Long-range Molecules Research Articles

A pump–probe study of the photoassociation of cold rubidium molecules

The dynamics of the excited state during the photoassociation of cold molecules from cold rubidium atoms is studied in a series of pump-probe experiments. Dipole transitions similar to those of the atoms are observed in the molecular signal. While such behaviour is characteristic of the long-range molecules, the photoassociation of bound molecules is confirmed in additional experiments. The pump-probe signal observed on a 250 ps time scale did not, however, reveal wavepacket oscillations predicted by theory. This result is discussed using numerical simulations of photoassociation and a modification to the current experiments that could lead to the detection of wavepacket dynamics is suggested.

Maternal communication with gametes and embryos

Mechanisms for gametes and embryos to interact with their maternal environment are crucial in achieving reproductive success, both in livestock and the human. Long-range (hormones) and short-range signalling molecules play important roles in mediating cell–cell maternal interactions/communications with gametes and embryos. Slight malfunctions or disturbances of the environment that host this interaction can retard embryonic development. This may lead to creation of a memory for the embryo leading to offspring prone to degenerative diseases in adulthood. Despite an overwhelming amount of research and the literature, not all signalling molecules involved and their relationship with each other are known. Progress in the application of high-throughput genomic and proteomic analytical tools, such as microarrays and quantitative proteomic technologies has had a positive impact on our understanding of various aspects of maternal communication with gametes and embryos. Recent advances point to the presence of a local mechanism in the female reproductive tract capable of recognising the arrival of gametes and embryos and modulating the tract's environment accordingly for the next stage. Further investigations are underway to characterise the details of this system. It is important to consider spatial or temporal components of maternal communication with gametes and embryos that may confer consequences for developmental potential. Finally, it seems that the application of a systems biology approach for creation of an interactome map of maternal communication with gametes and embryos is essential and provides an excellent opportunity for an inter-disciplinary collaboration with engineers and mathematical modellers.

Hedgehog Nanopackages Ready for Dispatch

Hedgehog proteins are intercellular long-range signaling molecules that spread within tissues and activate gene expression during development. Vyas et al. (2008) propose that Hedgehog forms nanometer-sized oligomers that localize in proteoglycan-rich clusters at the surface of cells expressing Hedgehog. This nanoscale organization and enrichment in clusters ensures that Hedgehog is able to spread and activate signaling over many cell diameters.

Hyperfine-Structure-Induced Purely Long-Range Molecules

We have experimentally observed and theoretically identified a novel class of purely long-range molecules. This novel purely long-range state is formed due to a very weak hyperfine interaction that is usually treated only as a small perturbation in molecular spectra. Photoassociation spectroscopy of ultracold ytterbium (171Yb) atoms with the 1S0-3P1 intercombination transition presents clear identification of molecular states and the shallowest molecular potential depth of about 750 MHz among the purely long-range molecules ever observed.

Publisher's Note: Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering [Rev. Mod. Phys.78, 483 (2006)

Publisher's Note: Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering [Rev. Mod. Phys.78, 483 (2006)

Rotational structures of long-range diatomic molecules

We present a systematic understanding of the rotational structure of a long-range (vibrationally highly-excited) diatomic molecule. For example, we show that depending on a quantum defect, the least-bound vibrational state of a diatomic molecule with $-C_n/r^n$ ($n>2$) asymptotic interaction can have only 1, 2, and up to a maximum of $n-2$ rotational states. A classification scheme of diatomic molecules is proposed, in which each class has a distinctive rotational structure and corresponds to different atom-atom scattering properties above the dissociation limit.

Photoassociation spectroscopy of ultra-cold long-range molecules

Spectroscopic study of so-called long-range molecules, with average interatomic distances much larger than usual for chemical bonds, is conveniently performed by photoassociation (PA) of ultracold atoms. We present here a review of our results obtained by one and two-photon PA spectroscopy of the Cs 2 molecule, using as intermediate the 0 g − and 1 u potentials correlated to the (6 s+6 p 3/2) asymptote. These results have been interpreted using an asymptotic theoretical approach, which was specifically build for such long-range molecules. To cite this article: N. Vanhaecke et al., C. R. Physique 5 (2004).

