原子-二聚物分子转化系统在受激拉曼绝热过程中的绝热保真度

从原子-二聚物分子转化系统的非U（1）对称性出发,将保真度的定义推广到了非线性系统.并利用绝热保真度定量地研究了原子-二聚物分子转化系统在受激拉曼绝热过程中的动力学和绝热性.研究发现,这个系统的相干布居俘获态——暗态的绝热保真度作为绝热参量的函数以幂律关系趋于1.这个函数关系与线性系统的绝热参量和绝热保真度的幂律关系非常相似,但该系统的幂指数要远小于线性系统的幂指数.此外,还进一步讨论了如何通过优化受激拉曼绝热过程的外部参量得到更高的绝热保真度,从而优化系统的绝热性,提高原子-分子转化效率. 关键词： 原子-二聚物分子转化系统 暗态 受激拉曼绝热过程 绝热保真度     

超冷原子向异核四聚物分子A3B的绝热转化

提出了利用Efimov共振辅助的受激拉曼绝热通道(ER-STIRAP) 过程实施超冷原子向异核四聚物分子A₃B转化的理论方案, 得到了转化过程中中间态分别为同核Efimov三聚物A₃和 异核Efimov三聚物A₂B两种途径下系统的暗态解, 证实了ER-STIRAP技术对超冷异核四聚物分子A₃B合成的可行性和有效性. 研究了外场参数, 包括缔合光脉冲的强度、脉宽、磁耦合强度及其失谐量等对A₃B形成的影响. 对两种不同中间态的转化途径进行比较发现, 与中间态为异核Efimov三聚物A₂B的途径相比, 经历中间态为同核Efimov三聚物A₃的途径时系统实现最终四聚物分子A₃B的产率更高. 另外, 还讨论了系统内禀的非线性和中间态的自发辐射损失对异核四聚物分子合成的影响.     

基于方波脉冲外场的超冷原子-分子绝热转化

基于受激拉曼绝热通道技术,研究了方波脉冲外场下的超冷原子-双原子分子转化.运用绝热保真度的方法,详细分析了该原子-分子转化系统相干布居俘获态的动力学演化过程.研究发现,相干布居俘获态的最终绝热保真度随脉冲激光强度的变化呈现出大幅度的周期振荡.这表明本文所设计的方波脉冲方案与高斯脉冲方案相比具有明显的优势,可以在较小的脉冲激光强度下达到较高的绝热保真度并实现较高效率的超冷原子-分子转化.     

外场参数对超冷原子向异核三原子分子转化的影响

文章研究了利用双光子受激拉曼绝热暗通道技术实现超冷原子向异核三原子分子转化过程中,可控外场参量(包括拉比脉冲的强度,脉宽以及单光子失谐等)对系统绝热性和转化效率的影响. 结果发现,系统的转化效率随斯托克斯光强度的增大先减小,后振荡,最终趋于小于1的稳定值,而随抽运光强的增大先增大,然后很快趋于1,表明抽运光和斯托克斯光对超冷分子的形成具有不同的作用. 脉冲宽度既能决定最终转化效率的大小,也能反映达到稳定转化所需的时间. 单光子失谐为红失谐时,系统有比较高的稳定转化效率,而蓝失谐光脉冲则不利于超冷分子的形成. 另外,还讨论了超冷异核三原子分子转化系统在经历不同反应通道时绝热性和转化效率的差别. 关键词： 异核三原子分子 受激拉曼绝热暗通道 绝热参量 绝热保真度     

超冷原子-分子转化动力学：受激拉曼绝热过程

超冷分子是超冷原子分子物理领域的新的热点研究课题。分子具有更多的自由度,能级结构密集、复杂,直接激光冷却存在困难。目前,人们一般借助外场把超冷原子耦合获得超冷分子。受激拉曼绝热暗通道技术~(stimulated Raman adiabatic passage,STIRAP)作为其中一种非常有效地将超冷原子转化为超冷分子的方法已被广泛地研究。该文主要针对STIRAP过程中超冷原子-分子转化系统的动力学,绝热性、稳定性等理论研究的进展进行综述。     

计算7Li2振动能级煌振动-转动能级的辛格式矩阵法

利用辛格式矩阵法计算了双原子分子⁷Li₂在A¹Σ_u⁺态的振动能级和振动-转动能级,并与Ley-Koo等的计算结果作了比较.结果显示,辛格式矩阵法是收敛的和可靠的,是计算双原子分子的振动能级和振动-转动能级的合理的数值方法.     

利用绝热过程实现远距离量子纠缠

提出利用绝热过程实现远距离量子纠缠的方案.Λ型原子和经典场、单模腔场发生相互作用,系统的绝热演化在暗态中进行.利用这种绝热演化进行远距离原子、腔场纠缠,可有效地抑制原子的自发辐射噪声.     

外场形式对超冷原子-多聚物分子转化效率的影响

通过改变激光场Rabi频率和原子-多聚物分子耦合强度, 探索了外场形式对超冷原子-多聚物分子转化效率的影响. 首先通过定义时间指数, 对文献所给出的外场做出改进, 讨论了时间指数对转化效率的影响; 然后选取一种更优化的外场形式, 其具有很好的参数鲁棒性, 该外场作用下的绝热过程几乎不存在振荡, 其绝热保真度接近于1, 系统误差较小, 可以稳定、高效地实现超冷原子-多聚物分子的转化. 关键词： 超冷多聚物分子 转化效率 外场形式 绝热保真度     

