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Cold elastic collisions of sodium and rubidium

John Breuer

Published Jul 1, 2009• 0 citations
OpenAlex

Abstract

In this thesis we numerically compute the scattering lengths and bound states for sodium-rubidium collisions at low energy. This work was motivated by experiments which aim to produce Bose-Einstein condensates (BEC) mixtures of sodium-rubidium. Elastic collision properties are important for the rethermalization of the atoms during the evaporative cooling process. Inelastic processes, which we also discuss to some extent, cause trap losses in those experiments. In order to reach the required temperature and density the elastic collision rates should be sufficiently large compared to the inelastic rates. The scattering lengths, which completely specify the elastic collision parameters at low energy, determine the miscibility and phase diagram of the sodium-rubidium condensate mixture. We calculate the scattering lengths approximately and find agreement with previous calculations indicating that miscible phases of sodium and rubidium condensates do not appear to be feasible in the absence of external fields.

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In this thesis we numerically compute the scattering lengths and bound states for sodium-rubidium collisions at low energy. This work was motivated by experiments which aim to produce Bose-Einstein condensates (BEC) mixtures of sodium-rubidium. Elastic collision properties are important for the rethermalization of the atoms during the evaporative cooling process. Inelastic processes, which we also discuss to some extent, cause trap losses in those experiments. In order to reach the required temperature and density the elastic collision rates should be sufficiently large compared to the inelastic rates. The scattering lengths, which completely specify the elastic collision parameters at low energy, determine the miscibility and phase diagram of the sodium-rubidium condensate mixture. We calculate the scattering lengths approximately and find agreement with previous calculations indicating that miscible phases of sodium and rubidium condensates do not appear to be feasible in the absence of external fields.
This thesis deals with elastic and inelastic collisions among ultra cold rubidium atoms. In particular, the impact of increased interaction on the stability of Bose-Einstein condensates is investigated both, experimentally and theoretically. A new decay mechanism is identified that significantly reduces the life time of condensates with respect to the expectation based on the known inelastic collision rates. Along with the interaction also the column density of the condensate is increased so that it eventually becomes impenetrable to products of exoergic collisions. These products then trigger avalanches of elastic collisions in which a significant part of the energy released in the initiatory exoergic collision is distributed among condensate atoms. Collisional avalanches are favoured by the isotropy of the differential scattering cross section in the low energy (s-wave) limit and occur as soon as the elastic collision rate exceeds a critical value. Since avalanches not only reduce the life time of the condensate but also disturb its thermodynamic equilibrium, their occurrence restricts the possibilities to explore the strongly interacting regime. A simple model is introduced to quantify the impact of avalanches on the decay and agrees well with experimental data. The thesis further contains the description and the characterisation of a new experimental apparatus which allows to create large atomic condensates with excellent reproducibility and high repetition rate complying with the requirements for the investigation of field-induced elastic scattering resonances.
In this thesis we investigate theoretically the cold collision properties of metastable neon (Ne*). The collisions of metastable rare gases (Rg*) exhibit a plethora of interesting phenomena: Due to the high internal excitation energies of the metastable atoms ionization processes are very likely. The produced ions can be detected with single-ion efficiency in the experiment. In experiments with atomic Rg* gases at cold temperatures T~1 mK, this allows for in-situ monitoring of the real-time dynamics of the atomic gas and for example for the study of two-particle correlations. Furthermore, in cold Rg* gases one can examine the prospects of creating a Bose-Einstein condensate or a degenerate Fermi gas of Rg*. Ne* is a promising candidate for Bose-Einstein condensation and in the group of G. Birkl the properties of cold gases of Ne* are investigated experimentally. Two-body loss rate coefficients due to the ionization processes and elastic cross sections have been measured. It is useful to complement the experimental measurements with a theoretical study in order to obtain a better understanding of the cold Ne* gases and the collision physics of Ne*. At the low temperatures of the atomic gases, these gases are dilute with particle number densities of n~10^9 cm^{-3}. For these low densities, the behavior of the gas is determined mainly by two-body collision physics which is solved by quantum scattering theory in terms of the S matrix. The collision physics is given by short-range interactions and long-range interactions of the atoms. The short-range and long-range interaction potentials of Ne* have been calculated in the molecular basis of Ne2. In this thesis we first calculate