Mapped grid methods for long-range molecules and cold collisions.

The paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels ("ghosts") then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate "ghost" solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian J(x) of the R-->x coordinate transformation.

Formation of ultracold molecules by photoassociation: theoretical developments

In recent years several groups of researchers have succeeded in making samples of cold molecules, at temperatures below 1 K, and of ultracold molecules, at temperatures below 1 mK. We concentrate on the formation of Cs2 dimers. Starting with laser-cooled atoms, photoassociation forms molecules in an excited electronic state. Various mechanisms are presented for stabilizing these molecules by spontaneous emission into a bound level of the ground electronic state. The design of new formation schemes requires precise knowledge of molecular potential curves that is well beyond the accuracy of ab initio calculations. We show that analytical long-range potentials can be fitted on photoassociation spectra and yield, through the determination of the C3 long-range coefficient, a value of the radiative lifetime of the 6P3/2 cesium level with an unprecedented accuracy. For short-range potentials it is possible to avoid explicit calculations by using asymptotic methods that generalize to long-range molecules the quantum-defect concepts developed for Rydberg atoms. Considering two coupled channels, we show how generalized Lu–Fano plots can extract precise information from experimental spectra.

Lu-Fano plot for interpretation of the photoassociation spectra

Recently, the method of Lu-Fano plots was extended to potentials with general R - n asymptotic behavior. The aim of this paper is to discuss the efficiency of this method for the interpretation of experimental vibrationalspectra of long-range diatomic molecules when two channels are coupled. A Lu-Fano analysis is implemented on experimental data for the Cs 2 0 + u (6S+6P 1 / 2 , 3 / 2 ) photoassociation spectra below the 6S+P 1 / 2 and 6S+P 3 / 2 dissociation limits. The parameters are fitted on level energies and predissociation widths, giving information about the asymptotic coefficients C 3 for both channels and about a coupling parameter which determines the variation of predissociation widths as a function of detuning. This parameter can be extrapolated above the 6S+P 3 / 2 threshold to yield the fine-structure transition cross section between the two channels. The probability for such a transition in a model where hyperfine structure effects are neglected is found to be 0.54.

Cesium satellite band at 875.2 nm stemming from the Cs20g+(6 p2 P1/2+6 s2 S1/2) state

We measured a very distinct satellite band at 875.2 nm between two resonance lines of cesium. Spectral simulation using Spies and Meyer [#!ref1!#] ab initio potential curves and an appropriate transition dipole moment function was compared with experimental profile. Implications of the investigated satellite band at 875.2 nm in the field of ultracold cesium atom collisions are discussed with a special emphasize to new possibilities of the photoassociation of two ground state atoms leading to the formation of ultracold intermediate long-range molecules.

Optimal control of photoassociation of cold atoms and photodissociation of long-range molecules: Characteristic times for wave-packet propagation

This paper aims at studying the time-dependent effects involved in the photoassociation reaction for a sample of cold alkali-metal atoms, within a two-channel model where the vibrational motion in the excited state is coupled by laser light to the continuum state describing two colliding atoms in the lowest triplet electronic state $(a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}).$ Both photodissociation and photoassociation processes are considered at a time scale shorter than the radiative lifetime, so that spontaneous emission does not have to be considered. The characteristic times are then the vibrational period in the excited state, which for alkali-metal dimers can be estimated of the order of a few hundreds of picoseconds, and the Rabi period, depending upon the laser intensity. Numerical calculations using wave-packet propagation are performed for the coupling of the vibrational motion in the ${\mathrm{Cs}}_{2}{1}_{g}{(6s+6p}_{3/2})$ and ${a}^{3}{\ensuremath{\Sigma}}_{u}^{+}(6s+6s)$ channels by a cw laser slightly red detuned relative to the ${\mathrm{D}}_{2}$ resonance line. The results show Rabi oscillations in the populations of the two channels during time intervals when the vibrational motion is stopped at the outer turning point. At intensities of $\ensuremath{\approx}250\mathrm{kW}{\mathrm{cm}}^{\ensuremath{-}2},$ a new characteristic time appears, a factor of 2 larger than the classical vibrational period, which corresponds to vibrational motion in the upper adiabatic potential created by the coupling. Such an effect modifies the scattering length for collisions in the lower state, and it clearly opens a possibility of control by tuning the laser intensity.

