Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
Doi
Abstract
The field of quantum simulations has achieved a remarkable success through the
development of highly controllable and accessible quantum platforms, which pro-
vide insights into the microscopic properties of complex large-scale systems that
are otherwise difficult to analyze. Many of the platforms utilized in this pursuit are
derived from the field of atomic, molecular, and optical physics. One particularly
popular candidate is provided by trapped ions, whose vibrational and electronic
degrees of freedom can be effectively combined through laser pulses to engineer
desired model Hamiltonians or quantum circuits. Trapped ions constitute as well
the basis for modern atomic clocks, the most precise frequency standards currently
available. They find further applications in metrology, geodesy, and fundamental
physics experiments.
In this Thesis, we investigate the dynamics of vibrational modes in trapped
ion crystals, utilizing them as a versatile platform to explore various many-body
phenomena.
We first focus on the expansion dynamics of local excitations and on heat
transport within ion crystals hosting structural defects that undergo a sliding-
to-pinned transition. We observe a significant reduction in conductivity when
the crystal symmetry is spontaneously broken during the transition, and show
that resonances between crystal eigenmodes lead to distinct softening signatures
associated with energy localization. We then delve into the effects of thermal and
quantum fluctuations on the vibrational modes of ion crystals near two distinct
structural transitions. We observe the emergence of a prolonged symmetric phase
stabilized by thermal and quantum fluctuations, and develop effective theories that
reduce the degrees of freedom to the modes that drive the transitions.
Finally, we discuss how to engineer spin-orbit coupling and on-site interaction
energies for vibrational quantum excitations using two different external driving
schemes. While the simulation of spin models with ions typically involves the use
of two electronic states, we propose interpreting the two local oscillation modes
in an ion crystal as a pseudospin. We show how using Floquet engineering ideas
allows for spin flips in Coulomb-induced vibron hopping, resulting in a non-trivial
coupling between spatial motion and spin evolution, that results in a markedly non-Abelian dynamics. Subsequently, we explore the simulation of Hubbard models in
trapped ions by coupling the vibrational Fock states to an internal level system.
Our findings include the observation of bound states in the strong interaction limit
of the resulting Jaynes-Cummings-Hubbard model.
By investigating these topics, we aim to contribute to the understanding of
vibrational dynamics in trapped ion crystals, and shed light on their potential for
simulating condensed matter systems, offering insights into phenomena that are
otherwise challenging to explore.DFG/Sonderforschungsbereich 1227 DQ-mat/274200144/E