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.