Application of B-splines to determining eigen-spectrum of Feshbach molecules

The B-spline basis set method is applied to determining the rovibrational eigen-spectrum of diatomic molecules. A particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the commonly-used discrete variable representation (DVR) approach. Several model cases, including the Morse potential and realistic potentials with 1/R^3 and 1/R^6 long-range dependence of the internuclear separation are studied. We find that the B-spline method is superior to the DVR approach and it is robust enough to properly describe the Feshbach molecules. The developed numerical method is applied to studying the universal relation of the energy of the last bound state to the scattering length. We numerically illustrate the validity of the quantum-defect-theoretic formulation of such a relation for a 1/R^6 potential.Comment: submitted to can j phys: Walter Johnson symposu

Potential energy and dipole moment surfaces of H3- molecule

A new potential energy surface for the electronic ground state of the simplest triatomic anion H3- is determined for a large number of geometries. Its accuracy is improved at short and large distances compared to previous studies. The permanent dipole moment surface of the state is also computed for the first time. Nine vibrational levels of H3- and fourteen levels of D3- are obtained, bound by at most ~70 cm^{-1} and ~ 126 cm^{-1} respectively. These results should guide the spectroscopic search of the H3- ion in cold gases (below 100K) of molecular hydrogen in the presence of H3- ions

Uncertainty Estimates for Theoretical Atomic and Molecular Data

Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We concentrate on model uncertainties due to approximations to the fundamental many-body quantum mechanical equations and we aim to provide guidelines to estimate uncertainties as a routine part of computations of data for structure and scattering.Comment: 65 pages, 18 Figures, 3 Tables. J. Phys. D: Appl. Phys. Final accepted versio

Enhancement of the formation of ultracold 85^{85}Rb2_2 molecules due to resonant coupling

We have studied the effect of resonant electronic state coupling on the formation of ultracold ground-state $^{85}$Rb$_2$. Ultracold Rb$_2$ molecules are formed by photoassociation (PA) to a coupled pair of $0_u^+$ states, $0_u^+(P_{1/2})$ and $0_u^+(P_{3/2})$, in the region below the $5S+5P_{1/2}$ limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X ^1\Sigma_g^+$. The population distribution of these $X$ state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2 ^1\Sigma_u^+$ state. We find that the populations of vibrational levels $v''$=112$-$116 are far larger than can be accounted for by the Franck-Condon factors for $0_u^+(P_{1/2}) \to X ^1\Sigma_g^+$ transitions with the $0_u^+(P_{1/2})$ state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of $0_u^+$ state vibrational levels. Both of these effects are explained by a new calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two $0_u^+$ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.Comment: 6 pages, 5 figures; corrected author lis

Field-linked States of Ultracold Polar Molecules

We explore the character of a novel set of ``field-linked'' states that were predicted in [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field's strength. We clarify the nature of these quasi-bound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as functions of both the intermolecular distance and the angle that the intermolecular axis makes with the electric field. Within an adiabatic approximation we solve the 2-D Schrodinger equation to find bound states, whose energies correlate well with resonance features found in fully-converged multichannel scattering calculations

Formation of ultracold RbCs molecules by photoassociation

The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the ^85Rb(5S_1/2)+^133Cs(6P_3/2) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0^+ or the 4th 0^- electronic states correlated to the Rb(5P_1/2,3/2)+Cs(6S_1/2) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state

Correlation diagrams in collisions of three identical particles

We discuss collision of three identical particles and derive scattering selection rules from initial to final states of the particles. We use either laboratory-frame, hyperspherical, or Jacobian coordinates depending on which one is best suited to describe three different configurations of the particles: (1) three free particles, (2) a quasi-bound trimer, or (3) a dimer and a free particle. We summarize quantum numbers conserved during the collision as well as quantum numbers that are appropriate for a given configuration but may change during the scattering process. The total symmetry of the system depends on these quantum numbers. Based on the selection rules, we construct correlation diagrams between different configurations before and after a collision. In particular, we describe a possible recombination of the system into one free particle and a dimer, which can be used, for example, to identify possible decay products of quasi-stationary three-body statesComment: 14 pages,4 figure

Formation of ultracold dipolar molecules in the lowest vibrational levels by photoassociation

We recently reported the formation of ultracold LiCs molecules in the rovibrational ground state X1Sigma+,v''=0,J''=0 [J. Deiglmayr et al., PRL 101, 133004 (2008)]. Here we discuss details of the experimental setup and present a thorough analysis of the photoassociation step including the photoassociation line shape. We predict the distribution of produced ground state molecules using accurate potential nergy curves combined with an ab-initio dipole transition moment and compare this prediction with experimental ionization spectra. Additionally we improve the value of the dissociation energy for the X1Sigma+ state by high resolution spectroscopy of the vibrational ground state.Comment: Submitted to Faraday Discussions 142: Cold and Ultracold Molecules 18 pages, 8 figure

Optimal trapping wavelengths of Cs2_2 molecules in an optical lattice

The present paper aims at finding optimal parameters for trapping of Cs$_2$ molecules in optical lattices, with the perspective of creating a quantum degenerate gas of ground-state molecules. We have calculated dynamic polarizabilities of Cs$_2$ molecules subject to an oscillating electric field, using accurate potential curves and electronic transition dipole moments. We show that for some particular wavelengths of the optical lattice, called "magic wavelengths", the polarizability of the ground-state molecules is equal to the one of a Feshbach molecule. As the creation of the sample of ground-state molecules relies on an adiabatic population transfer from weakly-bound molecules created on a Feshbach resonance, such a coincidence ensures that both the initial and final states are favorably trapped by the lattice light, allowing optimized transfer in agreement with the experimental observation