Quantum action-angle variables for harmonic oscillators

The well-known difficulties of defining a phase operator of an oscillator, caused by the lower bound on the number operator, is overcome by enlarging the physical Hilbert space by means of a spin-like, two-valued quantum number. On the enlarged space a phase representation exists on which trigonometric functions of the phase are numbers, and the “number of quanta” is a differential operator. Physical results are recovered by projection on the “upper components.” Coherent states, indeterminacy relations, as well as generalizations to other Hamiltonians, including the quantum analog of the quasi-periodic case, are discussed.     

Quantum beats from dressed three-level atoms

By extending a previously developed unitary transformation technique to dress three-level atoms by a strong driving radiation field, we show that quantum beats can be induced by the presence of the driving field also when the decay channels lead from a singlet to a doublet of lower energy. A qualitative explanation of this effect is presented, which is based on the quantum theory of measurement.     

V型三能级原子双模光场系统中光场压缩性质

本文利用格子液体方法对文献中给出的V型三能级原子玻色-爱因斯坦凝聚体与双模压缩相干态光场相互作用系统的哈密顿量进行分析,发现文献中对原子间相互作用部分的处理有不合理之处,从而对该哈密顿量作出了改进并研究了V型三能级原子双模光场系统中光场压缩性质.结果表明:光场两正交分量交替呈现周期性压缩现象,其压缩深度与光场初始压缩因子密切相关,而压缩时间与双模光场的频率有关. 关键词： 玻色-爱因斯坦凝聚 V型三能级原子 压缩相干态 双模压缩态光场     

Elliptic solution for two nonlinear interacting oscillators

Bykovskij and Inozemtsev have obtained the exact solution for two nonlinear oscillators with a certain type of interaction. Here more general cases are considered, and exact solutions have been obtained.     

两纠缠原子与相干态光场相互作用过程中光场的量子特性

采用时间演化算符和数值计算方法,研究了两全同二能级纠缠原子与相干态光场相互作用过程中光场的量子特性,结果表明:两原子初始纠缠度和相干态光场强度对系统光场的二阶相干性质和压缩效应有很大的影响.     

Quantum entanglement in the system of two two-level atoms interacting with a single-mode vacuum field

The entanglement properties of the system of two two-level atoms interacting with a single-mode vacuum field are explored. The quantum entanglement between two two-level atoms and a single-mode vacuum field is investigated by using the quantum reduced entropy; the quantum entanglement between two two-level atoms, and that between a single two-level atom and a single-mode vacuum field are studied in terms of the quantum relative entropy. The influences of the atomic dipole--dipole interaction on the quantum entanglement of the system are also discussed. Our results show that three entangled states of two atoms--field, atom--atom, and atom--field can be prepared via two two-level atoms interacting with a single-mode vacuum field.     

Entropy of field interacting with two two-qubit atoms

We use quantum field entropy to measure the degree of entanglement for a coherent state light field interacting with two atoms that are initially in an arbitrary two-qubit state. The influence of different mean photon number of the coherent field on the entropy of the field is discussed in detail when the two atoms are initially in one superposition state of the Bell states. The results show that the mean photon number of the light field can regulate the quantum entanglement between the atoms and light field.     

二项式光场与级联三能级原子的量子纠缠

利用量子熵理论，研究了二项式光场与级联三能级原子的量子纠缠，讨论了光场与原子的初始参量对其量子纠缠性质的影响.结果表明，利用二项式光场的特性，可以揭示从相干态到数态之间的所有态光场与三能级原子相互作用时的量子纠缠性质.选择适当的系统参数可以制备稳定的光场-原子qutrit纠缠态. 关键词： 二项式光场 级联三能级原子 光场熵 量子纠缠     

Quantum theory of electromagnetic fields interacting with atoms and molecules

This paper reviews the recent achievements in nonrelativistic quantum electrodynamics, especially nonlinear and coherent phenomena. The general properties of coupled radiation and matter are presented within simple models in section 1. The following sections treat in some detail three main aspects of the system and can be read independently of each other. Section 2 discusses some experiments with long-wave-length radiation (r.f.) and atoms. Section 3 presents the quantum theory of a laser and the ensuing photon distributions. Section 4 treats the case of strongly correlated emission of radiation called superradiance. The use of statistical ensembles is briefly discussed in Appendix A, whereas Appendices B, C and D present some technical details of the text.     

