Eigenstates Transition Without Undergoing an Adiabatic Process

TL;DR

This paper presents a novel class of non-Hermitian Hamiltonians enabling rapid state transitions without slow adiabatic processes, reducing complexity and cost while applicable across various physical systems.

Contribution

Introduction of a simple, lower-cost non-Hermitian Hamiltonian framework for shortcut to adiabaticity applicable in multiple dimensions.

Findings

Eigenvalues include one real and one complex, enabling exponential decay or amplification.

The method achieves adiabatic-like outcomes through diabatic processes.

Extension to higher dimensions broadens practical applications.

Abstract

We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to short-cut to adiabaticity (DASA). In particular, in our proposed 2 * 2 Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This specific form of the eigenvalues helps us to exponentially decay the population in an undesired eigenfunction or amplify the population in the desired state while keeping the probability amplitude in the other eigenfunction conserved. This provides us with a powerful method to have a diabatic process with the same outcome as its corresponding adiabatic process. In contrast to standard shortcuts to adiabaticity, our Hamiltonians have a much simpler form with a lower thermodynamic cost. Furthermore, we show that DASA can be extended to higher dimensions using the parameters associated with our 2 * 2 Hamiltonians. Our proposed Hamiltonians not only have application in DASA but also can be used for tunable mode selection and filtering in acoustics, electronics, and optics.