Matthew D. Frye

Modeling sympathetic cooling of molecules by ultracold atoms.

We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the s-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the s-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to 100μK in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to 1 μK within 30 s.

Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF (J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.

Interspecies thermalization in an ultracold mixture of Cs and Yb in an optical trap

We present measurements of interspecies thermalization between ultracold samples of 133Cs and either 174Yb or 170Yb. The two species are trapped in a far-off-resonance optical dipole trap and 133Cs is sympathetically cooled by Yb. We extract effective interspecies thermalization cross sections by fitting the thermalization measurements to a kinetic model, giving σCs174Yb = (5 ± 2) × 10−13 cm2 and σCs170Yb = (18 ± 8) × 10−13 cm2. We perform quantum scattering calculations of the thermalization cross sections and optimize the CsYb interaction potential to reproduce the measurements. We predict scattering lengths for all isotopic combinations of Cs and Yb. We also demonstrate the independent production of 174Yb and 133Cs Bose-Einstein condensates using the same optical dipole trap, an important step toward the realization of a quantum-degenerate mixture of the two species.

Quantum chaos in ultracold collisions between Yb(

We calculate and analyze Feshbach resonance spectra for ultracold Yb(1S0)+Yb(3P2) collisions as a function of an interatomic potential scaling factor λ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in λ, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.

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We investigate the behaviour of single-channel theoretical models of cold and ultracold collisions that take account of inelastic and reactive processes using a single parameter to represent short-range loss. We present plots of the resulting energy-dependence of elastic and inelastic or reactive cross sections over the full parameter space of loss parameters and short-range phase shifts. We then test the single-channel model by comparing it with the results of coupled-channel calculations of rotationally inelastic collisions between LiH molecules and Li atoms. We find that the range of cross sections predicted by the single-channel model becomes increasingly accurate as the initial LiH rotational quantum number increases, with a corresponding increase in the number of open loss channels. The results suggest that coupled-channel calculations at very low energy (in the s-wave regime) could in some cases be used to estimate a loss parameter and then to predict the range of possible loss rates at higher energy, without the need for explicit coupled-channel calculations for higher partial waves.

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The collision cross section that controls thermalization of gas mixtures is the transport cross section σ(1)η and not the elastic cross section σel. The two are the same for pure s-wave scattering but not when higher partial waves contribute. We investigate the differences between them for prototype atomic mixtures and show that the distinction is important at energies above 100μK for LiYb and 3μK for RbYb and RbCs. For simple systems, both σ(1)η and σel follow universal energy dependence that depends only on the s-wave scattering length when expressed in reduced length and energy units.

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We describe procedures for converging on and characterizing zero-energy Feshbach resonances that appear in scattering lengths for ultracold atomic and molecular collisions as a function of an external field. The elastic procedure is appropriate for purely elastic scattering, where the scattering length is real and displays a true pole. The regularized scattering length procedure is appropriate when there is weak background inelasticity, so that the scattering length is complex and displays an oscillation rather than a pole, but the resonant scattering length a res is close to real. The fully complex procedure is appropriate when there is substantial background inelasticity and the real and imaginary parts of a res are required. We demonstrate these procedures for scattering of ultracold 85 Rb in various initial states. All of them can converge on and provide full characterization of resonances, from initial guesses many thousands of widths away, using scattering calculations at only about ten values of the external field.