A method of preparing individual excited eigenstates of small quantum many-body systems

Abstract

Any quantum-mechanical system can be conveniently described in terms of a powerful set of states called eigenstates, which each possess a fixed energy and collectively encode crucial insights into the system's character and dynamics. Experiments in the field of quantum many-body mechanics have historically been focused on studying either systems close to their ground states, i.e. their lowest-energy eigenstates, or systems occupying many eigenstates simultaneously, whether coherently or in a thermal mixture. Experimental investigations of individual excited eigenstates, i.e. of eigenstates of much higher energy than the ground state, have not been performed, in large part due to technological challenges preventing their preparation. In this thesis, I propose a method which leverages the unique capabilities of quantum-gas microscopy to allow for the preparation of individual highly excited eigenstates of small quantum many-body systems. Following a brief introduction to the field of quantum-gas microscopy, I explain in detail how the proposed method can be used to prepare several highly excited eigenstates of a minimal many-body system comprised of four strongly interacting bosons on a four-site optical-lattice. I identify optical-potential disorder to be the biggest hurdle to the method's implementation in state-of-the-art experiments and comment extensively on how this challenge can be overcome, presenting an original proposal for in-situ disorder calibration in the process. In the second part of the thesis, I give an introduction to quantum thermalization and argue that methods like the one proposed here have the potential to provide the first experimental evidence for eigenstate thermalization, which is widely believed to be the fundamental mechanism by which generic quantum-mechanical systems thermalize. I illustrate this point by explaining how the proposed method can be used to prepare highly excited eigenstates of a four-particle, six-site system which is large enough to exhibit the level-spacing statistics typical of eigenstate-thermalizing systems. The thesis ends with a concluding chapter describing several ways in which the method might be further optimized and generalized in the near future.