非线性相干态光场与二能级原子相互作用的量子特性

借助于数值计算方法, 研究了非线性相干态光场与一个二能级原子相互作用过程中原子的布局反转、 光子的反聚束效应以及光场振幅平方压缩的时间演化特性, 并讨论了光场参量α、原子的初始状态以及非线性相 干态Lamb-Dicke参数η对该相互作用系统量子特性的影响.     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

V型三能级原子玻色-爱因斯坦凝聚体与双模压缩光场相互作用系统中光场的压缩特性

研究了V型三能级原子的玻色爱因斯坦凝聚体与双模压缩相干态光场相互作用系统中光场的压缩特性.结果表明:光场的两正交分量交替呈现周期性压缩现象,其压缩时间和压缩深度与光场的初始压缩因子密切相关 关键词： 玻色爱因斯坦凝聚体 V型三能级原子 双模压缩态光场 光场正交压缩     

The entropy of entangled three-level atoms interacting with entangled cavity fields: Entanglement swapping

The dynamics of an entangled atomic system, partially interacting with entangled cavity fields and characterizing an entanglement swapping, has been studied through their von Neumann entropies. The aforementioned interaction is implemented via a two-photon process, given by either the full microscopical Hamiltonian approach or the two-photon Jaynes-Cummings model. Numerical simulations furnish the explicit expressions for each sub-system entropy, which allow us to estimate the multiperiodicity in the evolution of the entangled atom-field system. The effects of the detuning parameter upon the period and the amplitude of the entropies are also discussed as well as the power spectrum of the entropy.     

原子与耦合腔相互作用系统中的量子失协

本文研究由两个全同的二能级原子和耦合腔构成的系统,利用Dakic等提出的几何量子失协的度量方法,采用数值计算方法计算了系统中两原子间和两腔场间量子失协的演化.讨论了原子间初始纠缠度和腔场间耦合系数变化对几何量子失协演化的影响.研究发现:随腔场间耦合系数的增大,量子失协周期性演化的频率增大;随原子间初始纠缠度的增大,两原子间的关联增强,两腔场间的关联减弱.     

System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of N interacting harmonic oscillators in uniform field and a system of N particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of N free particles in uniform field in rotationally invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of N harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.     

双模场与V型三能级原子玻色-爱因斯坦凝聚体相互作用系统的光场压缩效应

研究了V型三能级原子玻色-爱因斯坦凝聚体与双模压缩相干态光场相互作用系统中的光场压缩的特性.数值计算结果表明:光场的正交分量呈现周期性压缩,其周期与原子间相互作用密切相关,而最大压缩量与持续时间与初始光场的压缩因子有关.     

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.     

The energy level spacing for two harmonic oscillators with generic ratio of frequencies

The limit distribution of energy level spacing is studied for the system of two harmonic oscillators with generic ratio of frequencies. It is proved that for any fixed generic ratio no limit distribution exists, but for random with any absolutely continuous distributionp()d on [0, 1] a universal random limit distribution of the energy level spacing exists. Some properties of the random limit distribution are discussed.     

包含三能级原子环形腔的动态非稳与混沌过渡

在包含三能级原子的环形腔的输出光场中, 观察到了由电磁感应透明(EIT) 效应导致的动态非稳及混沌. 该动态非稳及向混沌的过渡可以通过耦合光场而加以很好地控制. 同时, 由三能级EIT导致的原子相干改变了系统的吸收、色散及非线性效应, 从而极大地增强了系统的动态非稳和混沌过渡特性. 建立了一个理论模型来定量地解释观察到的现象.