Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle E((B, V, A) associated to a quantum principal bundle P (B, A) are in bijective correspondence with equivariant maps V → P, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with Ad_R-covariant maps A → P.     

Stark效应对量子纠缠信息交换传递的影响

用多个“二能级原子与单模光场”组成的联合物理模型,考虑Stark效应后,推导了该系统的态矢演化式,得到光场纠缠度的数值计算结果.讨论了Stark效应和初始场强对量子纠缠信息交换传递的影响.结果发现,在一定条件下,原子纠缠态与光场纠缠态之间可以转化,实现了量子纠缠信息的交换传递,且Stark效应和初始场强对此过程有着显著的影响:光场的纠缠程度随着初始场强的增强而增大;在强场条件下,光场纠缠度出现崩塌-回复现象.Stark移位参量越大,光场纠缠度振荡越剧烈,说明Stark效应破坏了光场纠缠程度的稳定性.     

Fredholm modules for quantum Euclidean spheres

The quantum Euclidean spheres, S_q^N−1, are (noncommutative) homogeneous spaces of quantum orthogonal groups, SO_q(N). The *-algebra A(S^N−1_q) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres S_q^N−1. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i.e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra A(S^N−1_q).     

Quantum Logic Gates and Cluster States with Four-level Atoms in Cavity QED

We propose a model to implement the two-qubit quantum logic gates, i.e., the quantum phase gate and the Controlled-NOT gate, and generate the atomic qubits cluster states with a large detuned interaction between four-level atoms and a single-mode cavity field. In the presented protocol, the quantum information is encoded on the stable ground states of the atoms, and the effect of decoherence from atomic spontaneous emission is negligible. In addition, the interaction between atoms and the cavity is large detuned, and the cavity is only virtually excited. Therefore, the scheme is insensitive to the cavity decay. The experimental feasibility of our proposal is also discussed.     

Entanglement dynamics and quasiprobability distribution for the degenerate Raman process

In this paper, we consider the model which consists of a degenerate Raman process involving two degenerate Rydberg energy levels of an atom interacting with a single-mode cavity field. The influence of the atomic coherence on the von Neumann entropy of the atom and the atomic inversion is investigated. It is shown that the atomic coherence decreases the amount of atom-field entanglement. It is also found that the collapse and revival times are independent of the atomic coherence, while the amplitude of the revivals is sensitive to this coherence. Moreover, the Q function and the entropy squeezing of the field are examined. Some new conclusions can be obtained.     

Non—conservation of energy arising from atomic dipole interactions and its effects on light field and coupled atoms

The interactions between coupled atoms and a single mode of a quantized electromagnetic field, which involve the terms originating from the dipole interactions, are discussed. In the usual Jaynes－Cummings model for coupled atoms, the terms of non-conservation of energy originating from dipole interactions are neglected, however, we take them into consideration in this paper. The effects of these terms on the evolutions of quantum statistic properties and squeezing of the field, the squeezing of atomic dipole moments and atomic population inversion are investigated. It has been shown that the coupling between atoms modulates these evolutions of fields and atoms. The terms of non-conservation of energy affect these evolutions of fields and atoms slightly. They also have effects on the squeezing of the field, the squeezing of atomic dipole and atomic population inversions. The initial states of atoms also affect these properties.     

Dynamics of Two-Level Trapped Ion in a Standing Wave Laser in Noncommutative Space

We study the dynamics of a two-level trapped ion in a standing wave electromagnetic field in two-dimensional （2D） noncommutative spaces in the Lamb-Dicke regime under the rotating wave approximation. We obtain the explicit analytical expressions for the energy spectra, energy eigenstates, unitary time evolution operator, atomic inversion, and phonon number operators. The Rabi oscillations, the collapse, and revivals in the average atomic inversion and the average phonon number are explicitly shown to contain the information of the parameter of the space noncommutativity, which sheds light on proposing new schemes based on the dynamics of trapped ion to test the noncommutativity.     