short-range and long-range interactions of atoms and molecular basis states of diatomic molecules with a simpler electronic structure than Ne* and Ne2 in order to introduce the notation and to discuss the characteristics of the calculated molecular interaction potentials and in order to employ them in the scattering calculations for Ne*. Instead of solving the full scattering equations by taking into account all the molecular interaction potentials, we demonstrate that the collision physics of Ne* can be described in terms of a coupled two-channel model with a single interaction potential only which describes the elastic scattering of Ne*. In this model, ionization in Ne* collisions is described by the transition of the upper elastic interaction channel to the lower channel, representing the loss or ionization channel. We introduce two versions of the two-channel model in this work. In the first version, the two channels are given by square-well potentials. We can solve the scattering equations analytically and for complex wave numbers k and study the solutions in the complex k plane. With an expansion of the S matrix in terms of its poles in the complex k plane we find a parametrization of the two-body loss rate coefficients. We show that these coefficients describe ionizing collisions of Ne* by comparing them to the experimental measurements and to the numerical results obtained by the two-channel model in the second version. In this second version of the two-channel model, the elastic scattering channel is given by a realistic interaction potential of Ne*, consisting of a calculated short-range and long-range molecular potential, and the loss channel by a model ionization potential. For this model we calculate the two-body loss rate coefficients and the elastic cross sections for the isotope mixtures of Ne* which have been measured experimentally and demonstrate that the free potential parameters can be optimized to the experimental data to achieve very good agreement of the numerical results with the experimental measurements. We discuss the validity of the two-channel model by comparing the results to existing models for cold Rg* collisions and find that the two-channel model of this work is a useful extension to these models.
The calculation of the elastic scattering properties of mixtures composed by rubidium and potassium atoms is reported and compared with experimental results in detail. The improved potentials for both molecular states the singlet and the triplet of the RbK are presented, and the scattering lengths a_{t} and the effective range r_{e} are calculated with the help of this potential using WKB and Numerov methods for Rb-K in the triplet and singlet state. In addition, the convergence of these scattering properties as the depending on a K_{0} parameter is investigated using Quantum Defect Theory. The evaporative cooling other results that include the cross section and the spin-charge cross section, the rate coefficient as a function of the energy and the ultra-low temperature are also presented in this study.
We study the elastic scattering length and inelastic decay rate associated with collisions of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb atoms in different hyperfine states: one with atoms in the |f=2,mf{\mathrm{m}}_{\mathrm{f}}mf​=2〉 and one with atoms in the |f=1,mf{\mathrm{m}}_{\mathrm{f}}mf​=-1〉 state. For Na the real part of the ${\mathrm{a}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$ scattering length for |22〉+|1-1〉 collisions is predicted to be positive and equal to 65\ifmmode\pm\else\textpm\fi{}5 Bohr length units a0{\mathrm{a}}_{0}a0​ for small B. The zero-temperature low-field decay rate is of the order of a typical exchange rate: ${\mathrm{G}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$=(1.5\ifmmode\pm\else\textpm\fi{}0.7)${10}^{\mathrm{\ensuremath{-}}11}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, showing that a two-condensate experiment is not feasible for a Na gas sample in a static magnetic trap. For the case of Rb atoms the present knowledge of the singlet interaction does not allow a similar calculation. The extreme suppression of ${\mathrm{G}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$ demonstrated by a recent experiment is shown to be very restrictive for the value of the singlet accumulated phase.
Evaporative cooling is a proven strategy for reaching new regimes of temperature and density in magnetically trapped vapors. The technique works, however, only if the intratrap collision rate dominates the rates of undesirable processes such as spin-flip inelastic collisions and collisions with untrapped background vapor. Our measurement of the elastic scattering cross section in Cs at temperatures down to 30 {mu}K, in combination with recent theoretical calculations of the inelastic scattering rate, shows that inelastic spin-flip collisions do not pose a significant obstacle to attaining Bose condensation. We measure the elastic scattering cross section by observing the rate of thermal equilibration in a trapped sample which is initially far from thermal equilibrium. I will discuss this work and other developments relevant to attaining Bose condensation.
The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, the observed rate of inelastic collisions was strongly enhanced in a sodium Bose-Einstein condensate when the scattering length was tuned to both larger or smaller values than the off-resonant value. These strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates.