Continuous Observation of Interference Fringes from Bose Condensates

We use continuous measurement theory to describe the evolution of two Bose condensates in an interference experiment. It is shown how the system evolves in a single run of the experiment into a state with a fixed relative phase, while the total gauge symmetry remains unbroken. Thus, an interference pattern is exhibited without violating atom number conservation.Comment: 4 pages, Postscrip

Exciting, Cooling And Vortex Trapping In A Bose-Condensed Gas

A straight forward numerical technique, based on the Gross-Pitaevskii equation, is used to generate a self-consistent description of thermally-excited states of a dilute boson gas. The process of evaporative cooling is then modelled by following the time evolution of the system using the same equation. It is shown that the subsequent rethermalisation of the thermally-excited state produces a cooler coherent condensate. Other results presented show that trapping vortex states with the ground state may be possible in a two-dimensional experimental environment.Comment: 9 pages, 7 figures. It's worth the wait! To be published in Physical Review A, 1st February 199

Quantum Limits of Stochastic Cooling of a Bosonic Gas

The quantum limits of stochastic cooling of trapped atoms are studied. The energy subtraction due to the applied feedback is shown to contain an additional noise term due to atom-number fluctuations in the feedback region. This novel effect is shown to dominate the cooling efficiency near the condensation point. Furthermore, we show first results that indicate that Bose--Einstein condensation could be reached via stochastic cooling.Comment: 5 pages, 3 figures, to appear in Phys. Rev.

Condensate fluctuations of a trapped, ideal Bose gas

For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground state occupation becomes macroscopic, the condensate number fluctuations remain micrscopic. However, this is the only significant aspect in which the grand canonical description differs from canonical or microcanonical in the thermodynamic limit. General arguments and estimates including some vanishingly small quantities are compared to explicit, fixed-number calculations for 10^2 to 10^6 particles.Comment: 16 pages (REVTeX) plus 4 figures (ps), revision includes brief comparison of repulsive-interaction vs. fixed-N fluctuation damping. To be published in Phys. Rev.

Renormalization Effects in a Dilute Bose Gas

The low-density expansion for a homogeneous interacting Bose gas at zero temperature can be formulated as an expansion in powers of $\sqrt{\rho a^3}$, where $\rho$ is the number density and $a$ is the S-wave scattering length. Logarithms of $\rho a^3$ appear in the coefficients of the expansion. We show that these logarithms are determined by the renormalization properties of the effective field theory that describes the scattering of atoms at zero density. The leading logarithm is determined by the renormalization of the pointlike $3 \to 3$ scattering amplitude.Comment: 10 pages, 1 postscript figure, LaTe

Three-Fluid Description of the Sympathetic Cooling of a Boson-Fermion Mixture

We present a model for sympathetic cooling of a mixture of fermionic and bosonic atomic gases in harmonic traps, based on a three-fluid description. The model confirms the experimentally observed cooling limit of about 0.2 T_F when only bosons are pumped. We propose sequential cooling -- first pumping of bosons and afterwards fermions -- as a way to obtain lower temperatures. For this scheme, our model predicts that temperatures less than 0.1 T_F can be reached.Comment: 9 pages, 6 figure

Frequency down conversion through Bose condensation of light

We propose an experimental set up allowing to convert an input light of wavelengths about $1-2 \mu m$ into an output light of a lower frequency. The basic principle of operating relies on the nonlinear optical properties exhibited by a microcavity filled with glass. The light inside this material behaves like a 2D interacting Bose gas susceptible to thermalise and create a quasi-condensate. Extension of this setup to a photonic bandgap material (fiber grating) allows the light to behave like a 3D Bose gas leading, after thermalisation, to the formation of a Bose condensate. Theoretical estimations show that a conversion of $1 \mu m$ into $1.5 \mu m$ is achieved with an input pulse of about $1 ns$ with a peak power of $10^3 W$, using a fiber grating containing an integrated cavity of size about $500 \mu m \times 100 \mu m^2$.Comment: 4 pages, 1 figure

Order Parameter at the Boundary of a Trapped Bose Gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

A Closed Class of Hydrodynamical Solutions for the Collective Excitations of a Bose-Einstein Condensate

A trajectory approach is taken to the hydrodynamical treatment of collective excitations of a Bose-Einstein condensate in a harmonic trap. The excitations induced by linear deformations of the trap are shown to constitute a broad class of solutions that can be fully described by a simple nonlinear matrix equation. An exact closed-form expression is obtained for the solution describing the mode {n=0, m=2} in a cylindrically symmetric trap, and the calculated amplitude-dependent frequency shift shows good agreement with the experimental results of the JILA group.Comment: RevTex, 4 pages, 1 eps figure, identical to the published versio