镓原子的Stark能级结构

里德堡原子的Stark效应在偶极偶极相互作用、量子信息和量子调控等方面具有潜在的应用前景. 本文首先根据零场时镓原子的能级数据, 通过非线性拟合方法获得了镓原子各态的量子亏损, 仔细分析了量子亏损随主量子数的变化特征; 然后利用Numerov算法计算了镓原子的径向波函数; 最后采用矩阵对角化方法, 数值计算了镓原子高里德堡态在场强范围F=0-3000 V·cm^{- 1}时n=7和n=18附近的Stark能级结构. 结果显示在主量子数n=7多重态以上的能级结构中, (n+1)P态的能级接近并大于nD态的能级, 在n=7多重态以下的能级结构中, (n+1)P态的能级接近并小于nD态的能级. 这一现象不同于通常的碱金属原子的Stark结构, 论文对该现象及其他Stark能级结构特征进行了详细分析, 为相关研究工作提供了重要参考价值.     

频率变化的压缩态光场与原子的相互作用

研究了频率随时间变化的压缩态光场与二能级原子的相互作用，主要讨论了光场频率随时间作正弦调制和脉冲调制两种典型情况下原子布居数反转随时间的演化特性.当光场频率随时间作正弦调制时，不仅光场频率调制，而且压缩态的压缩系数和压缩相位均对原子布居数反转的崩塌-回复过程有影响.当光场频率随时间作脉冲调制时，脉冲调制的突变使各拉比振荡之间的相干性发生改变，并在原子布居数反转随时间演化过程中诱导出新的崩塌-回复过程，尤其在脉冲出现的区间内，原子布居数反转表现出持续的小幅快速振荡，这与压缩态的压缩系数无关. 关键词： Jaynes-Cummings模型 压缩态 原子布居数反转     

Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices

We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.     

场频率变化时原子与场的相互作用

讨论了场频率随时间变化时二能级原子与相干态光场的相互作用. 分析了两种典型的情况，即场频率随时间作正弦变化以及作脉冲变化的情况. 研究发现：当场频率随时间作正弦变化时，原子布居数反转的崩塌和回复现象将消失；当场频率随时间作脉冲变化时,布居数反转随时间的演化将诱发出新的崩塌和回复过程. 关键词： Jaynes-Cummings模型 布居数反转 拉比振荡     

两纠缠原子与光场相互作用系统场熵演化特性

研究了两纠缠原子与相干态光场相互作用系统场熵的时间演化特性,运用全量子力学理论和数值方法,讨论了初始两原子所处的纠缠状态、纠缠度和腔内光场的强弱对场熵的影响.随着光场平均光子数的增加,系统场熵均值和振荡频率增大;光场较弱时,场熵呈现一定的周期性振荡;光场增强后,场熵呈现出周期性的崩塌与回复,且随初始两原子纠缠度的增加,场熵的振幅增大.     

多模腔场与耦合原子之间量子纠缠信息的传递规律

提出了多个“耦合双原子-腔-多模光场”相互作用系统的集合模型,发现了该物理系统中量子纠缠信息的传递规律.即：处于基态的原子以特定速度通过处于纠缠态的腔场时,原子能够将光场的纠缠信息据为已有;反之,纠缠原子以特定速度通过真空场时,原子能把纠缠信息释放于腔中,这样便实现了腔-原子之间纠缠信息的交换传递.利用原子能够捡起、释放量子纠缠信息的特点,进一步实现腔-腔之间异地量子纠缠信息的传递.在不同条件下,量子纠缠信息还可以保持.     

Two-Photon Jaynes-Cummings Model Governed by Milburn Equation with Phase Damping

In this paper, we find an analytic solution of the master equation of a non-resonant two-photon JaynesCummings model (JCM) with phase damping with the help of the super-operator technique. We study the influence of phase damping on non-classical effects in the JCM, such as oscillations of the photon-number distribution, revivals of the atomic inversion, and sub-Possion photon statistics. It is demonstrated that the phase damping suppresses the revivals of the atomic inversion and non-classical effects of the cavity field in the JCM.     

