F. Masnou-Seeuws

Editorial Quo vadis, cold molecules?

We give a snapshot of the rapidly developing field of ultracold polar molecules abd walk the reader through the papers appearing in this topical issue.

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.

Formation of ultracold molecules (T≤200 μK) via photoassociation in a gas of laser-cooled atoms

Publisher Summary This chapter discusses the formation of ultracold molecules—that is, at temperatures well below 1 mK, the photoassociation scheme in a sample of laser-cooled ultracold atoms is currently the best route, yielding a few millions of molecules at a translational temperature in the microkelvin range, which were successfully trapped. In photoassociation experiments, a pair of ultracold ground-state atoms absorbs a photon slightly (∼ a fraction of cm -1 to 1000 cm -1 ) red-detuned relative to the resonance line. Because of the ultracold conditions, the width of the statistical distribution of the kinetic energy E c is markedly reduced. For a gas of atoms at thermal equilibrium with a temperature T, this width is of the order of k B T. It corresponds to ∼200 cm -1 at room temperature (300 K), yielding the well-known appearance of diffuse spectra, but only to ∼ 2 MHz or 7 × 10 –5 cm -1 , at 100 μK yielding well-resolved spectral lines, similar to bound–bound transitions. Besides, only a few partial waves have to be considered in the description of the initial continuum state, so the rotational structure is most often limited to J

Stabilization of ultracold molecules using optimal control theory

In recent experiments on ultracold matter, molecules have been produced from ultracold atoms by photoassociation, Feshbach resonances, and three-body recombination. The created molecules are translationally cold, but vibrationally highly excited. This will eventually lead them to be lost from the trap due to collisions. We propose shaped laser pulses to transfer these highly excited molecules to their ground vibrational level. Optimal control theory is employed to find the light field that will carry out this task with minimum intensity. We present results for the sodium dimer. The final target can be reached to within 99% provided the initial guess field is physically motivated. We find that the optimal fields contain the transition frequencies required by a good Franck-Condon pumping scheme. The analysis identifies the ranges of intensity and pulse duration which are able to achieve this task before any other competing processes take place. Such a scheme could produce stable ultracold molecular samples or even stable molecular Bose-Einstein condensates.

Making ultracold molecules in a two-color pump-dump photoassociation scheme using chirped pulses

This theoretical paper investigates the formation of ground state molecules from ultracold cesium atoms in a two-color scheme. Following previous work on photoassociation with chirped picosecond pulses [Luc-Koenig et al., Phys. Rev. A, 70, 033414 (2004)], we investigate stabilization by a second (dump) pulse. By appropriately choosing the dump pulse parameters and time delay with respect to the photoassociation pulse, we show that a large number of deeply bound molecules are created in the ground triplet state. We discuss (i) broad-bandwidth dump pulses which maximize the probability to form molecules while creating a broad vibrational distribution as well as (ii) narrow-bandwidth pulses populating a single vibrational ground state level, bound by 113 cm{sup -1}. The use of chirped pulses makes the two-color scheme robust, simple, and efficient.

Associative Ionization: Experiments, Potentials, And Dynamics

Publisher Summary This chapter presents an account of research into fundamental questions, spanning roughly the past decade, and provides continuity from earlier reviews of collisional ionization. The chapter discusses progress along three principal lines: (1) experimental investigation of the fundamental questions, (2) the calculation of molecular potential curves required for the interpretation of experiments, and (3) a review of theoretical approaches developed to grapple with the physics of electron bound-free coupling in heavy particle associative and dissociative processes. The chapter explains the problem of molecular potentials and dynamics of associative ionization. The treatment of associative ionization necessitates knowledge of accurate potential curves and dynamical couplings characterizing the quasi-molecule formed during the collision. Dynamics of associative ionization reviews and classifies the theoretical approaches. It assumes that the basic molecular data, the potential curves and couplings responsible for the ionization process are either known from first principles or have been parametrically fit to experimental results.

Photoassociation in a gas of cold alkali atoms: I. Perturbative quantum approach

We develop a quantum-mechanical approach to the photoassociation phenomenon in a sample of cold atoms initially at thermal equilibrium with temperature T. We calculate the rate of formation of molecules in the weak field regime using a perturbative approach. Analytical expressions are obtained for the overlap between the initial and final molecular wavefunctions, and are shown to agree with numerical calculations. The photoassociation rate is found to decrease with increasing atomic mass m, from Li to Cs. Also considered is the heating of the atomic sample through spontaneous photodissociation.

Short-pulse photoassociation in rubidium below the D1 line

Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the 5S +5 P1/2 asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range 1 / R 3 potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the 0 u states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.

Optimizing the photoassociation of cold atoms by use of chirped laser pulses

Abstract.Photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a non-perturbative treatment by following the wavepacket dynamics on the ground and excited surfaces. The initial state is described by a Boltzmann distribution of stationary continuum states. The chosen example is photoassociation of cesium atoms at temperature

Simple determination of Na2 scattering lengths using observed bound levels at the ground state asymptote

T = 54 \mu