aqora

In this thesis I present the results of photoassociation measurements in ensembles of atomic calcium over an intensity range of below 1 W/cm2 up to 600 W/cm2. The temperature of the atoms was reduced to 1 μK by laser and evaporative cooling. Afterwards the two most-weakly bound states in the excited molecular potentials that dissociate to the asymtote 3P1+1S0 have been investigated regarding the shape and absolute rate of the resonances. The investigation showed that the measured rates differ by more than an order of magnitude compared to theoretical calculations. The predictions are based on a scattering formalism by Bohn & Julienne and wave functions derived from coupled-channel calculations. The shape of the resonances, the width in particular, agrees well with the numerical calculations. Especially the power broadening at high intensity is reproduced by the experiment. Further the light shift introduced by the photoassociation laser has been measured which also differs from the predictions. In the further course of the thesis the numerical simulations were improved by considering additional influences like the exact dependence of the Franck-Condon density and the light shift of the photoassociation laser as a function of the collision energy. Additionally the modeling of the experimental setup with a special emphasis on the volume of the optical trap and thus the density of the atomic ensemble was improved and the influence of varying trap depth and photoassociation duration has been studied. Investigating possible explanations for the discrepancy of the measured rates compared to theory, I show that by a modification of the coupling parameter and the spontaneous decay rate of the molecular state the rates measured in the experiment can be reproduced theoretically, with the restriction that at high intensity the calculated line shape no longer agrees with the measurement. In the last chapter an improved experimental apparatus is presented that by using an optical lattice suppresses thermal broadening and thus simplifies the analysis substantially.

A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ and excited $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to $\ensuremath{-}3000\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. This frequency range corresponds to vibrational levels of the ${J}^{\ensuremath{'}}=1$ state of

{\mathrm{Ca}}_{2}

that can mostly be assigned to the $c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}$ state. The two by far most intense lines at a detuning frequency around $\ensuremath{-}800\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ correspond to the last two bound rovibrational levels lying below the

1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S

asymptote which are heavily mixed and can partly be assigned to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.

This thesis describes the results of several experiments that studied the photoassociation of an ultracold atomic Rb gas. In the first experiment, we produced ultracold diatomic molecules from an atomic gas via single-color photoassociation. The molecules were detected with resonance-enhanced multiphoton ionization. Trapping of these molecules in a quadrupole magnetic trap, with lifetimes up to 20 seconds, was also demonstrated. In addition, the rate constant for inelastic collisions between the trapped molecules and atoms was determined from measurements of the atomic density dependence of the decay rate of the trapped molecules. In another experiment, stimulated Raman photoassociation of Rb atoms in a Mott insulator state was studied. A Bose-Einstein condensate (BEC) of 87Rb atoms was loaded into a three-dimensional optical lattice formed by the interference pattern of three orthogonal standing wave laser fields. This system constitutes a very good realization of the Bose-Hubbard model, which predicts a quantum phase transition between a superfluid state and a Mott insulator state at a particular lattice height. A time-of-flight imaging method was used to study the state of the atomic gas, and the quantum phase transition was observed at the predicted lattice height. The signature of the phase transition was the disappearance and reappearance of peaks in the image that arose from the interference of atoms originating from different lattice sites. Two coherent laser fields were applied to the gas in its Mott insulating state, and tuned close to a Raman photoassociation resonance, and this resulted in an observable loss of atoms due to the formation of molecules. This transition exhibited a double-peaked spectrum, with one of the peaks arising from photoassociation of atoms in sites containing only two atoms, and the other from sites containing three atoms. Also, the loss of atoms vs. the duration of the Raman photoassociation period was studied, with the lasers tuned to the peak corresponding to two atoms per site. It was found that a central core of the gas, containing about 40 percent of the atoms, exhibited a coherent oscillation between an atomic and molecular quantum gas.