Table of contents

The present special issue intends to provide an instantaneous picture of the research on cold molecules in 2006, through a collection of 32 experimental and theoretical papers written by groups with long experience and by new ones in the field. It focuses on the numerous recipes which are now available, or proposed, for creating cold molecules of various species and in various environments. Several papers illustrate the amazingly detailed knowledge which can be extracted from their study, opening the way to the ultimate control of elementary chemical processes by mastering both the preparation of the initial state and the reaction path. In this introductory review, we will review the main stages of the developments of research on cold molecules, as reflected by the accompanying series of papers.

New photoassociation data on the 0_u⁺ levels of Rb₂ below the 5S+5P_1/2 limit are combined with older data (Cline et al 1994 Phys. Rev. Lett.73 632) in a fit to potentials and spin–orbit functions. The P_1/2 data exhibit oscillations in the B(v) values due to coupling between the two 0_u⁺ series, as modelled accurately by a coupled potentials approach. The fitted value for the C₃ dispersion parameter from the combined data agrees well with the value derived from the pure long-range 0_g⁻ state.

We study the role of Penning ionization on the photoassociation spectra of He(2³S₁)–He(2³S₁). The experimental set-up is discussed and experimental results for different intensities of the probe laser are shown. For modelling the experimental results we consider coupled-channel calculations of the crossing of the ground state with the excited state at the Condon point. The coupled-channel calculations are first applied to model systems, where we consider two coupled channels without ionization, two coupled channels with ionization, and three coupled channels, for which only one of the excited states is ionizing. Finally, coupled-channel calculations are applied to photoassociation of He(2³S₁)–He(2³S₁) and good agreement is obtained between the model and the experimental results.

We have studied resonance-enhanced two-photon ionization of ultracold ³⁹K⁸⁵Rb molecules in highly excited long-range vibrational levels of the X ¹Σ⁺ and a ³Σ⁺ states. These molecules are formed by photoassociation (PA) of ultracold ³⁹K and ⁸⁵Rb atoms, followed by spontaneous emission to the X ¹Σ⁺ and a ³Σ⁺ states. In the range 15 500–17 200 cm⁻¹, we observe many intermediate and long-range levels of the previously unobserved 4 ³Σ⁺ and 4 ¹Σ⁺ states and evidence for the onset of the previously unobserved 3 ³Π state. The observed vibrational spectra of these states are in very good agreement with calculated vibrational levels based on the ab initio potentials of Rousseau, Allouche and Aubert-Frécon. Such experiments illustrate some of the unique advantages of using PA-produced ultracold molecules for investigation of long-range vibrational levels and long-range forces, and for unravelling dense spectra because only a few rotational levels are populated.

We form ultracold ground-state Rb₂ molecules by photoassociating pairs of atoms in a magneto-optical trap into the 0_u⁺ state, which decays radiatively into high vibrational levels of the X¹Σ_g⁺ state. Sensitive and vibrationally state-selective detection is achieved by means of resonantly-enhanced two-photon ionization with a pulsed laser. Frequency scans of the detection laser reveal a long vibrational progression to a previously unobserved electronic excited state, which we identify as the 2¹Σ_u⁺ state. Most of its vibrational spectrum is in excellent agreement with predictions based on ab initio potentials, although the lowest vibrational levels exhibit strong perturbative mixing with the triplet 2³Π_u state. The detection method reported here, with minor variations, should be effective for the entire potential well of the X state. In this work no transitions are observed from vibrational levels above v = 118, but this turns out to be a limitation not of the detection method but rather of the photoassociative formation scheme, due to re-excitation of the highest-v levels by the same photoassociation laser that produces them.

We investigated heteronuclear inelastic cold collisions in a mixed-species Li–Na magneto-optical trap, where the Li trap loss from collisions with Na was measured. Experimental results for the rate coefficient β^Na_Li for the isotopes ⁶Li as well as ⁷Li as a function of the Li-MOT laser intensity are presented. Furthermore, we discuss some unique characteristics of cold collisions of Na and Li which arise from (1) the very small spin–orbit splitting of Li, (2) the very small C₆ coefficients of the Na(3 ²S) + Li(2 ²P) asymptotes and (3) the very small and inverted hyperfine structure of Li.

