Search Results (14)

Bessel beams occupy an important position in optical research due to their characteristics of long focal depth, self-healing ability, and diffraction-free propagation. Traditional methods for generating Bessel beams suffer from complexity, a large size, low uniformity, and limited NA. Metasurfaces are considered to be a new technology for the miniaturization of optical devices due to their ability to regulate optical fields at subwavelength scales flexibly. Here, we generated Bessel beams by a complex-amplitude (CA) metasurface. The polarization conversion efficiency was controlled by the geometric size, while the phase value from 0 to 2π was manipulated based on the Pancharatnam–Berry (PB) phase. This approach enabled precise control over the axial intensity distribution of the optical field, which facilitated the generation of sub-millimeter-scale Bessel beams. Axial light field control based on CA metasurfaces has great potential for applications in a variety of fields, such as particle manipulation, large-depth-of-field imaging, and laser processing. Full article

We investigated Im-3m H₃S at 200 GPa, a pressure regime where crystalline H₃S is widely considered to be a superconductor. Simulated circularly polarized 10 femtosecond (fs) laser pulses were applied and we quantified the effects on the electron dynamics both during the application of the ultra-fast laser pulse and 5.0 fs after the pulse was switched off. In addition, the carrier-envelope phase (CEP) angle ϕ, which quantifies the relationship between the time-varying direction of electric (E)-field and the amplitude envelope, is employed to control the time evolution of the wavefunction ψ(r). This is undertaken for the first application of Next Generation Quantum Theory of Atoms in Molecules (NG-QTAIM) to the solid state. Ultra-fast phenomena related to superconductivity are discovered in the form of a geometric Berry phase angle associated with the H--H bonding in addition to very high values of the chirality–helicity function that correspond to values normally found in chiral molecules. Future applications are discussed, including chiral spin selective phenomena in addition to high-temperature superconductivity and organic superconductors where phonons do not play a significant role. Full article

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, $n_S$ and $n_T$, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) $Mp\left(n\right)$ representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp\left(n\right)$ group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of $Mp\left(2\right)$ are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition $-\infty <t<\infty$). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for $n\to \infty$), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic $Mp\left(n\right)$ group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it. Full article

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk–edge correspondence and symmetry-related topological invariants has been extended to non-Hermitian systems. Correspondingly, the value of geometric phases, such as the Pancharatnam–Berry or Zak phases, under the adiabatic quantum deformation process in the presence of non-Hermitian conditions, are now of significant interest. Here, we explicitly calculate the Zak phases of one-dimensional topological nanobeams that sustain guided-mode resonances, which lead to energy leakage to a continuum state. The retrieved Zak phases show as zero for trivial and as π for nontrivial photonic crystals, respectively, which ensures bulk–edge correspondence is still valid for certain non-Hermitian conditions. Full article

Vortex beams carrying orbital angular momentum (OAM) have become a research frontier due to the prospect of improving spectral efficiency and transmission capacity in communication systems. In this work, a hybrid phase-turning meta-atom that combines resonance and geometric (Pancharatnam-Berry) phase modulation is used to form a single-layer metasurface. A linearly polarized broadband vortex beam of mode l = −1 is obtained by the metasurface. An experimental prototype of the vortex beam generator has been fabricated and measured. The simulated and measured results demonstrate that the whole vortex beam generator exhibits over 70% mode purity from 26.5 GHz to 40 GHz (the relative bandwidth is 38.57%). In addition, a wide 3 dB gain bandwidth and low crosstalk are also provided by the proposed generator. This indicates that the proposed generator has important application value for vortex beam communication and its related applications. Full article

We report the topological properties, in terms of the Berry phase, of the 2D noninteracting system with electron–hole band inversion, described by the two-band generalized analogue of the low-energy Bernevig–Hughes–Zhang Hamiltonian, yielding the W-shaped energy bands in the form of two intersecting cones with the gap along the closed continuous loop. We identify the range of parameters where the Berry phase attains qualitatively different values: (a) the integer multiplier of $2\pi$, (b) the integer multiplier of $\pi$, and (c) the nontrivial value between the latter two, which depends on the system parameters. The system thus exhibits the anomalous quantum Hall effect associated with the nontrivial geometric phase, which is presumably tunable through the choice of parameters at hand. Full article

Based on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory’s puzzles and phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The singularities provide also new experimental insights and predictions that are presented in this article and establish a surprising new connection between the physical and social sciences. The key is the topology of spaces of quantum events and of the frameworks postulated by these axioms. These are quite different from their counterparts in classic probability and explain mathematically the interference between quantum experiments and the existence of several frameworks or ‘violation of unicity’ that characterizes quantum physics. They also explain entanglement, the Heisenberg uncertainty principle, order dependence of observations, the conjunction fallacy and geometric phenomena such as Pancharatnam–Berry phases. Somewhat surprisingly, we find that the same topological singularities explain the impossibility of selecting a social preference among different individual preferences: which is Arrow’s social choice paradox: the foundations of social choice and of quantum theory are therefore mathematically equivalent. We identify necessary and sufficient conditions on how to restrict experiments to avoid these singularities and recover unicity, avoiding possible interference between experiments and also quantum paradoxes; the same topological restriction is shown to provide a resolution to the social choice impossibility theorem of Chichilnisky. Full article

