Adiabatic Dynamics and Shortcuts to Adiabaticity: Fundamentals and Applications

TL;DR

This thesis advances understanding of adiabatic quantum dynamics and transitionless driving, introducing validation mechanisms, exploring decoherence effects, and proposing generalized shortcuts with experimental verification in ion and NMR systems.

Contribution

It introduces a validation method for adiabaticity, studies decoherence effects, and develops a generalized approach to shortcuts to adiabaticity using gauge freedom, with experimental demonstrations.

Findings

Adiabaticity can persist under decoherence in the infinite time limit for certain states.

Validation mechanisms for adiabatic conditions are established via non-inertial reference frames.

Experimental verification of theoretical predictions in ion traps and NMR systems.

Abstract

In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In the context of adiabatic dynamics in closed systems, it is introduced a validation mechanism for the adiabaticity conditions by studing the system dynamics from a non-inertial reference frame. By considering a decohering scenario, validity conditions of the adiabatic approximation are also studied. As a fresh general result with potential applications, it is shown that under decoherence the adiabaticity may still occur in the infinite time limit, as it happens for closed systems, for a class of initial quantum states. To end, the original contributions of this thesis to the theory of shortcuts to adiabaticity refers to a generalized approach of transitionless quantum driving, where one explores the gauge freedom of the quantal phase factors accompanying adiabatic trajectories. A number of theoretical applications are studied, where some theoretical prediction presented in this thesis are experimentally verified through two different experimental setups, namely a qubit encoded in the energy hyperfine structure of a Ytterbium trapped ion, and in nuclear magnetic resonance with a nuclear spin qubit.