Photoassoziations-Dynamik entarteter Quantengase: Vielteilchen-Quantentheorie fern des thermischen Gleichgewichts
Final Report Abstract
Atomic quantum gases belong to the most exciting challenges of modern physics. At temperatures below one Microkelvin, gases of bosonic atoms, i.e., such with an integer angular momentum quantum number, can contain a "Bose-Einstein condensate" in which all atoms are in the same state. Today, the theory of ultracold atomic gases is characterized by (semi-)classical field equations. Of outstanding importance are the Gross-Pitaevskii and Hartree-Fock(-Bogoliubov) theories as well as their perturbative extensions, cf. e.g.. These "mean-field" approximations are in general reliable for dilute gases, i.e., they presuppose that the gas atoms sufficiently rarely collide with each other. This is often equivalent to the condition that the gas is not too far from thermal equilibrium. The further the gas is driven or initially assumed to be away from equilibrium and the stronger the interactions between the atoms are, the shorter is the time over which semiclassical methods apply. Over longer times, collisions as well as classical and quantum fluctuations become important and require beyond-mean-field approaches. In the present project, non-perturbative techniques based on the two-particle-irreducible effective action have been extended for the description of non-equilibrium atomic quantum gases. It was shown that the theory describes well thermalization to an equilibrium Bose-Einstein distribution as well as the characteristics of the intermediate dissipative dynamics. With these methods, the consequences of complex multiple-scattering processes can be taken into account in an efficient way and quantum fluctuations be distinguished from classical ones. The focus was set on 1/M approximations, where M is the number of field components. The technique goes far beyond the quantum extension of the Boltzmann equation and therefore also beyond standard mean-field theory. The results of a subproject show that for a one-dimensional Bose-Hubbard gas, this non-perturbative approximation implies that for strong interactions the higher-order correlations are taken into account in a qualitatively correct way. However, they also show that for such a system with a low number of spatial degrees of freedom and thus of modes the considered approximation becomes quantitatively unreliable. The results obtained opened a number of important questions concerning the range of validity of the l/M equation, and the equilibration of integrable and non-integrable quantum systems. Moreover, concerning experiments with strongly interacting Bose and Fermi gases, the project has delivered the foundations for the development of a quantum dynamical many-body description which allows to investigate strongly correlated systems in more than one spatial dimension. This forms the basis for the study of many-body dynamics in the vicinity of so called magnetic and optical Feshbach resonance, both in Bose and Fermi gases of ultracold atoms. Not at last, making the advanced quantum-field theoretical methods accessible to precise atomic physics experimental verification, has important potential impact on other areas like heavy ion collisions or cosmology, where such methods are needed and much more difficult to check experimentally.
Publications
- Gasenzer, T, Berges, J., Seco, M., und Schmidt, M.G. (2007), Ultracold atomic quantum gases far from equilibrium, in: Proc. Int. Workshop on Strong and Electroweak Matter, SEWM 2006, BNL, Brookhaven, New York, May 2006; Nuclear Physics A 785, 214-217.
- Temme, K., und Gasenzer, T. (2006): Non-equilibrium dynamics of condensates in a lattice from the 2PI effective action in 1/N expansion, Physical Review A 74, 053603-1-9.
- Berges, J., und Gasenzer, T. (2007): Quantum versus classical statistical dynamics of an uitracold Bose gas, Physical Review A 76, 033604-1-19.
- Gasenzer, T, Berges, J., Seco, M., und Schmidt, M.G. (2005): Non-perturbative dynamical many-body theory of a Bose-Einstein condensate, Physical Review A 72, 063604-1-20.
