[PhD Thesis Presentation] ‐Irina Reshodko‐ State engineering in one-dimensional quantum gases

Abstract

  The development of quantum technologies requires the understanding, controlling and engineering of quantum states of interacting systems, a challenge currently driven by experimental progress. In this work I study, both analytically and numerically, two specific models of one-dimensional ultracold atomic systems to determine their states and accessible dynamical behaviour. The first part of the work deals with the creation of a bosonic atom dispenser, a tool which would allow to deterministically separate any number of atoms from an interacting ultracold gas or create a many-particle noonstate. By engineering
an effectively three-level system, I show that a robust adiabatic process exists that connects the initial and target Fock states. Moreover, I demonstrate its potential to be experimentally implemented using radio-frequency traps.
  In the second part, I derive an analytical single-particle solution for the arbitrary finite Kronig–Penney model. In this model the atoms are trapped in an infinite square well which contains an arbitrary number of arbitrarily positioned point-like barriers of arbitrary heights. I also demonstrate that using certain parameters in the model as extra (virtual) dimensions one can observe the emergence of higher-dimensional physics in this one-dimensional system. In particular, I show the appearance of edge states and the emergence of a Hofstadter butterfly-like momentum spectrum in various configurations of
the model. Finally, using the single-particle solutions, I study many-body correlations in a gas of either infinitely repulsive bosons or non-interacting fermions.