Research Group Prof. Dr. R. Graham  



  Quantum Optics including Bose-Einstein Condensation

Bose-Einstein Condensation

Bose-Einstein condensation occurs in a system of Bosons at low temperatures and high densities if the thermal wavelength approaches the order of the mean particle distance, as predicted by Einstein for the ideal Bose gas in 1925. Below the critical temperature a finite fraction of all particles occupies the same quantum state and forms a coherent matter sample, giving rise to macroscopic quantum effects like matter interference.

In 1995 two experimental groups succeeded in forming a Bose-Einstein condensate of Alkali atoms in magneto-optical atom traps at temperatures of some 100 nK. Since Alkali gases are weakly interacting many body systems, these experiments allow for the first time to test experimentally predictions about Bose condensation quantitatively.

This has been done extensively over the last decade culminating in the award of theNobel prize of 2001 to the experimentalists who achieved this break-through. Now many groups around the world are capable of routinely preparing Bose-Einstein Condensates in their laboratories.
Our theoretical group, which contributed since 1996 to this field, is at present mostly interested in the following aspects:

Strongly correlated quantum gases in periodic lattices:
Placing Bose or Fermi gases at negligibly small temperature in periodic optical potentials and/or reducing their dimensionality to 2 or 1 by suitably confining potentials can greatly enhance their internal interaction and may lead to strongly correlated phases like Mott insulators. In multi-component systems such as atoms with internal degrees of freedom this can lead to quite complicated phase diagrams such as shown in fig.1, which is taken from one of our recent publications. We are investigating e.g. the coexistence of localized insulating 'gapped' and delocalized superfluid 'ungapped' phases in multi-component systems.
Fig. 1 (Phys.Rev.Lett. 91(24) 2003)
Strongly correlated quantum gases in random lattices:
within two projects in the Sonderforschungsbereich/Transregio 12 Symmetries and Universality in Mesoscopic Systems, we investigate mathematical and physical aspects of 'random bosons' in general, with application to localized insulating but ungapped 'Bose-glass' or 'Anderson-glass' phases in particular.
Quantum chaos in Bose-Einstein condensates:
Our interest in 'random bosons' also encompasses dynamically induced randomness in many-boson systems whose classical manifestations, either on the level of the classical macroscopic wave-function or on the level of the quasi-particles, is dynamical chaos. Examples for such effects from our recent work are shown in figures 2 and 3.
Fig.2  (taken from B. Mieck and R. Graham, in preparation) portrays the chaos-induced diffusive increase of kinetic energy in a Bose-Einstein condensate in a quasi onedimensional ring-trap upon periodic pulsed electromagnetic excitations with and without time-reversal of the nonlinear matter-wave in the middle of the observation interval, which can be achieved by nonlinear 4-wave mixing. p2g50c.jpg
Fig. 2 (cond-mat/0405057)

Fig.3  displays a Poincaré cross-section of the chaotic quasi-particle dynamics in an anisotropic parabolic trap with energies intermediate between the collective mode (phonon) regime and the single-particle (free particle) regime.
Fig. 3 (Phys.Rev.A, 56(6) 1997)

Research Group Prof. Graham     last changes 11.2008