Non-Hermitian state control beyond conventional adiabatic theorem

Abstract

Non-Hermitian quantum systems, often characterized by gain and loss terms, have recently been developed, offering a new dimension for quantum state control by expanding the Hermitian Hamiltonian into the non-Hermitian regime. In this thesis, we aim to explore approaches for state control with non-Hermiticity that go beyond the conventional adiabatic theorem. Specifically, on the one hand, we focus on achieving state control through nonadiabatic transitions (NATs) near an exceptional point (EP, a non-Hermitian degeneracy), which arise from the competition between interband coupling and complex dynamic phase factors. Unlike NATs in Hermitian systems, which are typically triggered by strong interband coupling with rapidly varying parameters, these transitions are more robust, having no restrictions such as very fast parameter changes or specific initial and final state positions far from the band gap. To start my investigations, I explore the chiral behavior induced by NATs in a many-body spin-orbit-coupled cold-atom system through experimental collaboration. Here, the chiral behavior refers to the phenomenon in which the final state depends only on the encircling direction of parameter changes around an EP rather than on the initial state. Additionally, we found that NATs near the EP can serve as an intermediate process to facilitate interband transitions between energy bands in momentum space. Together with intraband transitions governed by the adiabatic theorem, we achieved full control of band transitions (both intraband and interband) in momentum space. On the other hand, we investigate how to avoid NATs and restore the adiabatic theorem in rapidly time-varying Hermitian and non-Hermitian systems. These methods, known as shortcuts to adiabaticity (STA), include approaches for minimizing or shutting down interband coupling. First, in a Hermitian system, I test and enhance minimization techniques, specifically fast quasiadiabatic driving (FAQUAD). This approach allows for seemingly adiabatic evolution in a significantly shorter time than conventional adiabatic methods permit. We utilize a coupled elastic waveguide system to mimic the quantum system for experiments, as the mapping of elastic waves facilitates easier examination of the intermediate processes. In non-Hermitian systems, we employ methods to shut down interband coupling, referred to as non-Hermitian shortcuts, to achieve seemingly adiabatic evolution near the EP. To consider practical implementation, I propose modifying the coupled elastic waveguide system by attaching a thin layer of polydimethylsiloxane (PDMS), which provides sufficient tuning capability for the lossy term and facilitates future experiments. In this thesis, with a comprehensive understanding of NATs in non-Hermitian systems, I have achieved full control of band transitions, including both intraband and interband transitions, between the energy bands in momentum space. Moreover, with the STA, I accelerated the adiabatic process in Hermitian systems and avoided NATs in non-Hermitian systems. These concepts have been demonstrated in a quantum system (cold atoms) and a classical system (elastic system).

Date of Award	2024
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Jensen Tsan Hang LI (Supervisor)