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In this work, we theoretically explore whether a parity-violating/chiral light–matter interaction is required to capture all relevant aspects of chiral polaritonics or if a parity-conserving/achiral theory is sufficient (e.g., long-wavelength/dipole approximation). This question is non-trivial to answer since achiral theories (Hamiltonians) still possess chiral solutions. To elucidate this fundamental theoretical question, a simple GaAs quantum ring model is coupled to an effective chiral mode of a single-handedness optical cavity in dipole approximation. The bare matter GaAs quantum ring possesses a non-degenerate ground state and a doubly degenerate first excited state. The chiral or achiral nature (superpositions) of the degenerate excited states remains undetermined for an isolated matter system. However, inside our parity-conserving description of a chiral cavity, we find that the dressed eigenstates automatically (ab initio) attain chiral character and become energetically discriminated based on the handedness of the cavity. In contrast, the non-degenerate bare matter state (ground state) does not show energetic discrimination inside a chiral cavity within a dipole approximation. Nevertheless, our results suggest that the handedness of the cavity can still be imprinted onto these states (e.g., angular momentum and chiral current densities). Overall, the above findings highlight the relevance of degenerate states in chiral polaritonics. In particular, because recent theoretical results for linearly polarized cavities indicate the formation of a frustrated and highly degenerate electronic ground state under collective strong coupling conditions, which, likewise, is expected to form in chiral polaritonics and, thus, could be prone to chiral symmetry breaking effects. [ABSTRACT FROM AUTHOR]

The molecular dynamics with electronic friction (MDEF) approach can accurately describe nonadiabatic effects at metal surfaces in the weakly nonadiabatic limit. That being said, the MDEF approach treats nuclear motion classically such that the nuclear quantum effects are completely missing in the approach. To address this limitation, we combine Electronic Friction with Ring Polymer Molecular Dynamics (EF-RPMD). In particular, we apply the averaged electronic friction from the metal surface to the centroid mode of the ring polymer. We benchmark our approach against quantum dynamics to show that EF-RPMD can accurately capture zero-point energy as well as transition dynamics. In addition, we show that EF-RPMD can correctly predict the electronic transfer rate near metal surfaces in the tunneling limit as well as the barrier crossing limit. We expect that our approach will be very useful to study nonadiabatic dynamics near metal surfaces when nuclear quantum effects become essential. [ABSTRACT FROM AUTHOR]

For |$X$| a smooth projective variety, the quantum cohomology ring |$QH^{*}(X)$| is a deformation of the usual cohomology ring |$H^{*}(X)$|⁠ , where the product structure is modified to incorporate quantum corrections. These correction terms are defined using Gromov–Witten invariants. When |$X$| is toric with geometric quotient description |$V/\!/ T$|⁠ , the cohomology ring |$H^{*}(V/\!/ T)$| also has the structure of a |$H^{*}(T)$| -module. In this paper, we introduce a new deformation of the cohomology of |$X$| using quasimap invariants with a light point. This defines a quantum |$H^{*}(T)$| -module structure on |$H^{*}(X)$| through a modified version of the WDVV equations. We explicitly compute this structure for the Hirzebruch surface of type 2. We conjecture that this new quantum module structure is isomorphic to the natural module structure of the Batyrev ring for a semipositive toric variety. [ABSTRACT FROM AUTHOR]

The electronic and optical properties of a mesoscopic heterostructure of a two-dimensional quantum ring composed of Gallium Arsenide (GaAs) semiconductors are investigated. Using the confinement potential proposed by Tan and Inkson to describe the system under analysis, we conducted a numerical study of the photoionization cross-section for a 2D quantum ring with and without rotation effects. The interior of the quantum ring is traversed by an Aharonov–Bohm (AB) flux. Our research aims to investigate how this mesoscopic structure's electronic and optical properties respond to variations in the following parameters: average radius, AB flux, angular velocity, and incident photon energy. Under these conditions, we establish that optical transitions occur from the ground state to the next excited state in the conduction subband, following a specific selection rule. One of the fundamental objectives of this study is to analyze how these rules can influence the general properties of two-dimensional quantum rings. To clarify the influence of rotation on the photoionization process within the system, we offer findings that illuminate the effects of the pertinent physical parameters within the described model. We emphasize that, although this is a review, it provides critical commentary, analysis, and new perspectives on existing research. Some results presented in this paper can be compared with those in the literature; however, new physical parameters and quantum ring configurations are used. [ABSTRACT FROM AUTHOR]

