Geometric contribution to adiabatic amplification in non-Hermitian systems

TL;DR

This paper explores how geometric phases in non-Hermitian systems influence wave amplification or decay, revealing path-independent amplification factors linked to symmetries and Petermann factors, with potential experimental applications.

Contribution

It identifies classes of non-Hermitian Hamiltonians with path-independent amplification factors determined by initial and final states, connecting geometric phases to observable quantities.

Findings

Path independence of amplification when imaginary Berry curvature is zero

Amplification factor expressed via Petermann factors at endpoints

Experimental method proposed to measure Petermann factors

Abstract

Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the non-Hermitian analog of the Berry phase for adiabatic processes was experimentally measured. In non-Hermitian systems, the Berry phase can have an imaginary part, which contributes to the amplification or decay of the total wave intensity. When the imaginary part of the Berry curvature is zero, this geometric amplification factor is determined solely by the initial and final points of the adiabatic path in parameter space, and it does not depend on how these points are connected by the path. We list classes of non-Hermitian Hamiltonians where this path independence is guaranteed by suitable symmetries, and we find that, for some of these classes, the amplification factor can be written only in terms of the Petermann factors of the initial and final points. Our result can, in turn, be used to experimentally obtain the Petermann factor by observing how the norm of the wave function changes under adiabatic processes. We validate our theory using a couple of concrete examples of physical relevance.