Two charges on plane in a magnetic field: special trajectories

A classical mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field perpendicular to a plane is considered. Special "superintegrable" trajectories (circular and linear) for which the distance between charges remains unchanged are indicated as well as their respectful constants of motion. The number of the independent constants of motion for special trajectories is larger for generic ones. A classification of pairs of charges for which special trajectories occur is given. The special trajectories for three particular cases of two electrons, (electron - positron), (electron - $\alpha$-particle) are described explicitly.Comment: 22 pages, 5 figure

Bose-Einstein Condensation of 88^{88}Sr Through Sympathetic Cooling with 87^{87}Sr

We report Bose-Einstein condensation of $^{88}$Sr, which has a small, negative s-wave scattering length ($a_{88}=-2$\,$a_0$). We overcome the poor evaporative cooling characteristics of this isotope by sympathetic cooling with $^{87}$Sr atoms. $^{87}$Sr is effective in this role in spite of the fact that it is a fermion because of the large ground state degeneracy arising from a nuclear spin of $I=9/2$, which reduces the impact of Pauli blocking of collisions. We observe a limited number of atoms in the condensate ($N_{max}\approx 10^4$) that is consistent with the value of $a_{88}$ and the optical dipole trap parameters.Comment: 4 pages, 4 figure

Degenerate Fermi Gas of 87^{87}Sr

We report quantum degeneracy in a gas of ultra-cold fermionic $^{87}$Sr atoms. By evaporatively cooling a mixture of spin states in an optical dipole trap for 10.5\,s, we obtain samples well into the degenerate regime with $T/T_F=0.26^{+.05}_{-.06}$. The main signature of degeneracy is a change in the momentum distribution as measured by time-of-flight imaging, and we also observe a decrease in evaporation efficiency below $T/T_F \sim 0.5$.Comment: 4 pages, 3 figure

Inelastic and elastic collision rates for triplet states of ultracold strontium

We report measurement of the inelastic and elastic collision rates for ^{88}Sr atoms in the (5s5p)^3P_0 state in a crossed-beam optical dipole trap. This is the first measurement of ultracold collision properties of a ^3P_0 level in an alkaline-earth atom or atom with similar electronic structure. Since the (5s5p)^3P_0 state is the lowest level of the triplet manifold, large loss rates indicate the importance of principle-quantum-number-changing collisions at short range. We also provide an estimate of the collisional loss rates for the (5s5p){^3P_2} state.Comment: 4 pages 5 figure

Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials

Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordinates and admit an independent fourth-order integral of motion. The general form of the potentials satisfies a linear ODE. In the classical case, the standard potentials coincide with the Tremblay-Turbiner-Winternitz (TTW) or Post-Winternitz (PW) models. In the quantum case new superintegrable systems are obtained, in addition to the TTW and PW ones. Their classical limit is free motion.Comment: 30 page

Runaway evaporation for optically dressed atoms

Forced evaporative cooling in a far-off-resonance optical dipole trap is proved to be an efficient method to produce fermionic- or bosonic-degenerated gases. However in most of the experiences, the reduction of the potential height occurs with a diminution of the collision elastic rate. Taking advantage of a long-living excited state, like in two-electron atoms, I propose a new scheme, based on an optical knife, where the forced evaporation can be driven independently of the trap confinement. In this context, the runaway regime might be achieved leading to a substantial improvement of the cooling efficiency. The comparison with the different methods for forced evaporation is discussed in the presence or not of three-body recombination losses