The first part of this work evaluates Al-doped ZnO (AZO) as an optically transparent top-gate material for studies on semiconductor quantum dots. In comparison with conventional Ti gates, samples with AZO gates demonstrate a more than three times higher intensity in the quantum dot emission under comparable excitation conditions. On the other hand, charges inside a process-induced oxide layer at the interface to the semiconductor cause artifacts at gate voltages above  U ≈  1 V. The second part describes an optical and simulation study of a vertical electric-field (F)-induced switching from a strong to an asymmetric strong–weak confinement in GaAs cone-shell quantum dots (CSQDs), where the charge carrier probability densities are localized on the surface of a cone. These experiments are performed at low U and show no indications of an influence of interface charges. For a large F, the measured radiative lifetimes are substantially shorter compared with simulation results. We attribute this discrepancy to an F-induced transformation of the shape of the hole probability density. In detail, an increasing F pushes the hole into the wing part of a CSQD, where it forms a quantum ring. Accordingly, the confinement of the hole is changed from strong, which is assumed in the simulations, to weak, where the local radius is larger than the bulk exciton Bohr radius. In contrast to the hole, an increasing F pushes the electron into the CSQD tip, where it remains in a strong confinement. This means the radiative lifetime for large F is given by an asymmetric confinement with a strongly confined electron and a hole in a weak confinement. To our knowledge, this asymmetric strong–weak confinement represents a novel kind of quantum mechanical confinement and has not been observed so far. Furthermore, the observed weak confinement for the hole represents a confirmation of the theoretically predicted transformation of the hole probability density from a quantum dot into a quantum ring. For such quantum rings, application as storage for photo-excited charge carriers is predicted, which can be interesting for future quantum photonic integrated circuits. [ABSTRACT FROM AUTHOR]

Let IG : = IG (2 , 2 n + 1) denote the odd symplectic Grassmannian of lines which is a horospherical variety of Picard rank 1. The quantum cohomology ring QH * (IG) has negative structure constants. For n ≥ 3 , we give a positivity condition that implies the quantum cohomology ring QH * (IG) is the only quantum deformation of the cohomology ring H * (IG) up to the scaling of the quantum parameter. This is a modification of a conjecture by Fulton. [ABSTRACT FROM AUTHOR]

Within the framework of the macroscopic dielectric continuum model, the dispersive spectra of polar optical phonon modes of III-nitride based nanostructures with different inner and outer dielectric media are investigated in this paper. The dielectric and quantum size effects on the dispersive frequencies of phonon modes are focused and emphasized. In the case of GaN quantum rings (QRs), we found that the dielectric constant of the inner/outer medium could significantly influence the dispersive spectra of the surface optical (SO) phonon mode as the high/low-frequency SO phonon modes are mainly localized at the inner/outer surface of QRs, respectively. Moreover, such effects associated with different crystallographic structures of GaN, i.e., the wurtzite (WZ) and zinc blende (ZB) crystal structures, are also studied in detail, showing the different degenerating behavior and electron–phonon coupling strength. The results obtained in this study provide a beneficial opportunity to independently adjust dispersive spectra of the two branches of SO modes in GaN nanostructures; thus, it could be used to design and develop phonon-based detectors and sensors. [ABSTRACT FROM AUTHOR]

The magnetic properties of the lattice formed by noninteracting semiconductor quantum rings in a longitudinal magnetic field are investigated. It was shown that when the value of the Rashba parameter ξ = 1.5, the magnetization varies from positive to negative with changes in the Aharonov–Bohm flux and amplitude oscillations decrease. [ABSTRACT FROM AUTHOR]

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements. [ABSTRACT FROM AUTHOR]

