Abstract. We give a snapshot of the rapidly developing field of ultracold polar molecules and walk the reader through the papers appearing in this Topical Issue.PACS. 33. Molecular properties and interactions with photons -33.80.Ps Optical cooling of molecules; trapping -34. Atomic and molecular collision processes and interactions -39. Instrumentation and techniques for atomic and molecular physics

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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 Ϫn behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a 0 using a minimal number of grid points. Calculations with two electronic states, A 1 ⌺ u ϩ and b 3 ⌸ u states, both correlated to the Rb(5s)ϩRb(5 p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb 2 (0 u ϩ ͒ spectrum, manifested under the 5s, 5p 2 P 1/2 dissociation limit by an oscillatory behavior of the rotational constants.

Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two-center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm−1, and ΔDe=57 cm−1.

This theoretical paper presents numerical calculations for photoassociation of ultracold cesium atoms with a chirped laser pulse and detailed analysis of the results. In contrast with earlier work, the initial state is represented by a stationary continuum wavefunction. In the chosen example, it is shown that an important population transfer is achieved to ≈ 15 vibrational levels in the vicinity of the v=98 bound level in the external well of the 0 − g (6s + 6p 3/2 ) potential. Such levels lie in the energy range swept by the instantaneous frequency of the pulse, thus defining a "photoassociation window". Levels outside this window may be significantly excited during the pulse, but no population remains there after the pulse. Finally, the population transfer to the last vibrational levels of the ground a 3 Σ + u (6s + 6s) is significant, making stable molecules. The results are interpreted in the framework of a two state model as an adiabatic inversion mechanism, efficient only within the photoassociation window. The large value found for the photoassociation rate suggests promising applications. The present chirp has been designed in view of creating a vibrational wavepacket in the excited state which is focussing at the barrier of the double well potential.

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.

We demonstrate the existence of a new mechanism for the formation of ultracold molecules via photoassociation of cold cesium atoms. The experimental results, interpreted with numerical calculations, suggest that a resonant coupling between vibrational levels of the 0+u (6s+6p1/2) and (6s+6p3/2) states enables formation of ultracold molecules in vibrational levels of the ground state well below the 6s+6s dissociation limit. Such a scheme should be observable with many other electronic states and atomic species.

Abstract. Photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a nonperturbative treatment by following the wavepackets dynamics on the ground and excited surfaces. The initial state is described by a Boltzmann distribution of continuum scattering states. The chosen example is photoassociation of cesium atoms at temperature T=54 µK from the a 3 Σ + u (6s, 6s) continuum to bound levels in the external well of the 0 − g (6s + 6p 3/2 ) potential. We study how the modification of the pulse characteristics (carrier frequency, duration, linear chirp rate and intensity) can enhance the number of photoassociated molecules and suggest ways of optimizing the production of stable molecules.