Cold Atoms, Cold Molelcules, and Spectroscopy

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

An understanding of nature, and of physical processes, proceeds most fruitfully when there are correlated theoretical predictions and experimental results. This theoretical and computational work builds on experimental advances achieved in the last 15 to 20 years, in exploitation of laser cooling of atoms. An ensemble of bosons, at cold enough temperature, can occupy just the lowest quantum state, producing Bose-Einstein condensation, while two fermions cannot be in the same quantum state. However, in one-dimension, if the density is low enough, both boson and fermion ensembles collide without penetration. As pointed out by M. Girardeau in 1960, in this regime bosons behave like fermions. Predictions and experiments could test theoretical models and thereby extend the understanding of cold atom dynamics in effective one-dimensional confinement. The second part of the proposed work relates to current efforts to develop experimental methods beyond those used for atoms, to simple molecules. The usual experimental approach is to start with cold atoms, induce them to combine in a magnetic field ("Feshbach resonance states"), then excite these loosely bound molecules into higher states of different electronic structure which can then decay into the lowest molecular vibrational-rotational quantum state, with minimal translational energy. This production method requires an accurate knowledge of molecular energy levels so as to know where to tune the lasers. This group's work has been to supply that data to find the optimum pathway for production of cold NaK molecules from cold sodium (Na) and potassium (K) atoms. This work is relevant to a broad range of areas including quantum information science and chemical reactions at ultracold energies. The group will study one-dimensional ensembles of fermions and bosons in one-dimension in the low density regiem. Recent experiments have tested theoretical models for oscillation frequencies of atomic ensembles in harmonic potentials under various conditions. This theory will be extended by performing calculations for the behavior of atomic ensembles over a range of densities when there is a central potential barrier, giving a "double-well" potential. In the cold atom regime when quantum wavefunctions extend so as to penetrate a possible barrier, there can be quantum tunneling through the barrier. But this will depend on the atomic density, which determines the extent to which the atom ensemble resembles either extreme limit of bosons or fermions. Because the intermediate cases present rather complicated situations, predictions and experiments could test theoretical models and thereby extend the understanding of cold atom dynamics in effective one-dimensional confinement. For bosons, the time-dependent Gross-Pitaevskii equation has successfully modeled dynamical behavior in a wide range of conditions. For fermions, a determinantal wavefunction with one particle in each basis state has been used, as in atomic theory. Dynamics calculations in effective one-dimensional (1D) potentials intermediate between bosonic and fermionic limits have been pursued only in special cases, such as a pure harmonic potential. Recent time-independent matrix diagonalization approaches to dynamical processses will be adapted. To extend the range of applications of theory for cold atoms in 1D, it is also worth considering hydrodynamic approaches without the usual simplification of small departures from equilibrium. Current work on the production of cold molecules via Feshbach resonance states has been limited primarily to molecules composed of potassium and rubidium. These atoms react on collision to make potassium and rubidium molecules. Molecules composed of sodium and potassium do not have this problem, so methods to produce cold NaK are being pursued in several laboratories. This work has been and will continue to have the goal of analyzing available spectroscopic data to accurately model a large number of possible intermediate molecular energy levels to select the optimum pathway for production of cold NaK molecules from cold Na and K atoms. This approach to diatomic molecular energy structure employs direct fits of experimental data to energy levels computed from numerical potentials and spin-orbit coupling functions. This is in contrast to the traditional Dunham expansions over vibrational and rotational parameters, which are quite satisfactory for unperturbed states, but which cannot easily be used to characterize singlet-triplet perturbation effects. This approach is motivated by the fact that singlet-triplet mixing is crucial in the stepwise formation of singlet cold molecules from typically triplet Feshbach resonance states.