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We discuss the appearance of a missing geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with the magnetic field produced by a uniform distribution of the magnetic charges inside an infinitely long non-conductor cylinder with an inner radius rₐ. This geometric quantum phase is associated with the missing magnetic charge per unit length in a region with a cylindrical shape of radius rₐ and gives rise to an analogue of the He–McKellar–Wilkens geometric quantum phase. By searching for bound state solutions, we show that an Aharonov–Bohm-type effect arises from the influence of the missing geometric quantum phase on the eigenvalues of energy.

Metasurfaces based on geometric phase acquired from the conversion of the optical spin states provide a robust control over the wavefront of light, and have been widely employed for construction of various types of functional metasurface devices. However, this powerful approach cannot be readily transferred to the manipulation of acoustic waves because acoustic waves do not possess the spin degree of freedom. Here, we propose the concept of acoustic geometric-phase meta-array by leveraging the conversion of orbital angular momentum of acoustic waves, where well-defined geometric-phases can be attained through versatile topological charge conversion processes. This work extends the concept of geometric-phase metasurface from optics to acoustics, and provides a new route for acoustic wave control.

We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a 'bichromatic' interaction picture, we show that either ˆ φ ˆ φ or ˆ z ˆ z geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. The ˆ z ˆ z gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.

Shared-aperture technology for multifunctional planar systems, performing several simultaneous tasks, was first introduced in the field of radar antennas. In photonics, effective control of the electromagnetic response can be achieved by a geometric-phase mechanism implemented within a metasurface, enabling spin-controlled phase modulation. The synthesis of the shared-aperture and geometric-phase concepts facilitates the generation of multifunctional metasurfaces. Here shared-aperture geometric-phase metasurfaces were realized via the interleaving of sparse antenna sub-arrays, forming Si-based devices consisting of multiplexed geometric-phase profiles. We study the performance limitations of interleaved nanoantenna arrays by means of a Wigner phase-space distribution to establish the ultimate information capacity of a metasurface-based photonic system. Within these limitations, we present multifunctional spin-dependent dielectric metasurfaces, and demonstrate multiple-beam technology for optical rotation sensing. We also demonstrate the possibility of achieving complete real-time control and measurement of the fundamental, intrinsic properties of light, including frequency, polarization and orbital angular momentum. Metasurfaces: improved multitasking Nanoantennas that alter the phase of optical signals using geometric parameters bring multiple light-shaping capabilities to a single device. Erez Hasman from the Technion — Israel Institute of Technology and co-workers patterned silicon surfaces into a two-dimensional array of interspersed nanorods to promote both geometric phase modulation and sharing of nanoantenna aperture space. While this approach enables control over photonic spin and wavefront generation, it also creates speckle noise that can affect performance. The team used Wigner distributions, a quantum-based signal analysis method, to determine the ultimate information capacities of channels within geometric phase metasurfaces. Their evaluations propose ways to combine data-carrying optical angular momentum (OAM) beams with swirling light vortices into a device that could simultaneously determine the frequency, polarization, and OAM of light at different wavelengths.

We propose in this article a quantum square ring that conveniently generates, annihilates and distills the Aharonov Casher phase with the aid of entanglement. The non-Abelian phase is carried by a pair of spin-entangled particles traversing the square ring. At maximal entanglement, dynamic phases are eliminated from the ring and geometric phases are generated in discrete values. By contrast, at partial to no entanglement, both geometric and dynamic phases take on discrete or locally continuous values depending only on the wavelength and the ring size. We have shown that entanglement in a non-Abelian system could greatly simplify future experimental efforts revolving around the studies of geometric phases.

