Research Group Prof. Dr. R. Graham 


Quantum Optics including BoseEinstein Condensation 
BoseEinstein 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 BoseEinstein condensate of Alkali atoms in magnetooptical 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 breakthrough. Now many groups around the world are capable of routinely preparing BoseEinstein 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 multicomponent 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 multicomponent 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 'Boseglass' or 'Andersonglass' phases in particular. 

Quantum chaos in BoseEinstein condensates:
Our interest in 'random bosons' also encompasses dynamically induced randomness in manyboson systems whose classical manifestations, either on the level of the classical macroscopic wavefunction or on the level of the quasiparticles, 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 chaosinduced diffusive increase of kinetic energy in a BoseEinstein condensate in a quasi onedimensional ringtrap upon periodic pulsed electromagnetic excitations with and without timereversal of the nonlinear matterwave in the middle of the observation interval, which can be achieved by nonlinear 4wave mixing. 
Fig. 2 (condmat/0405057) 
Fig.3 displays a Poincaré crosssection of the chaotic quasiparticle dynamics in an anisotropic parabolic trap with energies intermediate between the collective mode (phonon) regime and the singleparticle (free particle) regime. 
Fig. 3 (Phys.Rev.A, 56(6) 1997) 
Research Group Prof. Graham last changes 11.2008