Bose-Einstein Condensates

"Snapshot" of a BEC for a small positive scattering length

Theoretical descriptions of Bose-Einstein condensates (BECs) are typically based on so-called mean-field treatments such as the Gross-Pitaevskii or the Hartee-Fock equation. These approaches describe many properties of BECs impressively well, however, in some cases significant limitations of these approaches become apparent. Therefore, we follow an alternative avenue, namely, we consider the many-body Schroedinger equation. To solve this equation for many particles, however, we have to make some approximations. Our method of choice is the diffusion quantum Monte Carlo method (DMC). The figure on the left hand side shows one "snapshot" of a BEC with 50 particles confined in an external spherical trapping potential.

"Snapshot" of a BEC for a large positive scattering length

This picture shows, just as above, a condensate consisting of 50 particles in a spherical external trapping potential. In the picture above, we simulated the atom-atom potential through a hard-core potential with a small scattering length, here, in contrast, we use a hard core potential with a large scattering length. In this figure, the radius of the white balls, which each represent an atom, is equal to the two-body s-wave scattering length. Note, the scattering length in the above picture is so small that we have to represent the atoms through white balls with a radius that is a 100 times larger than the two-body scattering length (otherwise one wouldn't be able to see the atoms). We perform our studies as a function of the number of particles in the trap, of the scattering length, of the shape of the two-body potential, and of the frequency of the trapping potential, and compare our results with those obtained from mean-field treatments.

Our studies focuss on many-body effects of Bose-Einstein condensates. To assess the validity of commonly used mean-field treatments we solve the full Hamiltonian. To make such calculations feasible, we typically describe the atom-atom potential through a model potential, which "throws out" many of the deeply bound states. These deeply bound states can be ascribed to solid state/cluster physics rather than BEC physics. Currently, we're focussing on two sets of calculations. One set of calculations investigates the energy dependence of two or three particles under external confinement as a function of the two-body scattering length. The other set of calculations uses quantum Monte Carlo techniques, which allow us to treat as many as 100 particles in the trap.

Back to Doerte's Main Page

Doerte Blume

Last modified: 27 November, 2001