超冷原子-分子转化动力学:受激拉曼绝热过程

获得超冷分子是超冷原子分子物理领域的新的热点研究课题。分子具有更多的自由度,能级结构密集、复杂,直接激光冷却存在困难。目前,人们一般借助外场把超冷原子耦合获得超冷分子。受激拉曼绝热通道技术(stimulated Raman adiabatic passage,STIRAP)作为其中一种非常有效地将超冷原子转化为超冷分子的方法已被广泛地研究。该文主要针对STIRAP过程中超冷原子-分子转化系统的动力学,绝热性、稳定性等理论研究的进展进行综述。     

Λ型原子-分子三能级系统的分子转化率问题

利用解析和数值的方法对Λ型原子-分子三能级系统的量子动力学行为进行了详细研究，同时对该系统中分子转化率进行了研究.结果发现，不同的系统初态对转化率有比较大的影响，理想情况下，在初始态为原子态且在两个拉比频率相等时，可以得到较高的分子转化率，而光场的失谐会造成转化率的降低；初始态为暗态时，分子转化率为一常数，光场的失谐会增大转化率.     

Dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules

In this paper,we investigate the dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules through a stimulated Raman adiabatic passage aided by Feshbach resonance.We analytically obtain the regions where the dynamical instability appears and find that such instability in the Bose-Fermi mixture system is caused not only by bosonic interparticle interactions but also by Pauli blocking terms,which is different from the scenario of a pure bosonic system where instability is induced by nonlinear interparticle collisions.Taking a 40 K-87 Rb mixture as an example,we give the unstable regions numerically.     

Linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules

In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40 K and 6 Li atom–molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.     

Dynamical instability induced by the zero mode under symmetry breaking external perturbation

A complex eigenvalue in the Bogoliubov–de Gennes equations for a stationary Bose–Einstein condensate in the ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by the complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose–Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes.     

Is the Hamiltonian geometrical criterion for chaos always reliable?

It is found that the application of a newly developed geometrical criterion, in which negative eigenvalues of the associated matrix determined by the dynamical curvature of a conformal metric for a Hamiltonian system are used to identify the onset of local instability or chaos, is somewhat problematic in some circumstances. In fact, this criterion is neither necessary nor sufficient for the prediction of instability of orbits on a same energy hypersurface because it is not in good agreement with information on unstable or chaotic behavior given by the maximal Lyapunov exponent in general.     

On the Spectral Dynamics of the Deformation Tensor and New A Priori Estimates for the 3D Euler Equations

In this paper we study the dynamics of eigenvalues of the deformation tensor for solutions of the 3D incompressible Euler equations. Using the evolution equation of the L² norm of spectra, we deduce new a priori estimates of the L² norm of vorticity. As an immediate corollary of the estimate we obtain a new sufficient condition of L² norm control of vorticity. We also obtain decay in time estimates of the ratios of the eigenvalues. In the remarks we discuss what these estimates suggest in the study of searching initial data leading to possible finite time singularities. We find that the dynamical behaviors of L² norm of vorticity are controlled completely by the second largest eigenvalue of the deformation tensor. Part of this work was done while the author was visiting CSCAMM, University of Maryland, USA. The author would like to thank to Professor E. Tadmor for his hospitality     

Dynamical instability and adiabatic evolution of the atom--homonuclear--trimer dark state in a condensate system

This paper investigates the dynamical instability and adiabatic evolution of the atom--homonuclear--trimer dark state of a condensate system in a stimulated Raman adiabatic passage aided by Feshbach resonance. It obtains analytically the regions for the appearance of dynamical instability caused by the interparticle interactions. Moreover, the adiabatic property of the dark state is also studied in terms of a newly defined adiabatic fidelity. It shows that the nonlinear collisions have a negative effect on the adiabaticity of the dark state and hence reduce the conversion efficiency.     

Statistical properties of cross-correlation in the Korean stock market

We investigate the statistical properties of the cross-correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the cross-correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original cross-correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The b₄₇₃\beta_{473} coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function E(s)E(\sigma) with the portfolio risk σ for the original and filtered cross-correlation matrices are consistent with a power-law function, E(σ) ~ s^-g\sigma^{-\gamma}, with the exponent γ ~ 2.92 and those for Asian currency crisis decreases significantly.     

Effects of nuclear structure in the spin-dependent scattering of weakly interacting massive particles

We present calculations of the nuclear from factors for spin-dependent elastic scattering of dark matter WIMPs from¹²³Te and¹³¹Xe isotopes, proposed to be used for dark matter detection. A method based on the theory of finite Fermi systems was used to describe the reduction of the single-particle spin-dependent matrix elements in the nuclear medium. Nucleon single-particle states were calculated in a realistic shell model potential; pairing effects were treated within the BCS model. The coupling of the lowest single-particle levels in¹²³Te to collective 2⁺ excitations of the core was taken into account phenomenologically. The calculated nuclear form factors are considerably less then the single-particle ones for low momentum transfer. At high momentum transfer some dynamical amplification takes place due to the pion exchange term in the effective nuclear interaction. But as the momentum transfer increases, the difference disappears, the momentum transfer increases and the quenching effect disappears. The shape of the nuclear form factor for the¹³¹Xe isotope differs from the one obtained using an oscillator basis.     

Many-body exceptional points in colliding condensates

ABSTRACT

Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.     

Holographic Dark Energy Model with Time Varying G as Well as c 2 Parameter

In this paper, we study a holographic dark energy model with time varying gravitational constant G as well as holographic parameter c ² in flat FRW space-time geometry. We obtain the evolution of equation of state parameter and the exact differential equation, which determine the evolution of the dark energy density based on varying G and c ² parameter. Also, we determine the deceleration parameter to explain the expansion of the universe. Further, we study the validity of the generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological implication of our work by evaluating the holographic dark energy equation of state for low red-shifts containing both varying G and c ² parameter corrections.