Statistical mechanics, a century-old theory, is probably one of the most powerful constructions of physics. It predicts that the equilibrium properties of any system composed of a large number of particles depend only on a handful of macroscopic parameters, no matter how the particles exactly interact with each other. From the viewpoint of classical physics, equilibration occurs because the microstate of the system uniformly explores the phase space over time — this is the long-known concept of ergodicity. But in quantum mechanics things are different: because quantum dynamics constrains the microstate to evolve along a periodic orbit in the Hilbert space, which is the quantum equivalent of the classical phase space. In the absence of classical ergodicity, what mechanism can then lead to the equilibration of an isolated quantum system? And how long will it take? Answering these questions is not only of fundamental interest. It will also help understand what limits the speed at which quantum information can be transported, or how fast one can change the state of a quantum system, with direct impact on future quantum technologies.
The concept of this project is to take advantage of the great versatility offered by ultra-cold atom systems to investigate the relaxation dynamics in regimes well beyond the boundaries of our current knowledge. We focus our attention on two-dimensional systems and systems with both short- and long-range interactions. Specifically, we will set the system out of equilibrium by a sudden change of the interaction parameter, a ‘quantum quench’, and characterise both the relaxation dynamics and the final state through the measurement of two-point correlation functions. The realisation of the project hinges on the construction of a new-generation quantum gas microscope experiment for Strontium gases enabling us to induce long-range interactions between the atoms. Beside the construction of this apparatus, our main scientific objectives are: (i) to confront the locality of the dynamics to a two-dimensional geometry, where most of the existing results have been obtained in a one-dimension geometry; (ii) to explore situations where quasiparticles are absent or short-lived, and see whether correlations still propagate in ballistic manner; (iii) to study the relaxation dynamics in the presence of long-range interactions, where counter-intuitive behaviours have been predicted, but not yet observed.
