Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included

We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct a highly accurate and simple analytic approximation describing the time dynamics of the coupled atom-molecule system. We show that the approximation describing time evolution of the molecular state probability can be written as a sum of two distinct terms; the first one, being a solution to a limit first-order nonlinear equation, effectively describes the process of the molecule formation while the second one, being a scaled solution to the linear Landau-Zener problem (but now with negative effective Landau-Zener parameter as long as the strong coupling regime is considered), corresponds to the remaining oscillations which come up when the process of molecule formation is over.     

Index of refraction for cold lithium- and diatomic sodium waves traveling through cold noble gases

In the present paper we propose to measure the index of refraction for diatomic sodium molecules traveling through a cold helium gas. Theoretical calculations of the index of refraction for this system are presented as a function of the molecule velocity and atom gas temperature. Whereas previous theoretical efforts to compute the refractive index have been concerned with atomic systems and atomic matter waves, we extend the investigation to diatomic molecules in the present work. To enable such calculations the potential energy surface for the atom-molecule interaction is calculated ab initio, along with the long range dispersion coefficients for the atom-molecule system. The full close-coupled equations, describing the atom-molecule collisions, are solved numerically to work out the influence of the collisions on the matter waves. We investigate the sensitivity of the results upon changes and inaccuracies in the potential energy surface. Several molecular rotational levels are included in the present study, and the index of refraction is found to depend on the rotational state. In addition, the index of refraction for atomic lithium matter waves traveling through the cold noble gases helium and argon are computed, motivated by a recent experiment with atomic lithium matter waves. Different resonances (glory- and scattering resonances) are identified from the results. Such resonances offer an important opportunity for the comparison of experiment and theory.     

The temperature dependence of rotational tunnelling

A novel approach to the temperature dependence of rotational tunnelling is presented. By means of a projection operator technique a generalized Master equation is derived, where the effects of coupling to lattice vibrations are embraced in a memory function non-local in time. After an expansion in a power series in the coupling Hamiltonian, the Master equation is used for the calculation of two-times correlation functions of scattering operators, the Fourier transforms of which give the scattering function. The theory allows for all features of the spectrum obtained by neutron scattering methods, in particular for those of the central peak and the librational excitations. Furthermore, it is not confined to the low temperature regime, but rather covers the whole range of temperatures of experimental interest.     

Atom-molecule dark state: the exact quantum solution

Developments in ultracold atomic physics have enabled the generation of an atom-molecule dark state in dilute quantum gases. Previous studies of this dark state were all carried out in the mean-field regime. Here we present an exact quantum many-body wave function for the atom-molecule dark state for an ideal system (in the absence of losses and two-body collisions). Using this exact quantum wave function, we are able to validate the mean-field solution to be a good approximation when the particle number N is large. For small N, unique quantum features will become important.     

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.     

Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that for sufficiently narrow resonances three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.     

Confinement effects on the stimulated dissociation of molecular Bose-Einstein condensates

We show that a molecular Bose-Einstein condensate in a trap is stabilized against stimulated dissociation if the trap size is smaller than the resonance healing length (Planck's 2/2mgsqrt[n]);1/2. The condensate shape determines the critical atom-molecule coupling frequency. We discuss an experiment for triggering dissociation by a sudden change of coupling or trap parameters. This effect demonstrates one of the unique collective features of "superchemistry" in that the yield of a chemical reaction depends critically on the size and shape of the reaction vessel.     

Effective theory of Feshbach resonances and many-body properties of Fermi gases

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that, for resonances in the fermionic systems 6Li and 40K that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.     

Phase control of stimulated Raman atom-molecule conversion in a Bose-Einstein condensate

The possibility of phase control over coupling of Bose-condensed atoms into molecules is justified. It is shown that the time evolution of stimulated Raman atom-molecule conversion is determined significantly by the initial densities of particles and by the initial phase difference between material and electromagnetic waves.     

Adiabatic Berry phase in an atom-molecule conversion system

We investigate the Berry phase of adiabatic quantum evolution in the atom-molecule conversion system that is governed by a nonlinear Schrödinger equation. We find that the Berry phase consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule coupling. The total geometric phase can be still viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole. We also derive the classical Hannay angle of a geometric nature associated with the adiabatic evolution. It exactly equals minus Berry phase, indicating a novel connection between Berry phase and Hannay angle in contrast to the usual derivative form.     

