Short-pulse photoassociation in rubidium below the D1_1 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 $5S+5P_{1/2}$ 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 wavenumbers 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

Dynamical interferences to probe short-pulse photoassociation of Rb atoms and stabilization of Rb_2 dimers

We analyze the formation of Rb_2 molecules with short photoassociation pulses applied to a cold Rb-85 sample. A pump laser pulse couples a continuum level of the ground electronic state X ^1\Sigma_{g}^+ with bound levels in the 0_{u}^+ (5S+5P_{1/2}) and 0_{u}^+ (5S+5P_{3/2}) vibrational series. The nonadiabatic coupling between the two excited channels induces time-dependent beatings in the populations. We propose to take advantage of these oscillations to design further laser pulses that probe the photoassociation process via photoionization or that optimize the stabilization in deep levels of the ground state.Comment: 4 pages, 5 figures. v2: major changes in introduction, discussion clarified. v3: minor corrections. v4: matches published versio

Calculation of three-body resonances using slow-variable discretization coupled with a complex absorbing potential

We developed a method to calculate positions and widths of three-body resonances. The method combines the hyperspherical adiabatic approach, slow variable discretization method [O. I. Tolstikhin , J. Phys. B 29, L389 (1996)], and a complex absorbing potential. The method can be used to obtain resonances having short-range or long-range wave functions. In particular, we have applied the method to obtain very shallow three-body Efimov resonances for a model system [E. Nielsen , Phys. Rev. A 66, 012705 (2002)]

Creating Ground State Molecules with Optical Feshbach Resonances in Tight Traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for $^{87}$Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected

The dynamical hole in ultrafast photoassociation: analysis of the compression effect

Photoassociation of a pair of cooled atoms by excitation with a short chirped laser pulse creates a dynamical hole in the initial continuum wavefunction. This hole is manifested by a void in the pair wavefunction and a momentum kick. Photoassociation into loosely bound levels of the external well in Cs_2 0$_g^-$(6S + 6P$_{3/2}$ is considered as a case study. After the pulse, the free evolution of the ground triplet state wavepacket is analyzed. Due to a negative momentum kick, motion to small distances is manifested and a compression effect is pointed out, markedly increasing the density of atom pairs at short distance. A consequence of the hole is the redistribution of the vibrational population in the ground triplet state, with population of the last bound level and creation of pairs of hot atoms. The physical interpretation makes use of the time dependence of the probability current and population on each channel to understand the role of the parameters of the photoassociation pulse. By varying such parameters, optimization of the compression effect in the ground state wavepacket is demonstrated. Due to an increase of the short range density probability by more than two orders of magnitude, we predict important photoassociation rates into deeply bound levels of the excited state by a second pulse, red-detuned relative to the first one and conveniently delayed.Comment: 31 pages, 11 figure

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% if 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 is able to identify the ranges of intensity and pulse duration which are able to achieve this task before other competing process take place. Such a scheme could produce stable ultracold molecular samples or even stable molecular Bose-Einstein condensates

Etude théorique de la formation de molécules diatomiques dans un condensat par photoassociation

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Aspects théoriques de la formation de molécules froides (application à la photoassociation dans les condensats de Bose-Einstein)

Nous avons développé un formalisme indépendant du temps pour étudier la formation de molécules par résonances de Feshbach et de façon plus générale, pour-traiter l'interaction entre un état discret et un continuum. Nous avons utilisé la méthode de grille de Fourier avec un potentiel optique pour résoudre les équations de Schrödinger couplées avec de bonnes conditions aux limites asymptotiques pour les fonctions d'onde calculées. La diagonalisation de la matrice hamiltonienne donne des énergies complexes dont les parties réelles et imaginaires s'interprètent respectivement comme les positions et les largeurs des résonances. Ces paramètres interviennent dans l'expression du taux de formation de molécules. Nous avons appliqué cette méthode pour étudier la photo-association dans le régime des collisions ultra-froides et plus particulièrement dans les conditions des condensats de Bose-Einstein. Dans le cadre du modèle de la molécule habillée, la photo-association est équivalente à une résonance de Feshbach induite par laser et peut être traité non-perturbativement. Nous avons également interprété des phénomènes de prédissociation moléculaire.We have developed a time-independent formalism to study the formation of molecules by Feshbach resonances and more generally to treat the interaction between a discrete bound state and a continuum. We have used the Fourier grid method with an optical potential to salve the coupled Schrodinger equation system with appropriate boundary conditions for the calculated wave functions. The diagonalization of the total Hamiltonian matrix leads to complex eigenvalues where the real and imaginary parts respectively give the positions and the widths of the resonances. These parameters are used in the expression of the molecular formation rate. We have applied this method to study the photoassociation reaction at ultra-low temperature under typical Bose-Einstein conditions. In the dressed molecular picture, this process is equivalent to an optically induced Feshbach resonance and can be investigated non-perturbatively. Applications to predissociation studies are clone as well.ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure

In view of modelization of experiments involving cold atoms and molecules, we develop a method that allows us to calculate weakly bound levels of triatomic molecules. The method combines (1) the hyperspherical coordinates to describe interparticle motion in the three-body system, (2) the solution of the Schrodinger equation in two steps: determination of adiabatic states for a fixed hyper-radius and then solution of a set of coupled hyper-radial equations using the slow variable representation of Tolstikhin [J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)], (3) and a mapping procedure that reduces considerably the number of basis functions needed to represent wave functions of weakly bound levels. We apply the method to the three different systems: the helium trimer He-4(3), isotopomers of the H-3(+) ion, and finally a model three-body problem involving three nucleons. For all these systems, we show that the suggested method provides accurate results