算结果表明,当占空比和信道间隔变小时,不同信道内的随机比特序列的相对初始时延及光纤色散值的取值组合对四波混频效率的影响变得更大,为保证系统的低色散和低四波混频串扰特性,必须对这些量取值组合进行优化. 关键词： 非简并四波混频 脉冲走离 密集波分复用     

变耦合系数的简并拉曼耦合J-C模型中场熵的演化

研究了考虑耦合系数随时间线形变化的简并拉曼耦合J-C模型中场熵随时间演化特性,分析了耦合系数变化的快慢和不同的初始光场对场熵的影响。结果表明:(1)无论光场初始态如何,场熵均呈周期性演化,平均光子数n-的增加并不改变场熵演化周期的大小;(2)初始光场统计性质的不同对最大场熵值和最大场熵值变化的幅度产生较大的影响;(3)线形调制使场熵呈现的完美周期性振荡遭到破坏。当原子-场耦合系数变化缓慢时,原子进入统计混合态的速度被减缓;而当原子-场耦合系数变化较快时,则不仅使场熵演化曲线的振荡周期逐渐减小、振荡频率越来越快,而且使原子与场退纠缠的时刻增多。     

Spectral Determinant of the Two-Photon Quantum Rabi Model

The various generalized spectral determinants (G-functions) of the two-photon quantum Rabi model are analyzed with emphasis on the qualitative aspects of the regular spectrum. Whereas all of them yield at least a subset of the exact regular eigenvalues, only the G-function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. This function is derived rigorously employing the ${\mathbb{Z}}_4$-symmetry of the model and shown that its zeros correspond to the complete regular spectrum.     

Characterizing Superradiant Phase of the Quantum Rabi Model

Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model(QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two...     

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.     

Exact Solution of a Non-Hermitian Generalized Rabi Model

An integrable non-Hermitian generalized Rabi model is constructed.A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties.The Yang-Baxter integrability of the system is proven.The exact energy spectrum and eigenstates are obtained using the Bethe ansatz.The method given in this study provides a general way to construct integrable spin-boson models.     

The Algebraic Method to Solve the Fission F-P Equation

Using Lie algebraic method to solve the time evolution equation.The integration formula of the fission F-P equation in the harmonic potential is obtained.This method can be used to deal with the variable coefficients cases.     

A New Method to Solve the Spheroidal Wave Equations

The perturbation method in supersymmetric quantum mechanics is used to study the spheroidal wave functions＇ eigenvalue problem. The super-potential are solved in series of the parameter α, and the general form of all its terms is obtained. This means that the spheroidal problem is solved completely in the way for the ground eigen-value problem. The shape invariance property is proved retained for the super-potential and subsequently all the excited eigen-value problem could be solved. The results show that the spheroidal wave equations are integrable.     

Finslerian Perturbation for the ACDM Model

We present Finslerian perturbation for the ∧CDM model, which breaks the isotropic symmetry of the universe. The analysis on the Killing vectors shows that the Randers-Finsler spacetime breaks the isotropic symmetry even ff the scalar perturbations of the FRW metric vanish. In Randers-Finsler spacetime, the modified geodesic equation deduces a modified Boltzmann equation. We propose a perturbational version of the gravitational field equation in Randers-Finsler spacetime, where we have omitted the curvature tensor that does not belong to the base space of the tangent bundle. The gravitational field equations for the gravitational wave are also presented. The primordial power spectrum of the gravitational wave is investigated. We show that the primordial power spectrum for super-horizon perturbations is unchanged. For sub-horizon perturbations, however, the power spectrum is modified.     

相位微扰法在粗糙面光散射中的应用

根据粗糙面散射理论，用相位微扰法推导出了从随机粗糙介质表面散射的激光雷达散射截面的理论计算公式，计算了几种粗糙表面样品在１．０６μｍ下的单位面积激光雷达散射截面，数值结果与实验数据基本吻合。     

Quantum Thermalization and Thermal Entanglement in the Open Quantum Rabi Model

Quantum thermalization and thermal entanglement in the open quantum Rabi model (QRM), in which a two-level system and a single-mode bosonic field are coupled to either two individual heat baths or a common heat bath, are studied. By treating the QRM as an effective multilevel system and deriving global quantum master equations in the eigenstate representation of the QRM, the physical conditions for quantum thermalization of the QRM is studied. It is found that, in the individual heat-bath case, the QRM can only be thermalized when either the two heat baths have the same temperature or the QRM is only coupled to one of the two baths. In the common heat-bath case, differently, the QRM can always be thermalized. Thermal entanglement of the QRM in both the resonant- and non-resonant coupling cases is also studied. The logarithmic negativity for the thermal state of the QRM is obtained in a wide parameter space, ranging from the low- to high-temperature limits, and from the weak- to deep-strong-coupling regimes. This work paves the way toward the study of quantum effects in nonequilibrium ultrastrongly-coupled light-matter systems.     

Generalized Rotating-Wave Approximation for the Quantum Rabi Model with Optomechanical Interaction

The spectrum of energy and eigenstates of an hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction are investigated. In the spirit of approximations developed for the quantum Rabi model beyond rotating-wave approximation (RWA), the so-called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings is implemented. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a Rabi model with dressed atom-field states (polaritons) coupled to mechanical modes through reparametrized coupling strength and Rabi frequency. A more accurate energy spectrum for a wide range of values of the atom-photon and photon–phonon couplings, when compared to the RWA results is found. The fidelity between the numerical eigenstates and its approximated counterparts is also calculated. The degree of polariton-phonon entanglement of the eigenstates presents a non-monotonic behavior as the atom-photon coupling varies, in contrast to the characteristic monotonic increase in the RWA treatment.