High-precision evaluation of the vibrational spectra of long-range molecules

Vibrational spectra of long-range molecules are determined accurately and to arbitrary accuracy with the Canonical Function Method. The energy levels of the 0–g and 1u electronic states of the 23Na2 molecule are determined from the ground state up to the continuum limit. The method is validated by comparison with previous results obtained for different potentials adapted to long-range molecules. PACS Nos.: 03.65-w, 31.15Gy, 33.20.Tp

High-precision evaluation of the vibrational spectra of long-range molecules

Vibrational spectra of long-range molecules are determined accurately and to arbitrary accuracy with the Canonical Function Method. The energy levels of the $0^-_g$ and $1_u$ electronic states of the $^{23}{\rm Na}_2$ molecule are determined from the Ground state up to the continuum limit. The method is validated by comparison with previous results obtained by Stwalley et al. using the same potential and Trost et al. whose work is based on the Lennard-Jones potential adapted to long-range molecules.

Mapped Fourier methods for long-range molecules: Application to perturbations in the Rb2(0u+) photoassociation spectrum

Numerical calculations of vibrational levels of alkali dimers close to the dissociation limit are developed in the framework of a Fourier Grid Hamiltonian method. The aim is to interpret photoassociation experiments in cold atom samples. In order to avoid the implementation of very large grids we propose a mapping procedure adapted to the asymptotic R−n behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a0 using a minimal number of grid points. Calculations with two electronic states, A 1Σu+ and b 3Πu states, both correlated to the Rb(5s)+Rb(5p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb2(0u+) spectrum, manifested under the 5s, 5p 2P1/2 dissociation limit by an oscillatory behavior of the rotational constants.

Modes of cell:cell communication in the immune system

Different cell types in the immune system appear to mediate their effects by markedly different means. B lymphocytes couple information for specificity with information for function in a single long-range molecule, antibody. Major histocompatibility complex (MHC)-restricted T cells, which we have analyzed in detail, appear to recognize antigen only on the surface of cells bearing the appropriate MHC gene product. This interaction provokes the T cell to release short-range, non-antigen-specific mediators (lymphokines) that preferentially act on the target cell bearing the antigen and stimulating the T cell. Regulatory T cells appear to make antigen-specific long-range molecules that, like antibody, combine specificity with information for function. However, unlike antibody molecules, these regulatory T cell products display recognition for particular target cells in the form of genetic restrictions. These behaviors are compared to strategies of cell:cell communication in the nervous system.

Long-range molecules

Abstract Because of the long-range behaviour of the internuclear potential representing the interaction between two atoms (e.g. —C 6 R −6), there are usually a certain number of closely spaced vibrational-rotational levels that approach dissociation. The properties of molecules in these highest levels are quite unusual (although often simply related to the long-range forces), and we shall refer to such molecules by a special classification: ‘long-range molecules’. Restricting our attention to diatomic long-range molecules, we first review the general relationship between the potential energy curve and vibrational levels. The long-range portion of potential energy curves is examined in detail and the simple properties of vibrational levels sensitive to these long-range potentials discussed. Finally transitions (radiative, nonradiative, and collision-induced) are briefly described.