A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics

We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states appearing for non-Hermitian Hamiltonians. We start with an investigation of the space of non-degenerate operators on a finite-dimensional state space. We then show how the energy bands of a Hamiltonian family form a covering space. Likewise, we show that the eigenrays form a bundle, a generalization of a principal bundle, which admits a natural connection yielding the (generalized) geometric phase. This bundle provides in addition a natural generalization of the quantum geometric tensor and derived tensors, and we show how it can incorporate the non-geometric dynamical phase as well. We finish by demonstrating how the bundle can be recast as a principal bundle, so that both the geometric phases and the permutations of eigenstates can be expressed simultaneously by means of standard holonomy theory.

Ultrathin Spin-Decoupled Meta-Devices for Independent Control of Electromagnetic Waves With Dual-Orthogonal Circular Polarization

Inspired by the concept of miniaturized and integrated systems, an ultrathin and multifunctional metasurface device is highly desirable in microwave fields. It is an inherent characteristic that the two spin phase states of electromagnetic waves imparted by the geometric phase are always conjugate symmetric, i.e., the geometric phase produces anti-symmetrical phase responses between dual-orthogonal circular polarization states. So it is extremely crucial to break the conjugate constraints and realize the completely independent control of electromagnetic waves with dual-orthogonal circular polarization. Based on this perspective, ultrathin and bifunctional meta-devices operating in reflection mode are proposed to independently manipulate the left-handed and right-handed circularly polarized waves, which are constructed by anisotropic meta-atoms with synthetical geometric and propagation phases. It is worth noting that the component elements only need a single-layer structure with the thickness of 0.07λ0. Several design samples are presented to achieve functionalities of beam focusing, vortex wave generation, and beam deflection, respectively. Experiments are performed and show good consistence with the simulation results, successfully verifying the performance of the designed metasurfaces. The research results in this paper pave the way to design low-profile and bifunctional devices with independent controls of circularly polarized waves, which is expected to expand the working capacity of metasurfaces to realize complex electromagnetic wave manipulation with a new degree of freedom.

Angular momentum redirection phase of vector beams in a non-planar geometry

An electric field propagating along a non-planar path can acquire geometric phases. Previously, geometric phases have been linked to spin redirection and independently to spatial mode transformation, resulting in the rotation of polarisation and intensity profiles, respectively. We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle. The geometric phase acquired is proportional to j = ℓ + σ, where ℓ is the topological charge and σ is the helicity. Radial and azimuthally polarised beams with j = 0 are eigenmodes of the system and are not affected by the geometric path. The effects considered here are relevant for systems relying on photonic spin Hall effects, polarisation and vector microscopy, as well as topological optics in communication systems.