Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate

In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order of magnitude.     

Strong-coupling regime of the nonlinear landau-zener problem for photo- and magnetoassociation of cold atoms

We discuss the strong-coupling regime of the nonlinear Landau-Zener problem occurring at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation for the molecular state probability and construct an accurate approximation describing the time dynamics of the coupled atom-molecule system. The resultant solution improves the accuracy of the previous approximation [22]. The obtained results reveal a remarkable observation that in the strong-coupling limit, the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecule oscillations occurring soon after crossing the resonance are principally of a linear nature. This observation is supposedly general for all nonlinear quantum systems having the same generic quadratic nonlinearity, due to the basic attributes of the resonance crossing processes in such systems. The constructed approximation turns out to have a larger applicability range than it was initially expected, covering the whole moderate-coupling regime for which the proposed solution accurately describes ail the main characteristics of the system evolution except the amplitude of the coherent atom-molecule oscillation, which is rather overestimated.     

An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3 × 10^?6 for the final transition probability while at certain time points it might increase up to 10^?3. Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.     

Demkov-Kunike model in cold molecule formation: the fast resonance sweep regime of the strong interaction limit

We study a quadratic-nonlinear version of the level-crossing Demkov-Kunike problem relevant to coherent molecule formation via photo- or Feshbach-association of ultracold atoms. Using an exact third-order nonlinear differential equation for the molecular state probability, we construct an approximate solution to the problem in the fast sweep regime of the strong interaction limit. The constructed approximation, defined as a solution of a first-order nonlinear equation, contains a fitting parameter which we determine through a variational procedure. The suggested approach can be interpreted as a modification of the adiabatic approximation and can further be used for the treatment of analogous nonlinear two-state problems.     

Pseudopotential analog for zero-range photoassociation and Feshbach resonance

A zero-range approach to atom-molecule coupling is developed in analogy to the Fermi-Huang pseudopotential approach to collisions. It is shown by explicit comparison to an exactly solvable finite-range model that replacing the molecular bound-state wave function with a regularized delta function can reproduce the exact scattering amplitude in the long-wavelength limit. Using this approach, we find an analytical solution to the two-channel Feshbach resonance problem for two atoms in a spherical harmonic trap, highlighting the strong dependence of the effective scattering length and bare-molecule population on the atom-molecule coupling strength.     

Rosen-Zener model in cold molecule formation

The Rosen-Zener model for association of atoms in a Bose-Einstein condensate is studied. Using a nonlinear Volterra integral equation, we obtain an analytic formula for final probability of the transition to the molecular state for weak interaction limit. Considering the strong coupling limit of high field intensities, we show that the system reveals two different time-evolution pictures depending on the detuning of the frequency of the associating field. For both limit cases we derive highly accurate formulas for the molecular state probability valid for the whole range of variation of time. Using these formulas, we show that at large detuning regime the molecule formation process occurs almost non-oscillatory in time and a Rosen-Zener pulse is not able to associate more than one third of atoms at any time point. The system returns to its initial all-atomic state at the end of the process and the maximal transition probability 1/6 is achieved when the field intensity reaches its peak. In contrast, at small detuning the evolution of the system displays large-amplitude oscillations between atomic and molecular populations. We find that the shape of the oscillations in the first approximation is defined by the field detuning only. Finally, a hidden singularity of the Rosen-Zener model due to the specific time-variation of the field amplitude at the beginning of the interaction is indicated. It is this singularity that stands for many of the qualitative and quantitative properties of the model. The singularity may be viewed as an effective resonance-touching.     

New method for solving the time-dependent Schrödinger equation for molecules in a strong pulsed light field

A new approach to solution of the time-dependent Schrödinger equation for a quantum system affected by a strong electromagnetic laser field modulated in amplitude and frequency is proposed. This approach is based on application of the Floquet method and approximation of the Hamiltonian parameters slowly varying with time by step functions within the (t, t′) formalism. A relationship between the method developed and representation of the evolution operator in the form of the T-ordered product of operators acting at short time intervals is demonstrated. The method proposed is used to describe the response of a LiH molecule to the action of a radiation pulse and calculate the populations of the electronic states of the molecule under the pulse action. The evolution of the populations and dynamic susceptibility of the molecule and its relationship with the probabilities of Landau-Zener transitions between the electronic quasienergy states of the molecule have been analyzed.     

Gauging a quantum heat bath with dissipative Landau-Zener transitions

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.     

Dissociation of molecular hydrogen ions by an IR laser pulse

Dissociation dynamics of the simplest molecular systems, such as H₂ ⁺, D₂ ⁺ and HD⁺ ions, in an intense IR laser field has been investigated by numerical modeling. An n-term approximation has been developed to describe the molecular system dynamics in an intense electromagnetic field. Calculations by the n-term approximation have been compared to an accurate numerical solution of the two-particle problem. The dissociation probability as a function of the frequency and intensity of radiation for different isotopes in a molecular hydrogen ion is discussed. A quasistatic model of molecule dissociation in an IR field has been suggested, and limits of its applicability have been determined. Zh. éksp. Teor. Fiz. 113, 128–143 (January 1998)     

A reactive,two-state,curve-crossing study. A comparison between exact,distorted wave Born approximation,and Landau-Zener results

A ‘reactive’ two-state curve-crossing study is presented. The exact numerical results are compared with those obtained by applying various types of DWBA and the Landau-Zener approximation. It was found that a DWBA based on the uniform Airy functions correctly predicts the structure of the transition probability function (mainly the positions of the maxima and the minima) for all cases considered here. The Landau-Zener approximation was found to be equal to the various DWBA's for small coupling terms (except for low collision energies), but superior for large coupling terms.     

