Thermalization of an impurity cloud in a Bose-Einstein condensate

We study the thermalization dynamics of an impurity cloud inside a Bose-Einstein condensate at finite temperature, introducing a suitable Boltzmann equation. Some values of the temperature and of the initial impurity energy are considered. We find that, below the Landau critical velocity, the macroscopic population of the initial impurity state reduces its depletion rate. For sufficiently high velocities the opposite effect occurs. For appropriate parameters the collisions cool the condensate. The maximum cooling per impurity atom is obtained with multiple collisions.Comment: 4 pages 6 figure

Spectroscopic Temperature Determination of Degenerate Fermi Gases

We suggest a simple method for measuring the temperature of ultra-cold gases made of fermions. We show that by using a two-photon Raman probe, it is possible to obtain lineshapes which reveal properties of the degenerate sample, notably its temperature $T$. The proposed method could be used with identical fermions in different hyperfine states interacting via s-wave scattering or identical fermions in the same hyperfine state via p-wave scattering. We illustrate the applicability of the method in realistic conditions for $^6$Li prepared in two different hyperfine states. We find that temperatures down to 0.05 $T_{F}$ can be determined by this {\it in-situ} method.Comment: 7 pages, 4 figures, Revtex

A slow gravity compensated Atom Laser

We report on a slow guided atom laser beam outcoupled from a Bose-Einstein condensate of 87Rb atoms in a hybrid trap. The acceleration of the atom laser beam can be controlled by compensating the gravitational acceleration and we reach residual accelerations as low as 0.0027 g. The outcoupling mechanism allows for the production of a constant flux of 4.5x10^6 atoms per second and due to transverse guiding we obtain an upper limit for the mean beam width of 4.6 \mu\m. The transverse velocity spread is only 0.2 mm/s and thus an upper limit for the beam quality parameter is M^2=2.5. We demonstrate the potential of the long interrogation times available with this atom laser beam by measuring the trap frequency in a single measurement. The small beam width together with the long evolution and interrogation time makes this atom laser beam a promising tool for continuous interferometric measurements.Comment: 7 pages, 8 figures, to be published in Applied Physics

Stationary quantum statistics of a non-Markovian atom laser

We present a steady state analysis of a quantum-mechanical model of an atom laser. A single-mode atomic trap coupled to a continuum of external modes is driven by a saturable pumping mechanism. In the dilute flux regime, where atom-atom interactions are negligible in the output, we have been able to solve this model without making the Born-Markov approximation. The more exact treatment has a different effective damping rate and occupation of the lasing mode, as well as a shifted frequency and linewidth of the output. We examine gravitational damping numerically, finding linewidths and frequency shifts for a range of pumping rates. We treat mean field damping analytically, finding a memory function for the Thomas-Fermi regime. The occupation and linewidth are found to have a nonlinear scaling behavior which has implications for the stability of atom lasers.Comment: 12 pages, 2 figures, submitted to PR

Momentum distribution and correlation function of quasicondensates in elongated traps

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate, in a trap and in free expansion. We take the inhomogeneous density profile into account {\it{via}} a local density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.Comment: 5 pages, 2 figures; final version, references update

Mean field effects on the scattered atoms in condensate collisions

We consider the collision of two Bose Einstein condensates at supersonic velocities and focus on the halo of scattered atoms. This halo is the most important feature for experiments and is also an excellent testing ground for various theoretical approaches. In particular we find that the typical reduced Bogoliubov description, commonly used, is often not accurate in the region of parameters where experiments are performed. Surprisingly, besides the halo pair creation terms, one should take into account the evolving mean field of the remaining condensate and on-condensate pair creation. We present examples where the difference is clearly seen, and where the reduced description still holds.Comment: 6 pages, 4 figure

Bose-Einstein condensates in atomic gases: simple theoretical results

These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic interaction potential - finite temperature Hartree-Fock approximation - Gross-Pitaevskii equation for the condensate wavefunction - what we learn from a linearization of the Gross-Pitaevskii equation - Bogoliubov approach and thermodynamical stability - phase coherence properties of Bose-Einstein condensates - symmetry breaking description of condensatesComment: 146 pages, 17 figures, Lecture Notes of Les Houches Summer School 199