Non-equilibrium dynamics in strongly interacting 1D quantum

Non-equilibrium dynamics and relaxation is not only central to many of the most fundamental questions in modern physics, connecting statistical mechanics and quantum physics. What determines whether, and how, an isolated system out of equilibrium relaxes ? will it reach a thermal state? Significant progress has been made for weakly interacting systems, and for discrete lattice settings, but there are very few experimental investigations in the strongly interacting regime. In our project we will experimentally study non-equilibrium evolution and relaxation in strongly interacting 1D quantum systems of Bosons, Fermions and in the in-between BEC-BCS crossover regime. We focus on two main objectives exploring non-equilibrium evolution and relaxation in the strongly interacting regime: (1) Experimental tests of the recently developed Genralized Hydrodynamics (GHD), a new method to describe dynamics in 1D systems. We will investigate if the theory of GHD can be extended towards the very strongly interacting limit, the BEC-BCS crossover and to 1D Fermions. (2) Nonequilibrium evolution of 1D quantum systems in the whole range from strongly interacting Bosons through the BEC-BCS cross over deep into 1D fermion system. Experiments will be conducted with strongly interacting quantum gas of 6Li fermions and 6Li2 bosonic molecules in a single layer of 1D tubes. The 1D systems will be individually probed (1) in situ through the evolution of density and momentum (rapidity); and (2) by measuring interference and correlations, to observe how the many-body system and its macroscopic wavefunction evolves. Splitting a single 1D system into double well potentials enable matter wave interference and the study of coherence. Single-atom-sensitive florescence imaging will be used to observe the 1D gases at the single-atom level, and extract quantum correlations giving insight into the many body phases and their field theory description. Strong suppression of collisional loss processes for 6Li2 molecules offers an exceptionally long sample lifetime, hence a unique window to extend nonequilibrium studies into both, the strongly interacting regime, and to long evolution times. Tuning the interactions using Feschbach resonances allows us to explore a large variety of systems ranging from strongly interacting bosons to Tonks gas (fermionized bosons), and through the BEC-BCS crossover to superfluid BCS like fermion pairs. We will probe the quantum evolution of this superfluid fermi gas through novel methods employing interference and correlation. Our proposed setup has the advantages: - Directly imaging single systems of 1D gases mitigating effects of ensemble averaging. - Highly sensitive fluorescence imaging allows quantum limited measurement and detailed studies of (high order) correlations in density and phase. - By performing many experiments in parallel in the optical lattice, we significantly enhance the statistics.

This project developed the experiments with ultracold 6Li atoms for the investigation of strongly interacting one-dimensional (1D) systems of bosons, fermions, and in the BEC-BCS crossover. The dynamics and relaxation of strongly correlated non-equilibrium systems remains one of the fundamental challenges of modern physics. Whether and how exactly does a quantum many-body system - a collection of interacting quantum particles - find its way back to an equilibrium state? The goal of the project was the investigation of such non-equilibrium dynamics for strongly interacting systems and for long evolution times, made possible by the strong suppression of loss processes for 6Li-2 molecules. Through magnetic fields, the interactions can be tuned by means of so-called Feshbach resonances. This makes it possible to explore a multitude of strongly interacting systems from Tonks gases (fermionized bosons) through the BEC-BCS crossover to superfluid fermions. A central success was the preparation of one-dimensional "tubes" of strongly interacting atoms. Loading a single layer of these 1D clouds, together with the developed fluorescence imaging of single atoms and the first results on the interference of multiple clouds of bosonic Li6 molecules, enables further experiments which measure the fluctuations of density and/or phase within individual gases. In weakly interacting systems, this full counting statistics has in recent years contributed to significant developments in the understanding of complex many-body systems. An important achievement of this project is the implementation of an experimental platform for the investigation and expansion of these questions in the field of strongly correlated quantum systems. As a first extension, the measured relaxation of a strongly perturbed system could be described by universal behavior far from thermal equilibrium. Independent of the microscopic details and interactions, the evolution of the system near such non-thermal fixed points is completely determined by a few universal parameters. The demonstrated connection to universal dynamics in weakly interacting rubidium gases opens up exciting further investigations; from potential deviations from quantum field theoretical predictions due to the strong interactions or in the long-term evolution towards universal corrections to 1D dynamics due to the radial expansion of the atomic cloud. Experimental tests of the recently developed generalized hydrodynamics (GHD) further open up a complementary approach to understanding these dynamics here. Based on the mathematical integrability of special one-dimensional systems, GHD allows dynamical processes in 1D systems to be described independently of their interaction strength. The experimental control of the interactions and external potentials achieved in the project allowed for first implementations of the ongoing detailed investigation of the validity of GHD or its extensions. Taken together, these advances create a versatile platform for the exploration of quantum many-body physics and lay the foundation for future precision measurements in a variety of strongly interacting systems.