On long-time limit behavior of the solution of atom's master equation

We study long-time limit behavior of the solution of atom's master equation, for the first time we derive that the probability of the atom being in the α-th (α =j+1-j_z, j is the angular momentum quantum number, j_z is the z-component of angular momentum) state is {(1-K/G)/[1-(K/G)^2j+1]}(K/G)^α-1 as t→+∞, which coincides with the fact that when K/G > 1, the larger the α is, the larger probability of the atom being in the α-th state (the lower excited state). We also consider the case for some possible generalizations of the atomic master equation.     

On the Ladder Bethe-Salpeter Equation

The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass m interacting via an exchange of a scalar field (tieon) with mass . The BS equation is written in the form of an integral equation in the configuration Euclidean x-space with the kernel which for stable bound states M < 2m is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed.The analytical form of test functions for which the accuracy of calculations of bound-state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents.As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound states is demonstrated.     

Strong gravity and weak interactions

The strong gravity contribution to the nucleonic axial-vector form factor is evaluated in the nonrelativistic limit and in the approximation of exactSU ₃ symmetry. It is suggested also that the anomalous experimental results on the value of the axial coupling constant, in very light nuclei, may be explained as being an effect due to strong gravitational interactions.     

双折射晶体中旋光效应的耦合波理论

与传统的旋光效应理论不同，采用三阶赝张量κ⁽²⁾_jkl描述旋光现象，并将相关的电极化强度作微扰处理，直接从Maxwell方程组出发推导出了双折射晶体中自然旋光效应的耦合波方程组并得到解析解.该解析解包含了已有的旋光效应宏观理论结果，可方便地用于描述任意偏振态的单色光波在任意点群的双折射旋光晶体中沿任意方向的传播行为.最后，以石英晶体为例,通过对出射光波的偏振态分析，研究了波矢失配对旋光效应的影响. 关键词： 耦合波理论 旋光效应 非线性光学     

HF和DF分子双光子布居转移过程中的同位素效应

通过求解含时薛定谔方程,研究了XF(X=H,D)分子体系双光子共振条件下布居转移过程中的同位素效应.对于这两个分子体系,基电子态上的振动能级v=0和v=2被考虑成初始态和目标态.详细讨论了激光场峰值强度和脉冲持续时间对布居转移过程的影响.脉冲持续时间需要长于860 fs才能保证DF分子体系可以获得较为显著的布居转移几率(大于80%),而对于HF分子体系,该参数只需长于460 fs.与HF分子体系相比,中间态v=1和较高的v=3振动态会对DF分子体系的双光子共振布居转移过程产生更重要的影响.     

Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.     

Phases of atom-molecule vortex matter

We study ground state vortex configurations in a rotating atom-molecule Bose-Einstein condensate. It is found that the coherent coupling between the atomic and molecular condensates can render a pairing of atomic and molecular vortices into a composite structure that resembles a carbon dioxide molecule. Structural phase transitions of vortex lattices are also explored through different physical parameters including the rotational frequency of the system.     

Über die Durchführung einer Näherung der starken Kopplung beim Chew-Low-Formalismus

A strong-coupling approximation method for the Chew-Low meson-nucleon scattering formalism is developed, considering, for simplicity, the case of charged scalar mesons. As a starting point, the Low equation formulated for the case of strong coupling is stated. This formulation explicitly takes into account the formation of excited compound-nucleon states which arise in the case of strong coupling. The data concerning the zero-meson part and the compound-nucleon excitation energies, necessary to specify this Low equation, are introduced approcimatly by means of the field-splitting transformation developed in a previous paper. The one-meson approximation is constructed; this corresponds to a certain kind of many-meson approximation of the usual Low equation whose limit asg→∞ holds exactly. It is hoped that these considerations will serve to guide an analogous investigation using the pseudoscalar theory.     

Das Fluktuationsspektrum von Elektronen in einem stationären Nichtgleichgewichtszustand

The Boltzmann equation is used to calculate the time correlation function and the fluctuation spectrum for electrons obeying classical statistics. The stationary joint distribution for one electron to be initially ink ₀=k(0) and finally ink=k(t) is given by the product of the conditional probability and the stationary distribution. These quantities can be found from the Boltzmann equation if there exists, for any initial distribution, a unique solution which satisfies the Markov equation and tends to a stationary solution for large times under stationary conditions. It is proved that these conditions hold for linear collision operators and in the relaxation approximation. General operator expressions for the fluctuation spectrum and the differential conductivity in a stationary electric field are given, which can be evaluated within the usual approximation schemes known for the stationary, nonequilibrium solutions of the Boltzmann equation. In equilibrium they reproduce the classical fluctuation dissipation theorem. In a nonequilibrium state they define a noise temperature depending on the field. In the relaxation approximation and for polynomial band structure the exact solution can be found. For parabolic and biparabolic spherical bands the result is discussed explicitly.