具有非线性两模场和原子与场非线性耦合的Jaynes-Cummings模型的解

利用Lewis和Riesenfeld不变量方法求解了具有任意非线性场和依赖任意强度耦合的多光子双模场与二能级原子相互作用的JC模型,得到原子一光场的态矢、时间演化算符、原子布居和双模场的光子数算符的演化式.     

用不变量方法求解附加Kerr介质的非线性Jaynes-Cummings模型

利用不变量方法研究了充满Kerr介质的高Q腔中双模场与二能级原子非共振相互作用系统,得到了该系统的态矢、时间演化算符、原子布居数和双模场光子数随时间演化式.     

四模场中单原子系统的新算符求解方法

提出处理腔场与原子、腔场与腔场等系统的较为一般算符方法。基于此方法,通过构造四对时间依赖的产生和湮灭算符,简捷地求解四模腔场或四腔场与二能级原子非共振相互作用系统,得到其本征态、本征值和一般态矢。特别地,在四模场或四腔场和原子的初态分别为真空态和一般叠加态时,给出四场模平均光子数和原子布居数反转的时间演化。该新方法可应用于其它一些量子系统。     

耗散腔中多光子J-C模型中的密度算符间距

研究了腔场存在相位耗散时多光子J-C模型中光场、原子和系统的密度算符间距;讨论了原子初始态、光场强度以及腔场耗散系数对密度算符间距的影响;且比较了不同跃迁光子数下体系的密度算符间距.结果发现:①密度算符间距与原子的初始态密切相关.②光场和系统的密度算符间距在耗散腔中作减幅周期振荡最终达到稳定,达到稳定所需时间随腔的耗散系数增大而缩短;而原子的密度算符间距与腔的耗散无关.③随着光场初始强度的增加,光场和系统与各自初始态的偏离程度增大.④对于双光子跃迁,当腔场存在相位损耗时光场和系统的密度算符间距仍作减幅周期振荡,原子仍周期性的回到纯态.但由于光场与原子的纠缠和退纠缠速率加快,密度算符间距在每个周期内振荡加剧.     

场频率变化时多光子J-C模型中原子的动力学特性

利用多光子J-C模型,在旋波近似下,研究了场频率随时间变化时二能级原子通过多光子跃迁与单模辐射场相互作用系统中原子的动力学特性,分析了光场频率随时间以正弦函数形式作小量变化的典型情况,利用数值计算方法给出原子算符S3(t)平均值随时间的演化曲线.研究结果表明:原子算符S3(t)平均值随时间的演化受场频率随时间正弦函数形式变化的调制,场频率振荡的幅值u越大调制作用越强.     

非线性超场和夸克禁闭

利用非线性超场技术,我们讨论了超对称的非线性场论模型.找到了超对称运动方程精确静态解的一般形式,它可以作为袋模型的出发点。作为一个特殊情形,我们重新得到了 SLAC 袋模型,也就是说,SLAC 袋是超对称的.文中还讨论了超对称的 Sine-Gordon 模型、Sinh 模型和 exp 模型.     

非阿贝尔腔量子电动力学模型下偏振光场的影响

通过使用场正交算符,而不是传统的玻色算符,研究了非阿贝尔腔量子电动力学(QED)模型中原子和偏振光场的相互作用。讨论了初始双模偏振光场对于原子布居数反转以及偏振光场的压缩特性的影响。结果表明,原子布居数反转的演化不仅与偏振椭圆的相位角有关,也与偏振椭圆的椭率角有关;只有当偏振椭圆是右旋圆偏振光时,原子布居数反转随时间的演化基本不变,趋近于初始值0,而当偏振椭圆是左旋圆偏振光时,原子布居数反转随时间的演化呈现周期性的崩塌复苏变化。另外,当初始光场是左旋圆偏振光时,光场可以出现周期性的压缩;而当初始光场是右旋圆偏振光时,光场的压缩不会持续出现。     

耗散腔中多光子J-C模型中的密度算符间距

研究了腔场存在相位耗散时多光子J-C模型中光场、原子和系统的密度算符间距;讨论了原子初始态、光场强度以及腔场耗散系数对密度算符间距的影响;且比较了不同跃迁光子数下体系的密度算符间距。结果发现：①密度算符间距与原子的初始态密切相关。②光场和系统的密度算符间距在耗散腔中作减幅周期振荡最终达到稳定,达到稳定所需时间随腔的耗散系数增大而缩短;而原子的密度算符间距与腔的耗散无关。③随着光场初始强度的增加,光场和系统与各自初始态的偏离程度增大。④对于双光子跃迁,当腔场存在相位损耗时光场和系统的密度算符间距仍作减幅周期振荡,原子仍周期性的回到纯态。但由于光场与原子的纠缠和退纠缠速率加快,密度算符间距在每个周期内振荡加剧。     