We present an exhaustive analysis of the light-induced frequency shifts of the photoassociation lines of ultracold metastable ⁴He* atoms in a magnetic trap. The measurements of the shifts of several vibrational levels bound in the purely long-range J = 1, 0_u⁺ potential linked to the 2³S₁–2³P₀ asymptote were reported in a previous paper (Kim et al 2005 Europhys. Lett.72 548), and are analysed here. The simplicity of this system makes it very appropriate for a detailed study. Indeed, the purely long-range character of the excited potential allows one to calculate exact excited molecular wavefunctions and to use asymptotic expansions at large internuclear distances of the ground-state wavefunctions appearing in Franck–Condon-type integrals. Moreover, the number of collisional channels to be considered is strongly reduced by the absence of hyperfine structure for ⁴He* and the use of polarized ultracold atoms and polarized light. This allows us to derive semi-analytical expressions for the shifts showing explicitly their linear dependences on the s-wave scattering length a of spin polarized metastable ⁴He* atoms. This explains how it is possible to derive the measurement of a from these shifts.

In this work, we investigate the possibility of creating cold Fr₂, RbFr and CsFr molecules through the photoassociation of cold atoms. Potential curves, permanent and transition dipole moments for the francium dimer and for the RbFr and RbCs molecules are determined for the first time. The francium atom is modelled as one valence electron moving in the field of the Fr⁺ core, which is described by a new pseudopotential with averaged relativistic effects, and including effective core-polarization potential. The molecular calculations are performed for both the ionic species Fr⁺₂, RbFr⁺, CsFr⁺ and the corresponding neutrals, through the CIPSI quantum chemistry package where we used new extended Gaussian basis sets for Rb, Cs and Fr atoms. As no experimental data are available, we discuss our results by comparison with the Rb₂, Cs₂ and RbCs systems. The dipole moment of CsFr reveals an electron transfer yielding a Cs⁺Fr⁻ arrangement, while in all other mixed alkali pairs the electron is transferred towards the lighter species. Finally, the perturbative treatment of the spin–orbit coupling at large distances predicts that in contrast with Rb₂ and Cs₂ no double-well excited potential should be present in Fr₂, probably preventing an efficient formation of cold dimers via the photoassociation of cold francium atoms.

The states X¹Σ⁺ and a³Σ⁺ correlated to the ground-state asymptote of Na (3s) and Cs (6s) atoms have been experimentally investigated using high resolution Fourier-transform spectroscopy. The hyperfine splitting of the a³Σ⁺ state levels is partially resolved. Transitions to asymptotic vibrational levels of the a³Σ⁺ and X¹Σ⁺ states were recorded simultaneously. The joint evaluation of the data of both the a³Σ⁺ and the X¹Σ⁺ states allows us to determine accurate potential energy curves of both electronic states. Coupled-channels calculations are finally applied for deriving long range dispersion parameters and the exchange contribution of the molecular potentials, yielding a reliable description of cold collisions between Na and Cs atoms in their two different hyperfine ground states. Scattering lengths and Feshbach resonances are predicted for selected quantum states.

We calculate the rates of formation and detection of ultracold Cs₂ molecules obtained from the photoassociation of ultracold atoms through the double-well 0_g⁻(6S_1/2 + 6P_3/2) state. We concentrate on two features previously observed experimentally and attributed to tunnelling between the two wells (Vatasescu et al 2000 Phys. Rev. A 61 044701). We show that the molecules obtained are in strongly bound levels (v'' = 5, 6) of the metastable a³Σ_u⁺(6S_1/2 + 6S_1/2) ground electronic state.

The formation of electronic ground-state NaCs molecules from ultracold atoms by photoassociation is explored both experimentally and theoretically. We observe saturation of the photoassociation process as well as complete ionization of the molecular sample by resonant two-photon absorption. Measured absolute molecule formation rates are compared to theoretical calculations and shown to be in good agreement.

We investigate the feasibility of forming ultracold LiH from a mixture of the ultracold atomic gases, by using B¹Π as an intermediate state in the photoassociation process. Using accurate molecular potential energy curves and dipole transition moments, we calculate and compare two possible schemes to populate vibrational levels of the ground electronic state, X¹Σ⁺: (1) two-photon stimulated radiative association and (2) excitation to bound levels of the B¹Π state, followed by spontaneous emission to the X¹Σ⁺ state. With laser intensities and atomic densities that are easily attainable experimentally, we find that significant quantities of molecules can be formed in various v, J levels of the electronic ground state. We examine the spontaneous emission cascade which takes place from the upper vibrational levels on a time scale of milliseconds. We discuss the issue of back-stimulation for the two-photon process and ways to mitigate it. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in v = 0 can be achieved.

