Quantum dynamics of ultracold atomic gases far from equilibrium
Final Report Abstract
The theoretical formulation of non-equilibrium quantum dynamics is an outstanding and exciting problem of present-day physics. Non-equilibrium dynamics emerges in contrast to a slow gradual evolution during which a system keeps, at any time, essentially equilibrium properties. Despite almost seven decades of developing many-body theory, non-equilibrium quantum dynamics is relatively little understood. The research project was focused on the development and application of functional quantum field theoretical methods to describe non-equilibrium dynamics of quantum many-body systems. The methods include Kadanoff-Baym type equations derived from non-perturbative two-particle irreducible (2PI) effective actions, functional renormalisation-group methods, semi-classical simulations, as well as Bethe-ansatz techniques. Applications were focused on ultracold atomic quantum gases. The technological possibilities available today for studying quantum many-body dynamics with such systems are unique. They allow to freely and precisely model initial states, to control both the trapping geometries and the strength of the interatomic collisions. Refined optical systems allow to observe in detail the ensuing dynamical evolution. Major parts of the project focused on to the long-time evolution of one-dimensional (1D) quantum gases and on universal dynamics and turbulence in quenched superfluids. The 2PI techniques were adapted and applied successfully to study equilibration of 1D Bose and Fermi gases. While, initially, the phenomena of interest were, in particular, the long-time evolution towards thermal equilibrium, the later development of the project showed that relatively short-time evolution bears a wide range of interesting new aspects which had been essentially neglected before in condensed-matter and quantum many-body theory. As a result, the project could contribute essential steps in what can soon lead to a whole new field of research, viz. that of universal dynamical evolution far from thermal equilibrium. An important step was to show analytically that many-body quantum systems such as ultracold Bose gases can show new types of strongly wave turbulent states which can be related to previously proposed non-thermal fixed points (NTFP). This progress became possible by combining the non-perturbative 2PI dynamic equations with wave turbulence methods well developed in the context of kinetic theory. From this, an extensive research program emerged which lead to new exciting insight into far-from-equilibrium universal dynamics of quantum many-body systems. It was, in particular, shown that the NTFP solutions can be interpreted in the context of the dynamics of non-linear field excitations. A central result is that NTFPs are represented by characteristically correlated ensembles of (quasi-)topological defects such as vortices, vortex lines and rings, solitons, domain walls, or skyrmions, but can also be related to much less clearly shaped strongly non-linear excitations. In this way, the long-sought link between wave turbulence and hydrodynamic turbulence, in our case in a superfluid, could be established. While the project was focused mostly on ultracold gases, the results have a strong cross-disciplinary impact. Studying relativistic scalar and gauge field theories analogous results emerged in completely different phenomenological contexts, including quark-gluon plasma formation in heavy-ion collisions and early-universe inflation. The project initiated direct collaborations with experimental groups in the field of ultracold gases aiming at the realisation and study of universal dynamics.
Publications
- Fermi-Bose transformation for the time-dependent Lieb- Liniger gas, Phys. Rev. Lett. 100, 080406 (2008)
H. Buljan, R. Pezer, and T. Gasenzer
- Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach, Phys. Lett. B670, 135 (2008)
T. Gasenzer and J. M. Pawlowski
- Matter-wave turbulence: Beyond kinetic scaling, Phys. Rev. A 81(3), 033611 (Mar 2010)
C. Scheppach, J. Berges, and T. Gasenzer
- Far-from-equilibrium dynamics of an ultracold Fermi gas, Appl. Phys. B 102, 469 (2011)
M. Kronenwett and T. Gasenzer
- Real-time effective-action approach to the Anderson quantum dot, Phys. Rev. B 83, 165315 (2011)
D. Sexty, T. Gasenzer, and J. Pawlowski
- Superfluid Turbulence: Nonthermal Fixed Point in an Ultracold Bose Gas, Phys. Rev. B 84, 020506(R) (2011)
B. Nowak, D. Sexty, and T. Gasenzer
- Critical Dynamics of a Two-dimensional Superfluid near a Non-Thermal Fixed Point, Phys. Rev. A 86, 013624 (2012)
J. Schole, B. Nowak, and T. Gasenzer
(See online at https://doi.org/10.1103/PhysRevA.86.013624) - Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas, Phys. Rev. A 85, 043627 (2012)
B. Nowak, J. Schole, D. Sexty, and T. Gasenzer
(See online at https://doi.org/10.1103/PhysRevA.85.043627) - Tuning universality far from equilibrium, Scientific Reports 3 (Aug. 2013)
M. Karl, B. Nowak, and T. Gasenzer
- Gauge turbulence, topological defect dynamics, and condensation in Higgs models, Nucl. Phys. A 930, 163 (2014)
T. Gasenzer, L. McLerran, J. M. Pawlowski, and D. Sexty
(See online at https://doi.org/10.1016/j.nuclphysa.2014.07.030)
