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.

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.

Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.

Broadband Achromatic Metasurfaces for Longwave Infrared Applications

Longwave infrared (LWIR) optics are essential for several technologies, such as thermal imaging and wireless communication, but their development is hindered by their bulk and high fabrication costs. Metasurfaces have recently emerged as powerful platforms for LWIR integrated optics; however, conventional metasurfaces are highly chromatic, which adversely affects their performance in broadband applications. In this work, the chromatic dispersion properties of metasurfaces are analyzed via ray tracing, and a general method for correcting chromatic aberrations of metasurfaces is presented. By combining the dynamic and geometric phases, the desired group delay and phase profiles are imparted to the metasurfaces simultaneously, resulting in good achromatic performance. Two broadband achromatic metasurfaces based on all-germanium platforms are demonstrated in the LWIR : a broadband achromatic metalens with a numerical aperture of 0.32, an average intensity efficiency of 31%, and a Strehl ratio above 0.8 from 9.6 μm to 11.6 μm, and a broadband achromatic metasurface grating with a constant deflection angle of 30° from 9.6 μm to 11.6 μm. Compared with state-of-the-art chromatic-aberration-restricted LWIR metasurfaces, this work represents a substantial advance and brings the field a step closer to practical applications.