We present perturbations in photoassociation spectra of ultracold caesium. High-precision photoassociation spectra up to 54 cm⁻¹ below the Cs (6S_1/2)+Cs(6P_1/2) asymptote revealed perturbations related to resonant coupling between electronic states of the same symmetry but belonging to different asymptotes. The perturbations, which are manifested as irregularities in vibrational level spacings, are most pronounced for the 0_u⁺ state, but to some extent present in the 1_g and 0_g⁻ states, which are also affected by predissociation. We have performed theoretical calculations of perturbations for all three states and found qualitative agreement with the experimental results.

We present the first observation of ultracold LiCs molecules. The molecules are formed in a two-species magneto-optical trap and detected by two-photon ionization and time-of-flight mass spectrometry. The production rate coefficient is found to be in the range 10⁻¹⁸ cm³ s⁻¹ to 10⁻¹⁶ cm³ s⁻¹, at least an order of magnitude smaller than for other heteronuclear diatomic molecules directly formed in a magneto-optical trap.

We theoretically investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose, a perturbative model for light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of ⁸⁵Rb₂ molecules in a magneto-optical trap. We find that optimized pulse shapes may maximize the formation of ground state molecules in a specific vibrational state at a pump-dump delay time for which unshaped pulses lead to a minimum of the formation rate. Compared to the maximum formation rate obtained for unshaped pulses at the optimum pump-dump delay, the optimized pulses lead to a significant improvement of about 40% for the target level population. Since our model yields the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments.

The total number of molecules produced in a pulsed photoassociation of ultracold atoms is a crucial link between theory and experiment. A calculation based on first principles can determine the experimental feasibility of a pulsed photoassociation scheme. The calculation method considers an initial thermal ensemble of atoms. This ensemble is first decomposed into a representation of partial spherical waves. The photoassociation dynamics is calculated by solving the multichannel time-dependent Schrödinger equation on a mapped grid. The molecules are primarily assembled in a finite region of internuclear distances, the 'photoassociation window'. The ensemble average was calculated by adding the contributions from initial scattering states confined to a finite volume. These states are Boltzmann averaged where the partition function is summed numerically. Convergence is obtained for a sufficiently large volume. The results are compared to a thermal averaging procedure based on scaling laws which leads to a single representative initial partial wave which is sufficient to represent the density in the 'photoassociation window'. For completeness a third high-temperature thermal averaging procedure is described which is based on random phase thermal Gaussian initial states. The absolute number of molecules in the two first calculation methods agree to within experimental error for photoassociation with picosecond pulses for a thermal ensemble of rubidium or caesium atoms in ultracold conditions.

We present a theoretical study of the photostabilization of the ultracold Rb₂ molecule by tailored laser fields. The simulations involve the ground and two excited electronic states, taking into account spin–orbit coupling, and are based on the full quantum mechanical optimal control theory. We demonstrate starting from a highly excited bound vibrational state that almost 100% population of the ground state v = 0 vibrational level can be achieved. The obtained optimal pulse has a long temporal and very broad spectral range. Our results reveal the mechanism of the photostabilization process and allow the proposal of new strategies for the formation of ultracold molecules taking into account the necessary constraints for possible experimental realization.

Coherent femtosecond optical pulses provide a unique means to manipulate the collision process between a pair of ultracold atoms. The capability to arbitrarily shape strong electric fields gives the possibility of dynamically sculpting the system Hamiltonian on the collisional timescale. In this paper we explore theoretically physically intuitive excitation schemes by which a control field can manipulate the vibronic state populations in an ultracold molecular system, with the goal of bringing atom pairs to short (R < 10 Å) separations where they may form a tightly bound molecule. The microscopic dynamics of individual pairs of colliding atoms under the influence of an external optical field are explored through explicitly time-dependent numerical simulations. The results provide physical justification for the employment of optimal control techniques for the achievement of state-selective formation of ultracold molecules.