场频率随时间变化对原子偶极压缩效应的影响

利用J-C模型,考虑场频率随时间以正弦函数形式作小量变化,在旋波近似下,研究了二能级原子通过单光子跃迁与单模辐射场相互作用系统中原子算符Sy压缩效应的演化规律.利用数值计算方法给出压缩量随时间的演化曲线.研究结果表明:原子算符压缩效应的演化受场频率随时间正弦函数形式变化的调制,场频率振荡的幅值u越大调制作用越强.随场频率变化的幅值u的增大,压缩效应减弱.在场频率振荡的幅值u大于一定值后,压缩量将按场频率周期性的变化规律作周期性振荡,     

压缩真空场与原子非线性作用系统中原子的量子特性

研究了附加克尔介质的压缩真空场与二能级原子依赖强度耦合相互作用系统中原子的反转特性,并采用密度算符间的距离研究了该模型中原子量子态的演化规律.详细地讨论了克尔非线性作用的强度以及初始压缩真空场的压缩度对原子反转和原子量子态演化的影响.     

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes－Cummings model

On the basis of the fact that the two-level multiphoton Jaynes－Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.     

Exact solution for the thermo Jaynes--Cummings model

Based on the construction of supersymmetric generators, we use the Lewis--Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes--Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes--Cummings system.     

Local supersymmetry for spinning particles

First and second order forms of the covariant action for a spinning particle are exhibited. The action consistently incorporates the necessary constraints and is invariant under both local supersymmetry and general time parameter transformations, and provides a simple one-dimensional model for the interaction between matter and supergravity. A formulation invariant under general co-ordinate transformations in superspace is also given and shown to be equivalent to the locally supersymmetric one.     

Solving Multiphoton Jaynes–Cummings Model with Field Nonlinearity by Supersymmetric Unitary Transformation

We introduce a supersymmetric unitary transformation, to diagonalize the multiphoton Jaynes–Cummings model Hamiltonian based on supersymmetric quantum mechanics theory, that includes any forms of intensity-dependent coupling and field nonlinearity. On doing so, we obtain its eigenvalue and eigenstates, and the time evolution of state vector.     

Conserved charges and supersymmetry in principal chiral and WZW models

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess–Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess–Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.     

On the Schrödinger equation for the supersymmetric FRW model

We consider a time-dependent Schrödinger equation for the Friedmann–Robertson–Walker (FRW) model. We show that for this purpose it is possible to include an additional action invariant under reparametrization of time. The last one does not change the equations of motion for the minisuperspace model, but changes only the constraint. The same procedure is applied to the supersymmetric case.     

Supersymmetric chiral normal coordinates

The (anti-) chiral Killing vectors of the supersymmetric Kähler manifold associated with the nonlinear realization of a global symmetry are used to define (anti-) chiral normal coordinates. This in turn leads to a background superfield expansion of the super-Kähler potential that is manifestly gauge invariant and supersymmetric. The chiral normal coordinates are further employed to construct a background superfield expansion for a locally gauge invariant supersymmetric action.     

Pseudo-invariant Eigen-operator for Deriving Energy-Level Gap for Jaynes-Cummings Model

We extend the concept of invariant eigen-operator to pseudo-invariant eigen-operator case through analyzing the standard Jaynes-Cummings model. We find the pseudo-invariant eigen-operator in terms of supersymmetric generators of this model, which diretly leads to the energy-level gap for Jaynes-Cummings Hamiltonian.     

The 2-dimensionalN=2 supersymmetric Yang-Mills model on the discrete space-time lattice

We use the Dirac-Kähler formalism in order to put a two-dimensional Yang-Mills theory with a complex supersymmetry on the Euclidean space-time lattice. The theory presents two supersymmetric invariant actions related to each other by a kind of “time reflection” transformation.     

R parity from the heterotic string

In T-duality invariant effective supergravity with gaugino condensation as the mechanism for supersymmetry breaking, there is a residual discrete symmetry that could play the role of R parity in supersymmetric extensions of the standard model.