多光子过程中相位退相干时两原子布局数反转

利用全量子理论的方法,研究了存在相位退相干时多光子T-C模型中两个二能级原子与二项式光场相互作用系统中两原子的布居数反转。讨论了相位退相干系数、二项式光场系数、最大光子数、跃迁光子数对原子布居数反转的影响。结果表明：相位退相干减少了原子布居数反转的振幅、破坏了原子的量子特性。改变跃迁光子数,可以改变原子间布居数反转演化周期及演化强度。当二项式光场的最大光子数增大时,原子布居差的崩塌-回复现象就会逐渐消失。相位退相干因子不变时, 二项式光场从相干态过渡到数态过程中,原子布居的振荡频率由大变小,周期性的崩塌与回复现象逐渐消失。     

多光子过程中相位退相干时两原子布局数反转

利用全量子理论的方法,研究了存在相位退相干时多光子T-C模型中两个二能级原子与二项式光场相互作用系统中两原子的布居数反转。讨论了相位退相干系数、二项式光场系数、最大光子数、跃迁光子数对原子布居数反转的影响。结果表明：相位退相干减少了原子布居数反转的振幅、破坏了原子的量子特性。改变跃迁光子数,可以改变原子间布居数反转演化周期及演化强度。当二项式光场的最大光子数增大时,原子布居差的崩塌-回复现象就会逐渐消失。相位退相干因子不变时, 二项式光场从相干态过渡到数态过程中,原子布居的振荡频率由大变小,周期性的崩塌与回复现象逐渐消失。     

Quantum Entanglement in Two-Photon Tavis–Cummings Model with a Kerr Nonlinearity

The properties of quantum entanglement in the two-photon Tavis–Cummings model with a Kerr nonlinearity are studied in terms of quantum information entropy theory. The reduced quantum entropy is employed to investigate the quantum entanglement between two two-level atoms and a single-mode coherent field. The relative quantum entropy is employed to investigate the quantum entanglement between the two two-level atoms. The influences of the nonlinear interaction of the Kerr medium with the field and the atomic dipole-dipole interaction on the properties of quantum entanglement of the system are also examined. Some important results are obtained.     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

与两等同Bell态纠缠原子相互作用光场的量子场熵

利用全量子理论,并通过数值计算,研究了初始处于Fock态的单模光场与两等同双能级纠缠原子单光子共振相互作用过程中单模光场量子场熵的时间演化特性.结果发现:当两原子初始处于第一种Bell态时,光场量子场熵的时间演化周期为π/g2(2n+1);随着初始光强的增大,光场与原子之间的量子纠缠现象减弱;特别是当时间t为演化周期的整数倍时,场－原子系统处于退纠缠状态.当两原子初始处于第二种Bell态时,光场量子场熵不随时间变化,恒为零.当两原子初始分别处于第三种和第四种Bell态时,光场量子场熵的时间演化曲线呈现不等幅周期振荡现象;并且随着初始光场光子数的增加,光场量子场熵的振荡周期逐渐增大,但振荡幅值逐渐减小.     

Robustness of the unidirectional stripe order in the kagome superconductor CsV3Sb5

V-based kagome materials AV₃Sb₅ (A=K, Rb, Cs) have attracted much attention due to their novel properties such as unconventional superconductivity, giant anomalous Hall effect, charge density wave (CDW) and pair density wave. Except for the 2a₀×2a₀ CDW (charge density wave with in-plane 2×2 superlattice modulation) in AV₃Sb₅, an additional 1×4 (4a₀) unidirectional stripe order has been observed at the Sb surface of RbV₃Sb₅ and CsV₃Sb₅. However, the stability and electronic nature of the 4a₀ stripe order remain controversial and unclear. Here, by using low-temperature scanning tunneling microscopy/spectroscopy (STM/S), we systematically study the 4a₀ stripe order on the Sb-terminated surface of CsV₃Sb₅. We find that the 4a₀ stripe order is visible in a large energy range. The STM images with positive and negative bias show contrast inversion, which is the hallmark for the Peierls-type CDW. In addition, below the critical temperature about 60 K, the 4a₀ stripe order keeps unaffected against the topmost Cs atoms, point defects, step edges and magnetic field up to 8 T. Our results provide experimental evidences on the existence of unidirectional CDW in CsV₃Sb₅.