Multi-server authentication, called single sign-on, enables users to easily access the necessary services from multiple servers with a single registration. Users generally hesitate to sign up individually with each service provider due to the challenge of remembering numerous credentials and trust. Through real-time consumer validation on a public channel, the multi-server authentication allows speedy access to services. Several multi-server authentication techniques have been introduced. However, the existing efficient and robust authenticated key exchange (AKE) schemes are not secure against quantum attacks as they are constructed on traditional cryptographic primitives, integer factorization, and discrete log problems. Due to the advent of scalable quantum computers, these schemes will be breakable as per the application of Shor's algorithm. To address this issue, we propose a quantum secure ring learning with error based AKE mechanism for multi-server networking to establish a secure connection between users and multiple servers. Our suggested technique provides robust mutual authentication and fulfils the desired security attributes, as presented by the rigorous security analysis in the random oracle model. Additionally, we demonstrate a detailed comparative analysis with other AKE schemes currently in practice for multi-server environments to describe further our proposed scheme's increased efficiency and quantum security. [ABSTRACT FROM AUTHOR]

We investigate the energy spectra and optical absorption of a 3D quantum dot–double quantum ring structure of GaAs/Al0.3Ga0.7As with adjustable geometrical parameters. In the effective mass approximation, we perform 3D numerical computations using as height profile a superposition of three Gaussian functions. Independent variations of height and width of the dot and of the rings and also of the dot–rings distance determine particular responses, useful in practical applications. We consider that a suitable manipulation of the geometrical parameters of this type of quantum coupling offer a variety of responses and, more important, the possibility of a fine adjusting in energy spectra and in the opportunity of choosing definite absorption domains, properties required for the improvement of the performances of optoelectronic devices. [ABSTRACT FROM AUTHOR]

Recently, a novel semi-quantum ring signature protocol (Quantum Inf. Process., 22(9), 337(2023)) was proposed. Although it has the properties of semi-quantum protocol, its verification process will fail when more than two users take part in the signature protocol. We show an example, in which four participants including the trusted third-party Trent are used, to prove the signature cannot be verified. Then, an improved semi-quantum ring signature protocol is proposed. In the new ring signature protocol, Trent generates the shared keys with each ring user. According to the shared keys, Trent encodes the GHZ state such that the identity of the true ring signatory can be traced by Trent. What is more, in our protocol, by measuring the received particles, all the ring users can create the same session key to generate a ring signature, which can guarantee the anonymity of the voter in the protocol. The improved ring signature protocol overcomes the drawback of the old one and can be secure against various eavesdropping attacks and forgery attack. Compared with the similar quantum ring signature protocols, ours has better practicability and efficiency. [ABSTRACT FROM AUTHOR]

Matrix-valued holomorphic quantum modular forms are intricate objects associated to 3-manifolds (in particular to knot complements) that arise in successive refinements of the volume conjecture of knots and involve three holomorphic, asymptotic and arithmetic realizations. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the (- 2 , 3 , 7) -pretzel knot. [ABSTRACT FROM AUTHOR]

In this paper, we use multivariate polynomial rings to construct quantum error-correcting codes (QECCs) via Hermitian construction. We establish a relation between linear codes and ideals of multivariate polynomial rings. We give a necessary and suffcient condition for a multivariate polynomial to generate a Hermitian dual-containing code. By comparing with the literatures in recent years, we construct 31 new QECCs over F q , where q = 3 , 4 , 5 , 7 . Some of them reach quantum singleton bound and some of them exceed quantum GV bound. [ABSTRACT FROM AUTHOR]

An extended Su–Schrieffer–Heeger (SSH) model consisting of an SSH chain with an embedded quantum ring (QR) is investigated. In the case of two SSH chains with a symmetric distribution with respect to QR, by calculating the real‐space winding number and energy spectrum, the hopping amplitude‐induced topological phase is discovered. The probability distributions of gap states and the relationship between energy and magnetic flux prove the existence of the Aharonov–Bohm effect in the QR. Moreover, in the case of asymmetric distribution, the model possesses a zero‐energy mode within the energy gap, and it is found that it can realize quantum state transfer. By adjusting the connection site between the right SSH chain and QR, the direction of the output port can be flexibly engineered. Furthermore, it is shown that high‐fidelity quantum state transfer can still be achieved with the increasing of the system size. The tunable quantum state transfer based on the zero‐energy mode can be equivalent to a topological tunable directional switch with properties of non‐directional transfer. This work provides an approach for studying topological phase transition and tunable topological devices in an SSH chain with an embedded QR. [ABSTRACT FROM AUTHOR]