This article reviews recent progress leading to the generation of optical vortex beams. After introducing the basics of optical vortex beams and their promising applications, we summarized different approaches for optical vortex generation by discrete components and laser cavities. We place particular emphasis on the recent development of vortex generation by the planar phase plates, which are able to engineer a spiral phasefront via dynamic or geometric phase in nanoscale, and highlight the independent operation of these two different phases which leads to a multifunctional optical vortex beam generation and independent spin-orbit interaction. We also introduced the recent progress on vortex lasing, including vortex beam generation from the output of bulk lasers by modification of conventional laser cavities with phase elements and from integrated on-chip microlasers. Similar approaches are also applied to generate fractional vortex beams carrying fractional topological charge. The advanced technology and approaches on design and nanofabrications enable multiple vortex beams generation from a single device via multiplexing, multicasting, and vortex array, open up opportunities for applications on data processing, information encoding/decoding, communication and parallel data processing, and micromanipulations.

The photonic spin Hall effect (SHE) in the reflection and refraction at an interface is very weak because of the weak spin-orbit interaction. Here, we report the observation of a giant photonic SHE in a dielectric-based metamaterial. The metamaterial is structured to create a coordinate-dependent, geometric Pancharatnam–Berry phase that results in an SHE with a spin-dependent splitting in momentum space. It is unlike the SHE that occurs in real space in the reflection and refraction at an interface, which results from the momentum-dependent gradient of the geometric Rytov–Vladimirskii–Berry phase. We theorize a unified description of the photonic SHE based on the two types of geometric phase gradient, and we experimentally measure the giant spin-dependent shift of the beam centroid produced by the metamaterial at a visible wavelength. Our results suggest that the structured metamaterial offers a potential method of manipulating spin-polarized photons and the orbital angular momentum of light and thus enables applications in spin-controlled nanophotonics. Spin photonics: giant spin Hall effect observed A giant photonic spin Hall effect (SHE) has been predicted and experimentally observed in a dielectric metamaterial by scientists in China. The conventional SHE that occurs when light is reflected or refracted at an interface is inherently weak due to the weak spin–orbit interaction. Now, researchers at Hunan University, Hengyang Normal University and Shenzhen University have theoretically predicted and experimentally confirmed a giant SHE in a metamaterial structured to produce the Pancharatnam–Berry phase in one dimension and having a spatially varying birefringence. Unlike the tiny real-space shift induced by the Rytov–Vladimirskii–Berry phase gradient, the giant SHE occurs in momentum space and is sufficiently large to be observed directly. Such metamaterials could potentially be used to manipulate spin-polarized photons and the orbital angular momentum of light, enabling applications in spin-controlled nanophotonics.

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.

Control over symmetry breaking in three-dimensional electromagnetic systems offers a pathway to tailoring their optical activity. We introduce fractured Pancharatnam–Berry-phase metasurface systems, in which a full-waveplate geometric phase metasurface is fractured into two half-waveplate-based metasurfaces and actively configured using shear displacement. Local relative rotations between stacked half-nanowaveplates within the metasurface system are transduced by shear displacement, leading to dynamic modulation of their collective geometric phase properties. We apply this concept to pairs of periodic Pancharatnam–Berry-phase metasurfaces and experimentally showthat these systems support arbitrary and reconfigurable broadband circular birefringence response. High-speed circular birefringence modulation is demonstrated with modest shearing speeds, indicating the potential for these concepts to dynamically control polarization states with fast temporal responses. We anticipate that fractured geometric phase metasurface systems will serve as a nanophotonic platform that leverages systems-level symmetry breaking to enable active electromagnetic wave control.

We propose a novel framework to describe geometric phases in quantum systems under non-adiabatic conditions by introducing the concept of a hidden geometric phase. Conventional geometric phases, such as the Berry phase, rely on adiabatic evolution, limiting their applicability in rapidly changing systems. Here, we remove this constraint by reinterpreting the geometric phase as arising from a dynamically evolving reference basis, independent of the external topological features. The hidden phase is revealed through transitionless quantum control techniques, ensuring pure geometric phase accumulation even in non-adiabatic regimes. Our method offers an exact solution to the neutron spin rotation phase in the Bitter–Dubbers experiment, aligning more closely with experimental data without depending on adiabatic approximations. This unexpected result broadens our understanding of the geometric phase observed in neutron spin rotation beyond the adiabatic conditions that are conventionally required.