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Bose-Einstein Condensation in magneto-optical traps
Basics

In 1995 the first so-called atomic Bose-Einstein Condensate has been produced by a couple of physicists from Boulder/Colorado. Using a new type of atom trap the group at JILA managed to cool a dilute gas of around 2000 Rubidium 87 atoms to temperatures of a few hundred nanokelvins.
In 1925 - after a correspondence with Satyendrah Nath Bose - Albert Einstein predicted that identical particles with integer spin (bosons) under certain circumstances condense in a single quantum state. This means that in particular all particles have the same positions and velocities.
If you would like to know more about this topic, there is a very good introduction with lots of JAVA applets on the web: Physics 2000
A poster presentation for pupils (in german) is available as PDF and as PS file.

Some selected Links


Zeros of the canonical
partition function

We developed a Classification scheme for phase transitions in finite systems based on the Lee-Yang zeros in the complex temperature plane. Next to other systems we apply this classification scheme to Bose-Einstein condensates in a harmonic trap.
The results of a detailed study of finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.

Recursion formulars

We developed recursion formulars for the calculation of thermodynamic properties of finite systems, which can be utilized to describe Bose-Einstein condensates.
Click here for a recursion for the canonical partition function and here for a recent approach we utilized to study the ground state fluctuations and specific heats of ideal Bose-gases.
The parameters of the JILA TOP trap have been utilized to demonstrate the usefulness of the recursion formulars in detail. The results are given in a Diploma thesis. There are also lots of pictures and animations available.
There is a simple Java program which illustrates the use of our recursion formula. Just download the file BoseJava.tar.gz, unpack it, and type java Bose (This assumes that you have a properly installed java environment).

List of publications on Bose-Einstein Condensation:

  • O. Mülken, P. Borrmann, J. Harting, H. Stamerjohanns:
    Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros
    XXX-Eprint Cond-Mat 0006293


  • P. Borrmann, O. Mülken, J. Harting:
    Classification of phase transitions in small systems
    Phys. Rev. Lett. 84, 3511 (2000).

  • P. Borrmann, J. Harting, O. Mülken, E. R. Hilf:
    Calculation of thermodynamic properties of finite Bose-Einstein systems
    Physical Review A 60, pp. 1519-1522 (1999)


  • P. Borrmann, G. Franke:
    Recursion formulas for quantum statistical partition functions
    J. Chem. Phys. 98, p. 2484 (1993)


  • J. Harting:
    Bose-Einstein-Kondensation in magnetischen und optischen Fallen
    Diploma thesis, Dept. of physics, University of Oldenburg (1999)  - only available in german
    • Last updated on 8.12.2000
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