Three-body decay of a rubidium Bose-Einstein condensate

We have measured the three-body decay of a Bose-Einstein condensate of rubidium ($^{87}$Rb) atoms prepared in the doubly polarized ground state $F=m_F=2$. Our data are taken for a peak atomic density in the condensate varying between $2\times 10^{14}$ cm$^{-3}$ at initial time and $7\times 10^{13}$ cm$^{-3}$, 16 seconds later. Taking into account the influence of the uncondensed atoms onto the decay of the condensate, we deduce a rate constant for condensed atoms $L=1.8 (\pm 0.5) \times 10^{-29}$ cm$^{6}$s$^{-1}$. For these densities we did not find a significant contribution of two-body processes such as spin dipole relaxation.Comment: 14 pages, 4 figure

Multi-wavelength characterisation of z~2 clustered, dusty star forming galaxies discovered by Planck

(abridged) We report the discovery of PHz G95.5-61.6, a complex structure detected in emission in the Planck all-sky survey that corresponds to two over-densities of high-redshift galaxies. This is the first source from the Planck catalogue of high-z candidates that has been completely characterised with follow-up observations from the optical to the sub-millimetre domain. Herschel/SPIRE observations at 250, 350 and 500 microns reveal the existence of five sources producing a 500 microns emission excess that spatially corresponds to the candidate proto-clusters discovered by Planck. Further observations at CFHT in the optical bands (g and i) and in the near infrared (J, H and K_s), plus mid infrared observations with IRAC/Spitzer (at 3.6 and 4.5 microns) confirm that the sub-mm red excess is associated with an over-density of colour-selected galaxies. Follow-up spectroscopy of 13 galaxies with VLT/X-Shooter establishes the existence of two high-z structures: one at z~1.7 (three confirmed member galaxies), the other at z~2.0 (six confirmed members). This double structure is also seen in the photometric redshift analysis of a sample of 127 galaxies located inside a circular region of 1'-radius containing the five Herschel/SPIRE sources, where we found a double-peaked excess of galaxies at z~1.7 and z~2.0 with respect to the surrounding region. These results suggest that PHz G95.5-61.6 corresponds to two accreting nodes, not physically linked to one another, embedded in the large scale structure of the Universe at z~2 and along the same line-of-sight. In conclusion, the data, methods and results illustrated in this pilot project confirm that Planck data can be used to detect the emission from clustered, dusty star forming galaxies at high-z, and, thus, to pierce through the early growth of cluster-scale structures.Comment: 15 pages, 13 figures. Accepted for publication in Astronomy and Astrophysic

Frequencies and Damping rates of a 2D Deformed Trapped Bose gas above the Critical Temperature

We derive the equation of motion for the velocity fluctuations of a 2D deformed trapped Bose gas above the critical temperature in the hydrodynamical regime. From this equation, we calculate the eigenfrequencies for a few low-lying excitation modes. Using the method of averages, we derive a dispersion relation in a deformed trap that interpolates between the collisionless and hydrodynamic regimes. We make use of this dispersion relation to calculate the frequencies and the damping rates for monopole and quadrupole mode in both the regimes. We also discuss the time evolution of the wave packet width of a Bose gas in a time dependent as well as time independent trap.Comment: 13 pages, latex fil

Oscillations of rotating trapped Bose-Einstein condensates

The tensor-virial method is applied for a study of oscillation modes of uniformly rotating Bose-Einstein condensed gases, whose rigid body rotation is supported by an vortex array. The second order virial equations are derived in the hydrodynamic regime for an arbitrary external harmonic trapping potential assuming that the condensate is a superfluid at zero temperature. The axisymmetric equilibrium shape of the condensate is determined as a function of the deformation of the trap; its domain of stability is bounded by the constraint $\Omega<1$ on the rotation rate (measured in units of the trap frequency $\omega_0$.) The oscillations of the axisymmetric condensate are stable with respect to the transverse-shear, toroidal and quasi-radial modes of oscillations, corresponding to the $l= 2$, $| m| = 0,1,2$ surface deformations. In non-axisymmetric traps, the equilibrium constrains the (dimensionless) deformation in the plane orthogonal to the rotation to the domain $A_2 > \Omega^2$ with $\Omega< 1$. The second harmonic oscillation modes in non-axisymmetric traps separate into two classes which have even or odd parity with respect to the direction of the rotation axis. Numerical solutions show that these modes are stable in the parameter domain where equilibrium figures exist.Comment: 16 pages, including 4 figures, uses Revtex; v2 includes a treatment of modes in unisotropic traps; PRA in pres

Finite-temperature simulations of the scissors mode in Bose-Einstein condensed gases

The dynamics of a trapped Bose-condensed gas at finite temperatures is described by a generalized Gross-Pitaevskii equation for the condensate order parameter and a semi-classical kinetic equation for the thermal cloud, solved using $N$-body simulations. The two components are coupled by mean fields as well as collisional processes that transfer atoms between the two. We use this scheme to investigate scissors modes in anisotropic traps as a function of temperature. Frequency shifts and damping rates of the condensate mode are extracted, and are found to be in good agreement with recent experiments.Comment: 4 pages, 3 figure