We study the effect of the magnetic and Aharonov–Bohm (AB) flux fields on the two-photon absorption (2PA) in a quantum ring (QR) system. The expression of 2PA coefficient is expressed through the two-photon transition probability including both intraband and interband transitions. The effect of the polarization orientation of the incident light breaks the symmetry from the contribution between the AB flux field and the azimuthal quantum number. Magnetic and AB flux fields have a significant effect on the electronic properties of the QR. The 2PA spectra for intraband transitions are in the THz range and have a much higher magnitude compared to those for interband transitions, which are located in the near-infrared range. The increase in the magnetic field results in a blue-shift of the 2PA spectra for both intraband and interband transitions, whereas changes in the azimuthal quantum number only affect the spectra for interband transitions. [ABSTRACT FROM AUTHOR]

We consider quantum (skew) polynomial rings and observe that their graded automorphisms coincide with those of quantum exterior algebras. This allows us to define a quantum determinant that gives a homomorphism of groups acting on quantum polynomial rings. We use quantum subdeterminants to classify the resulting Drinfeld Hecke algebras for the symmetric group, other infinite families of Coxeter and complex reflection groups, and mystic reflection groups (which satisfy a version of the Shephard–Todd–Chevalley theorem). This direct combinatorial approach replaces the technology of Hochschild cohomology used by Naidu and Witherspoon over fields of characteristic zero and allows us to extend some of their results to fields of arbitrary characteristic and also locate new deformations of skew group algebras. [ABSTRACT FROM AUTHOR]

Let p be a prime number and q = p m for some positive integer m. In this paper, we find the possible Hermitian hull dimensions of λ -constacyclic codes over R e = F q 2 + u F q 2 + u 2 F q 2 + ⋯ + u e - 1 F q 2 , u e = 1 where F q 2 is the finite field of q 2 elements, e | (q + 1) and λ = η 1 α 1 + η 2 α 2 + ⋯ + η e α e for α l ∈ F q 2 ∗ of order r l such that r l ∣ q + 1 (for each 1 ≤ l ≤ e ). Further, we obtain some conditions for these codes to be Hermitian LCD. Also, under certain conditions, we establish a strong result that converts every constacyclic code to a Hermitian LCD code (Corollaries 2 and 3). We also study the structure of generator polynomials for Hermitian dual-containing constacyclic codes (Theorems 8 and 9), and obtain parameters of quantum codes using the Hermitian construction. The approach we used to derive Hermitian dual-containing conditions via the hull has not been used earlier. As an application, we obtain several optimal and near-to-optimal LCD codes, constacyclic codes having small hull dimensions, and quantum codes. [ABSTRACT FROM AUTHOR]

We present a unified model to describe the dynamics of optical frequency combs in quantum cascade lasers (QCLs), incorporating both ring and Fabry–Pérot (FP) cavity configurations. The model derives a modified complex Ginzburg–Landau equation (CGLE), leveraging an order parameter approach, and is capable of capturing the dynamics of both configurations, thus enabling a comparative analysis. This result demonstrates that FP QCLs, in addition to ring QCLs, belong to the same universality class of physical systems described by the CGLE, which includes, among others, systems in the fields of superconductivity and hydrodynamics. In the modified CGLE, a nonlinear integral term appears that is associated with the coupling between counterpropagating fields in the FP cavity and whose suppression yields the ring model, which is known to be properly described by a conventional CGLE. We show that this crucial term holds a key role in inhibiting the formation of harmonic frequency combs (HFCs), associated with multi-peaked localized structures, due to its anti-patterning effect. We provide support for a comprehensive campaign of numerical simulations in which we observe a higher occurrence of HFCs in the ring configuration compared to the FP case. Furthermore, the simulations demonstrate the model's capability to reproduce experimental observations, including the coexistence of amplitude and frequency modulation, linear chirp, and typical dynamic scenarios observed in QCLs. Finally, we perform a linear stability analysis of the single-mode solution for the ring case, confirming its consistency with numerical simulations and highlighting its predictive power regarding the formation of harmonic combs. [ABSTRACT FROM AUTHOR]

