Correlations and thermalization in 1D atomic gases

Correlations and coherence are important features of many-body (quantum) systems. Reduced dimensionality usually enhances the correlations, and often paves the way to analytic treatment of important fundamental aspects of the quantum system. Therefore one-dimensional (1D) systems are of great importance in many-body quantum theory. Relevant models, such as Lieb-Liniger, Gaudin-Yang, sine-Gordon or Hubbard, provide deep insight into many-body physics in general. They also establish theoretical concepts that can be further extended to non-ideal experimental settings and towards 2D and 3D systems. All experiments are carried out in a 3D world, and an important question that arises is to which extent is 1D physics applicable in the real 3D world implementation of 1D systems. To study the conditions and limits of one- dimensionality in ultracold-atom (bosonic) systems in elongated traps is the general goal of the proposed project. This physical system is especially interesting because there exist well-established experimental techniques for preparation, control and measurement, and new ones are steadily emerging. The goal of the present project is to bring together the theory of 1D systems with these powerful experimental techniques to probe many-body quantum effects and put our knowledge on low-dimensional quantum systems to a stringent test. For that we will have to adapt and develop novel theoretical methods to allow to describe realistic experimental setups, which are not fully 1D, which are at finite temperature, and which allow to probe non- equilibrium properties. The proposed research will test one-dimensional theory models on a real-world 3D implementation of (quasi) 1D systems using ultracold atoms. We expect that this project will yield insight into the applicability of reduced analytical models also for other physical realizations and device new methods for their characterizations.

Ultracold bosonic atoms trapped on atom chips provide quite a close experimental implementation of the celebrated quantum Lieb-Liniger model. The presence of the whole set of non-trivial integrals of motion, whose number is the same as the number of the degrees of freedom in the system, should strongly affect the dynamics of the system and was expected to prohibit thermalization. However, degenerate atomic samples trapped on atom chips always demonstrated properties describable, by all practical purposes, by a thermal ensemble. What was the reason for such behaviour? Contrary to our previous expectations, we found that relaxation to a steady state very close to a thermal state occurs in such a system for phonon modes. No violation of integrability is needed to redistribute populations between different phonon modes. However, our numerical studies show that if we prepare a non-equilibrium distribution of population of short-wavelength (free atom-like) modes than the relaxation is extremely slow and takes far longer than any realistic experiment duration. This thermalization process occurs for typical experimental conditions at times of the order of 100 ms or longer. However, experiments with fast-split atomic quasicondensates clearly show a transient process on times ~10 ms that leads to the establishment of a quasistationary state subject to further thermalization. The nature of this transient process, known as pre-thermalization, was understood in detail. The fast pre-thermalization process is shown to occur due to a dephasing (not a damping!) of phonons. These results make integrable 1D systems much more similar to conventional, non-integrable systems and, hence, more suitable as models for studies fundamental problems of the out-of-equilibrium dynamics. In other words, the physics of atomic quasicondenstaes on atom chips finds thereby a new, less isolated place in the general context of many-body non-equilibrium physics.