Photoassociation of Atomic BEC within Mean-Field Approximation： Exact Solutions

We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose- Einstein condensate, by linearizing the bilinear atom-molecule coupling, which allows us to conveniently probe the quantum dynamics and statistics of the system. By preparing different initial states of the atomic condensate, we can observe very different quantum statistical properties of the system by exactly calculating the quadrature- squeezed and mode-correlated functions.     

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.     

玻璃陶瓷PWG中的喇曼耦合系数对Raman散射的影响

应用修正的无序诱导散理论模型讨论了玻璃陶瓷（PbF2 WO3 GeO(PWG)中的喇曼耦合系数对Raman散射过程的影响。虽然普遍认为喇曼耦合系数是随频率而变化,但实际上它是空间相关函数的Furier分量,因此,严格地讲喇曼耦合系数是随动量（波矢q)而变化的,因而,玻璃陶瓷中的喇曼耦合系数描述了在Raman散射过程中发生在玻璃陶瓷中的动量交换相互作用。对于PWG中热活性拓动态的光谱分布曲线分析说明：指数衰减关系的卷积定性地表示了这个耦合系数。证明了简谐势与耦合系数有关的空间相关函数之和给出了非常类似于双阱势的畸变谐函数,根据弛豫模行为讨论了结合势的相关性。     

Dissociation and decay of ultracold sodium molecules

The dissociation of ultracold molecules was studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energies directly yielded the strength of the atom-molecule coupling. They showed nonlinear dependence on the ramp speed. This was explained by a Wigner threshold law which predicts that the decay rate of the molecules above threshold increases with the density of states. In addition, inelastic molecule-molecule and molecule-atom collisions were characterized.     

Electron and Phonon in Neutron Scattering of Semiconductor Crystals

An interaction of electron with harmonic, localized and anharmonic fields has been taken to develop the theory of neutron scattering. The Fourier transformed electron Green’s function is evaluated by Zubarev equation of motion technique of quantum dynamics and Dyson equation approach. The expression of Debye-Waller factor (DWF) has been obtained from electron phonon linewidth. The study of its (DWF) effect on differential scattering cross-section through temperature, electron phonon coupling constant and excitations has been investigated in this approach.     

A new approach to a practical subwavelength resolving microscope

Superresolution depends on near-field capture and transfer of high spatial frequencies from the scattering object. These evanescent waves are transferred to a near-field image domain using a negative index material. Measuring images with subwavelength scale resolution in the near field by scanning is not practical and ignores inevitable object–lens–image coupling phenomena as well as the need to employ inverse scattering algorithms. An alternative approach based on compressive sampling permits the use of a single fixed detector. Traditionally, in such a system, an image-bearing wavefront is projected onto a series of patterns (= basis functions) and the transmitted light integrated by a lens onto a single-point detector. Image reconstruction is possible by weighting each basis function with its measured coefficient and summing, including basis functions representing evanescent waves. We employ a single fixed detector in the back focal plane of a negative index concave lens and basis functions realized by structured illumination from combinations of a set of discrete sources. We have investigated this as an approach to recover subwavelength scale details about a scattering object and report our results.     

Spectrum and dynamics of the BCS-BEC crossover from a few-body perspective

The spectrum of two spin-up and two spin-down fermions in a trap is calculated using a correlated Gaussian basis throughout the range of the BCS-BEC crossover. These accurate calculations provide a few-body solution to the crossover problem. This solution is used to study the time evolution of the system as the scattering length is changed, mimicking experiments with Fermi gases near Fano-Feshbach resonances. The structure of avoiding crossings in the spectrum allow us to understand the dynamics of the system as a sequence of Landau-Zener transitions. Finally, we propose a ramping scheme to study atom-molecule coherence.     

Effects of collisions on linear and non-linear spectroscopic line shapes

A fundamental physical problem is the determination of atom-atom, atom-molecule and molecule-molecule differential and total scattering cross sections. In this work, a technique for studying atomic and molecular collisions using spectroscopic line shape analysis is discussed. Collisions occuring within an atomic or molecular sample influence the sample's absorptive or emissive properties. Consequently the line shapes associated with the linear or non-linear absorption of external fields by an atomic system reflect the collisional processes occuring in the gas. Explicit line shape expressions are derived characterizing linear or saturated absorption by two- or three-level “active” atoms which are undergoing collisions with perturber atoms. The line shapes may be broadened, shifted, narrowed, or distorted as a result of collisions which may be “phase-interrupting” or “velocity-changing” in nature. Systematic line shape studies can be used to obtain information on both the differential and total active atom-perturber scattering cross sections.