We generalize the dynamical analog of the Berry geometric phase setup to the quaternionic model of Avron et al. In our dynamical quaternionic system, the fast half-integer spin subsystem interacts with a slow two-degrees-of-freedom subsystem. The model is invariant under the 1:1:2 weighted SO$\left(2\right)$ symmetry and spin inversion. There is one formal control parameter in addition to four dynamical variables of the slow subsystem. We demonstrate that the most elementary qualitative phenomenon associated with the rearrangement of the energy super-bands of our model consists of the rearrangement of one energy level between two energy superbands which takes place when the formal control parameter takes the special isolated value associated with the conical degeneracy of the semi-quantum eigenvalues. This qualitative phenomenon is of topological origin, and is characterized by the second Chern class of the associated semi-quantum system. The correspondence between the number of redistributed energy levels and the second Chern number is confirmed through a series of examples. Full article

Polarization is measured very often to study the interaction of light and matter, so the description of the polarization of light beams is of both practical and fundamental interest. This review discusses the polarization properties of structured light in multimode graded-index optical fibers, with an emphasis on the recent advances in the area of spin-orbit interactions. The basic physical principles and properties of twisted light propagating in a graded index fiber are described: rotation of the polarization plane, Laguerre–Gauss vector beams with polarization-orbital angular momentum entanglement, splitting of degenerate modes due to spin-orbit interaction, depolarization of light beams, Berry phase and 2D and 3D degrees of polarizations, etc. Special attention is paid to analytical methods for solving the Maxwell equations of a three-component field using perturbation analysis and quantum mechanical approaches. Vector and tensor polarization degrees for the description of strongly focused light beams and their geometrical interpretation are also discussed. Full article

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Today, the basic structure is a 2D system to realize anyons with braiding operations. From the topological point of view, we have to deal with surface topology. However, usual materials are 3D objects. Possible topologies for these objects can be more complex than surfaces. From the topological point of view, Thurston’s geometrization theorem gives the main description of 3-dimensional manifolds. Here, complements of knots do play a prominent role and are in principle the main parts to understand 3-manifold topology. For that purpose, we will construct a quantum system on the complements of a knot in the 3-sphere. The whole system depends strongly on the topology of this complement, which is determined by non-contractible, closed curves. Every curve gives a contribution to the quantum states by a phase (Berry phase). Therefore, the quantum states can be manipulated by using the knot group (fundamental group of the knot complement). The universality of these operations was already showed by M. Planat et al. Full article

Optical components that are based on Pancharatnam–Berry phase feature a polarization-dependent diffraction that can be used to fabricate lenses and gratings with unique properties. In recent years, the great progress made in the fabrication of the metasurfaces that are required for these optical components has lowered their cost and has made them widely available. One of the often-overlooked properties of optical components based on geometrical phases (GPs) is that, contrary to dynamical phases, their phase can be measured while using a polarimetric technique without the need to resort to interferometry methods. This is possible because the Pancharatnam–Berry phase is not controlled by an optical path difference; it results from a space variant polarization manipulation. In this work, we apply Mueller matrix microscopy in order to measure the geometrical phase of GP lenses and polarization gratings. We show that a single space resolved Mueller matrix measurement with micrometric resolution is enough to obtain a full characterization phase-profile of these GP-based optical components and evaluate their performance. Full article

We show Zeeman-like splitting in the energy of spinors propagating in a background gravitational field, analogous to the spinors in an electromagnetic field, otherwise termed the Gravitational Zeeman Effect. These spinors are also found to acquire a geometric phase, in a similar way as they do in the presence of magnetic fields. However, in a gravitational background, the Aharonov-Bohm type effect, in addition to Berry-like phase, arises. Based on this result, we investigate geometric phases acquired by neutrinos propagating in a strong gravitational field. We also explore entanglement of neutrino states due to gravity, which could induce neutrino-antineutrino oscillation in the first place. We show that entangled states also acquire geometric phases which are determined by the relative strength between gravitational field and neutrino masses. Full article

The simultaneous processing of orbital angular momentum (OAM) and polarization has recently acquired particular importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical behavior, Pancharatnam–Berry optical elements (PBOEs), acting on the geometric phase, have proven to be useful for the manipulation of complex light beams with orthogonal polarization states using a single optical element. In this work, different PBOEs have been computed, realized, and optically analyzed for the sorting of beams with orthogonal OAM and polarization states at the telecom wavelength of 1310 nm. The geometric-phase control is obtained by inducing a spatially-dependent form birefringence on a silicon substrate, patterned with properly-oriented subwavelength gratings. The digital grating structure is generated with high-resolution electron beam lithography on a resist mask and transferred to the silicon substrate using inductively coupled plasma-reactive ion etching. The optical characterization of the fabricated samples confirms the expected capability to detect circularly-polarized optical vortices with different handedness and orbital angular momentum. Full article

A Pancharatnam–Berry optical element is designed, fabricated, and optically characterized for the demultiplexing of beams with different polarization and orbital angular momentum states at the telecom wavelength of 1310 nm. The geometric phase control is achieved by fabricating properly-oriented subwavelength gratings on a silicon substrate, inducing a spatially-variant form birefringence. The digital grating pattern is transferred to the silicon substrate with a two-step nanofabrication protocol, using inductively coupled plasma reactive ion etching to transfer the resist pattern generated with high-resolution electron beam lithography. The optical characterization of the sample confirms the expected capability to sort circularly polarized optical beams with different handedness and orbital angular momentum. Encompassing optical element design and silicon photonics, the designed silicon metasurface paves the way to innovative devices for total angular momentum mode division multiplexing with unprecedented levels of integration. Full article