We report on the production of a pulsed molecular beam of metastable NH (a¹Δ) radicals and present first results on the Stark deceleration of the NH (a¹Δ, J = 2, MΩ = −4) radicals from 550 m s⁻¹ to 330 m s⁻¹. The decelerated molecules are excited on the spin-forbidden A³Π ← a¹Δ transition, and detected via their subsequent spontaneous fluorescence to the X³Σ⁻, v = 0 ground state. These experiments demonstrate the feasibility of our recently proposed scheme (2001 Phys. Rev. A 64 041401) to accumulate ground-state NH radicals in a magnetic trap. In addition, we propose to transfer the NH radicals from the a¹Δ state to the X³Σ⁻ state using a cw-laser to allow cooling of the beam during trap loading.

We have measured the Stark effect of several vibrational bands in the excited ¹B₂ state of SO₂. Electric field strengths of up to 100 kV/cm were applied. The spectra were measured by pulsed laser excitation and compared with simulations. The dipole moment of the state was determined to be D. We discuss the possibility of influencing the near-threshold photodissociation of SO₂ by static electric fields.

We describe the deceleration of nitric oxide, benzene and xenon atoms in a molecular beam using one-dimensional pulsed optical lattices created by fields with intensities in the 10¹² W cm⁻² range. We show that for the same pulse duration and lattice intensity the velocity of the molecules can be controlled by tailoring the lattice velocity. By utilizing the time-dependent oscillatory motion of the molecules within the lattice, we demonstrate the deceleration of nitric oxide from an initial velocity of 400 m s⁻¹ to a final velocity of 290 m s⁻¹ in a single 5.8 ns pulse. Using higher intensities, we measure the deceleration of benzene molecules from 380 m s⁻¹ to 191 m s⁻¹, representing a 75% reduction in the kinetic energy within the lattice over the same duration.

We report the successful buffer-gas cooling and magnetic trapping of chromium atoms with densities exceeding 10¹² atoms per cm³ at a temperature of 350 mK for the trapped sample. The possibilities of extending the method to buffer-gas cool and magnetically trap molecules are discussed. To minimize the most important loss mechanism in magnetic trapping, molecules with a small spin–spin interaction and a large rotational constant are preferred. Both the CrH (⁶Σ⁺ ground state) and MnH (⁷Σ⁺) radicals appear to be suitable systems for future experiments.

The supersonic free-jet expansion technique has been used in different fields of research in physics, physical chemistry and chemistry to study vibrational and rotational molecular structures in ground and excited electronic energy states as well as in cold chemistry to study chemical reactions in a unique environment. The supersonic beam technique, as a widely used method in laser spectroscopy of molecules, exploits a source of monokinetic, rotationally and vibrationally cold molecules, that are very weakly bound in their ground electronic states (van der Waals molecules). In experiments at Jagiellonian University the supersonic free-jet beam serves as a source of ground-state van der Waals objects in studies of neutral–neutral interactions between group 12 metal (M = Zn, Cd, Hg) and noble gas (NG) atoms. Recently, the method has been applied as a source of entangled ¹⁹⁹Hg atom pairs in order to test Bell's inequality in an experiment at Texas A&M University.

The dynamics of vibrational wave packets excited in K₂ dimers attached to superfluid helium nanodroplets is investigated by means of femtosecond pump–probe spectroscopy. The employed resonant three-photon-ionization scheme is studied in a wide wavelength range and different pathways leading to K₂⁺ formation are identified. While the wave packet dynamics of the electronic ground state is not influenced by the helium environment, perturbations of the electronically excited states are observed. The latter reveal a strong time dependence on the timescale 3–8 ps which directly reflects the dynamics of desorption of K₂ off the helium droplets.

KRb and Rb₂ dimers are formed on cold helium nanodroplets. Laser excitation and emission spectra from the transition (1)³Π_g–³Σ_u⁺ of Rb₂ and the transition (2)³Π–³Σ⁺ of KRb have been measured. A thorough analysis of the emission, which takes place after desorption of the dimers from the surface of the helium cluster, has been performed. It allows us to determine the redistribution of vibrational population on the droplet surface. A comparison of the experimental spectra with simulations, obtained with the potential energy curves and dipole moments calculated by Aymar and Dulieu, allows a test of the accuracy of the ab initio potentials.

Silver dimers embedded in ultracold helium nanodroplets are ionized by two-photon excitation via a strong resonance which extends from 3.85 eV up to 4.1 eV. The corresponding photoelectron spectra reveal that the ionization threshold is shifted by more than 1.4 eV towards lower values when compared to the gas phase. This gives strong evidence that weakly bound dimers in the lowest lying triplet state are present, thus enabling convenient spectroscopy of the triplet Ag₂. A comparison with predictions from theory allows an assignment of the structure in the spectra. The successful identification of triplet silver dimers embedded in helium droplets shows exemplarily that the formation of such weakly bound systems is not restricted to surface locations as with the alkalis, but represents a general feature of the ultracold helium droplet environment.

