Eigenstates and eigenenergies of four-wave-mixing models

We present explicit analytical expressions of all the eigenenergies and eigenstates for two different kinds of four-wave-mixing model in terms of a parameter lambda without the so-called Bethe ansatz assumption. The parameter lambda is shown to be determined by the roots of a simple polynomial. We also obtain the exact explicit analytical expressions of infinite eigenstates and energies without any unknown parameter.     

七玻色模混和模型的本征态及本征值

利用参数 ，我们没有运用Bethe ansatz假设，直接求解了三种七玻色模混和模型的所有本征态和本征值。而此参数取决于一多项式的根，并且是可以在数字上严格求解的。     

Exact eigenstates for a class of models describing two-mode multiphoton processes

We present an efficient approach to studying the spectra and eigenstates for nonlinear models describing multiphoton processes. We obtain the exact explicit analytical expressions of all the energy spectra and eigenstates in terms of a parameter for a class of models describing two-mode multiphoton processes. The parameter is shown to be determined by the roots of a simple polynomial.     

Analytical Results of Eigenstates and Eigenenergies for Three Kinds of Models Describing N-mode Multiphoton Process

We obtain the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter λ for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.     

Exact Eigenstates for a Class of Model Describing Interactions Among Five Bosonic Modes with Multiphoton Process

We present an efficient approach to studying the spectra and eigenstates for the model describing interactions among five bosonic modes without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter A for a class of models describing five-mode multiphoton process. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.     

Analytical Results for Model Describing Interactions Among Six Bosonic Modes

We present the explicit analytical results of all the eigenstates and eigenvalues using a parameter λ without the assumption of Bethe ansatz for three different kinds of six bosonic modes models. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.     

Analytical method for yrast line states in interacting Bose-Eeinstein condensates

We propose a method to investigate the energy eigenvalue problem and corresponding yrast line for harmonically trapped interacting N-boson systems. This method is particularly simple and effective to obtain the explicit analytical expressions of low-L energy eigenstates with L denoting systems' total angular momentum but with an arbitrarily large N. We have derived the explicit analytical results for L = 0,1,....,9 and discussed the yrast line for these low- L energy eigenstates.     

Quantum-jump approach to dipole dephasing: Application to inversionless amplification

We present a model for simulating atomic dipole dephasing within the Monte-Carlo wave function formalism which leads to the same results as the standard density-matrix formalism. In this model dipole dephasing processes are accounted by quantum-jumps into one of the atomic energy eigenstates. This fact allows us to obtain analytical expressions for the effects of elastic collisions on the various physical processes responsible for amplification without population inversion in a cascade three-level atomic configuration.     

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.     

Raman Theory for a Molecule in a Vibrating Microcavity Oscillating in Fundamental Resonance

We propose a model to describe the energy structure and dynamics of a system of a molecule interacting with infinite photon modes in a vibrating microcavity whose boundary oscillates in the fundamental resonance.By constructing an so(2,1) Lie algebra for the infinite photon modes,we obtain analytical expressions of the energy eigenstates,energy eigenvalues and the system‘s evolution operator for this Raman model under certain conditions.     

Initial-Slip Term Effects on the Dissipation-Induced Transition of a Simple Harmonic Oscillator

We investigate the effects of the initial-slip term by studying the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. The general analytical expressions for the transition probabilities are obtained, then the special cases of transition probabilities ignoring the Brownian motion from the ground state to the first few excited states are discussed. It is found that the initial-slip term not only makes the forbidden transitions between states of different parity possible but also lifts the initial value of the transition probabilities.     

SU(2) andSU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states

We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset of algebra eigenstates. We develop the general formalism and apply it to theSU(2) andSU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in both cases by a method that employs analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states and intelligent states are examined and relations between them are studied by using their analytic representations.     

Emission spectrum of a qubit in Rabi model in strong coupling regime

The analytical eigenenergies and eigenstates of the Rabi model are obtained approximately based on a unitary transformation and a generalized rotating-wave approximation (GRWA). Using these analytical expressions without the rotating wave approximation (RWA), we generalize the definition of the physical emission spectrum valid with the RWA in order to meet without the RWA with some modifications. Taking into account the counter-rotating wave terms and the intercrossing of energy level in the strong coupling regime, the physical emission spectrum of qubit is investigated. Different from the case with RWA, the multi-peak vacuum Rabi splitting, even when the qubit initially in its ground state and the bosonic field initially in vacuum, can emerge. These new features of physical emission spectrum originate from the effect of counter-rotating wave terms. Moreover, the intercrossing of energy level can also be observed in the strong coupling regime.     

Quantum oscillations and wave packet revival in conical graphene structure

We present analytical expressions for the eigenstates and eigenvalues of electronsconfined in a graphene monolayer in which the crystal symmetry is locally modified byreplacing a hexagon by a pentagon, square or heptagon. The calculations are performed inthe continuum limit approximation in the vicinity of the Dirac points, solving Diracequation by freezing out the carrier radial motion. We include the effect of an externalmagnetic field and show the appearance of Aharonov-Bohm oscillations and find out theconditions of gapped and gapless states in the spectrum. We show that the gauge field dueto a disclination lifts the orbital degeneracy originating from the existence of twovalleys. The broken valley degeneracy has a clear signature on quantum oscillations andwave packet dynamics.     

Eigenstates of Electromagnetic Field in the Presence of External Source

We study electromagnetic field theory in the presence of external source and show how eigenstates of electromagnetic field are related to the external source. With the help of coherent state and functional integral techniques, we derive explicit expressions of the eigenstates.     

Holonomy structure of parameter manifolds

The Berry holonomy phase is usually attributed to homotopically nontrivial maps induced by the Hamiltonian in the space of orthonormal eigenstates constructed over a parameter manifold. We show that the issues of mappings and eigenstates should be addressed separately and that equivalence between them implies a trivial Berry phase.     

Nonlinear Landau--Zener Tunnelling with Two and Three-Body Interactions

We investigate the nonlinear Landau-Zener tunnelling of Bose-Einstein condensate （BEC） in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both anaJytically and numerically. The analytical eigenstates and the tunnelling probability are obtained, which are verified by numerical methods. It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.     

Symmetry violating trial wave functions

A variational procedure using trial wave functions projected on to symmetry eigenstates is investigated. In the individual particle model it leads to generalized self-consistent single-particle equations being dependent on the symmetry eigenvalue. A perturbation expansion appropriate for the case of strong symmetry violations is described. Model independent expressions for the moment of inertia and the decoupling parameter are derived by applying the method to rotational symmetry.     

量子玻色流体中的压缩玻色子对数态

导出参量相关的Bogoliubov幺正变换的封闭性表达式，在原粒子数表象中对角化量子玻色流体的约化Hamiltonian．将两模辐射场的非经典特性的表述推广到与流体的相互作用机制相应的量子玻色场，从波动和粒子统计的角度确认Hamiltonian本征态是非经典的压缩玻色子对数态． 关键词：     

用赝角动量方法求解同调谐振子

采用赝角动量的方法研究了同调谐振子(带有附加有心势垒项的谐振子)的定态薛定谔方程的严格解.详细讨论了有心势垒项的参量对于形成体系束缚定态的有效取值区域,及该参量的不同取值区域对能谱的影响.给出了能谱的确切的全面表述和对应本征态的解析表达式.对于不同文献作者的不同处理予以分析和澄清 关键词： 同调谐振子 类角动量方法 广义湮没算符 广义产生算符 本征值谱 本征态