Quantum-mechanical simulations of the excitation spectra of KRb from the lowest vibrational level of the lowest triplet and singlet electronic states have been performed using recently calculated interaction potential curves and corresponding transition dipole moments. The obtained spectra can be used for a comparison with experimental absorption spectra of KRb molecules produced in their vibronic ground state or attached to cold helium droplets. In addition, we compare the semiclassically simulated spectra with absorption measurements in dense K–Rb vapour at high temperatures, which helped us to identify three diffuse bands as 1 ³Σ⁺–3 ³Π, 1 ³Σ⁺–4 ³Π and 1 ¹Σ⁺–4 ¹Σ⁺ transitions. The first may be observable in an excitation spectrum of KRb dimer formed on cold helium droplets.

A newly computed potential energy surface which describes the interaction between the two title partners is employed to evaluate collisional quenching of the rotational levels of the OH⁻(X¹Σ⁺) anion by ⁴He atoms at ultralow energies. The calculations are carried out within the exact coupled channel (CC) formalism and both elastic and inelastic quenching cross sections for rotationally 'hot' molecules are obtained. The present results indicate the process to be a fairly efficient one and allow us to discuss, in some detail, the qualitative propensity rules on the quenching which can be extracted from calculations at ultralow collision energies.

The main characteristics of cold and ultracold chemical reactions are reviewed through the illustrative study of the O(³P) + H₂ reaction dynamics. Using separate analytic representations of the lowest H₂O(³A'') electronic state which differ essentially by their descriptions of long-range forces, quantum-mechanical scattering calculations show the crucial role played by the van der Waals interaction potential in chemical reactions at low temperatures. Furthermore, the presence of zero-energy resonances is found to significantly enhance chemical reactivity in the ultracold regime. At translational energies comparable to the well depth of the van der Waals potential, initial-state-selected probabilities and excitation functions are characterized by Feshbach resonances arising from the decay of quasibound states supported by the van der Waals well in the entrance channel of the reaction.

The study of molecular inelastic collision processes at cold and ultracold temperatures is of considerable interest as schemes are currently being developed to efficiently cool and trap neutral polar molecules. In this work, quantum-mechanical scattering calculations are presented for the quenching of rotationally excited CO due to collisions with H, He and H₂ for collision energies between 10⁻⁵ and 10 cm⁻¹. The calculations were performed using the close-coupling approach and the coupled-states approximation. Cross sections for the quenching of the j = 1–10, 20, 30 and 40 levels of CO are presented and mechanism and trends of energy transfer in these systems are discussed.

We have produced large samples of ultracold (<20 mK) ArH⁺, ArD⁺, N₂H⁺, N₂D⁺, H₃⁺, D₃⁺, D₂⁺, H₂D⁺ and D₂D⁺ molecular ions, by sympathetic cooling and crystallization via laser-cooled Be⁺ ions in a linear radio-frequency trap. As technique, we used chemical reactions with sympathetically cooled noble gas atomic ions or N₂⁺ and O₂⁺ molecular ions. These ultracold molecules are interesting targets for high-precision measurements in fundamental physics and may open new routes for the study of state-selective chemical reactions relevant to interstellar chemistry.

We propose how to prepare a single molecular ion in a specific internal quantum state in a situation where the molecule is trapped and sympathetically cooled by an atomic ion and where its internal degrees of freedom are initially in thermal equilibrium with the surroundings. The scheme is based on the conditional creation of correlation between the internal state of the molecule and the translational state of the collective motion of the two ions, followed by a projection measurement of this collective mode by atomic ion shelving techniques. We estimate that state preparation in a large number of internal states is possible.

We show that the rotational degree of freedom of a polar heteronuclear molecular ion can be cooled through an optical coupling to the collective motional modes of the molecular ion and a simultaneously trapped and laser cooled atomic ion. Since the dissipative part of the rotational cooling is realized through laser cooling of the two-ion systems motional modes, the scheme should be applicable to a large range of molecules. As a test case for our cooling scheme we consider rotational cooling of a MgH⁺ ion trapped with a laser cooled ⁴⁰Ca⁺ ion.