The impurity states in the InGaAsP/InP quantum ring were calculated using the plane wave expansion method within the theoretical framework of the effective mass envelope function approximation. The impurity binding energies of the 1s and 2p± states, as well as the impurity transition energies between them, were calculated and analyzed in detail. Calculations show that the quantum ring height and outer radius have different effects on the impurity transition energy. When the impurity moves in the radial direction, the binding energy reaches a maximum in the quantum ring, but shows an asymmetric distribution, while the transition energy gradually decreases. When the impurity moves in the axial direction, both the binding energy and transition energy reach their maximum values in the axial center and are symmetrically distributed. When the impurity is located at the position of zi ≥ 0, the impurity binding energy and transition energy both decrease due to the application of electric field, however, when the impurity is located at the position of zi < 0, they both increase with the application of electric field. [ABSTRACT FROM AUTHOR]

We study the relation between isolated hypersurface singularities (e.g., ADE) and the quantum cohomology ring by using spectral invariants, which are symplectic measurements coming from Floer theory. We prove, under the assumption that the quantum cohomology ring is semi-simple, that (1) if the smooth Fano variety degenerates to a Fano variety with an isolated hypersurface singularity, then the singularity has to be an A m -singularity, (2) if the symplectic manifold contains an A m -configuration of Lagrangian spheres, then there are consequences for the Hofer geometry, and that (3) the Dehn twist reduces spectral invariants. [ABSTRACT FROM AUTHOR]

We conducted a joint anion photoelectron spectroscopy and theoretical investigation on hybrid lanthanum-copper oxides clusters, LaCu2On−/0 (n=4, 5). The experimental vertical detachment energies of LaCu2O4− and LaCu2O5− are determined to be 3.70 and 3.79 eV, respectively. Theoretical calculations show that the most stable structures of LaCu2O4,5− are mainly composed of LaCu2O3 six-membered ring, with an additional O atom or O2 unit interacting with the La atom. In LaCu2O4−, covalent interaction is presented between the external O atom and the LaCu2O3 six-membered ring. As for LaCu2O5− anion, a weak interaction dominated by inductive force is presented between the external O2 unit and the LaCu2O3 six-membered ring. [ABSTRACT FROM AUTHOR]

In this paper we investigate the effect of a topological defect, such as a screw dislocation in an α - T 3 Aharonov–Bohm quantum ring and scrutinized the effects of an external transverse magnetic field and Rashba spin-orbit coupling therein. The screw dislocation yields an effective flux which reshape the periodic oscillations in the persistent current in both charge and spin sectors, with a period equal to one flux quantum. Moreover, they suffer a phase shift proportional to the degree of dislocation, and include scattering effects due to the dislocation present in the system. Such tunable oscillation of the spin persistent current highlights applications of our system as potential spintronic devices. Further, the behaviour of the current induced by the Burgers vector ( b z ) which denotes the strength of the dislocation is investigated in the absence and presence of an external magnetic field. In both the scenarios, an almost linear decrease in the current profile as a function of the Burgers vector is observed. Notably, without the external magnetic field, the Burgers current suffers a back flow for α = 1 (dice lattice), while in the presence of the external magnetic field, for other values of α (e.g., α = 0.5 ) this back flow occurs for a specific value of b z . Additionally, the presence of the distortion induces a chirality effect, giving rise to an additional chiral current even in the absence of an external field. Furthermore, in the absence of field, the Burgers spin current initially rises, attains a maximum before diminishing as b z is enhance for all values of α . However, such a non-monotonicity in the Burgers spin current is conspicuously non-existent in the presence of an external field. The chiral current discussed above may hold important applications to spintronics. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT)-based calculations were performed for 36, 72 and 108 water molecules forming twisted ribbon-like nano-ring structures of diameter 1.54, 3.10 and 4.56 nm, respectively. We explore the electric field evolution of the structure, energetics and stability of the water nano-ring structures that are essentially symmetric and non-polar, or less-symmetric and polar, hydrogen-bonded clusters. The results suggest that for fields applied perpendicular to the ring, larger rings are more susceptible to the field influence, while fields applied parallel to the ring quickly transform the ring structures into arbitrary ones, regardless of the ring size. Infrared and Raman spectral analysis of local modes demonstrate the typical vibrational response of water molecules to various H-bonding environments and applied fields, providing a spectroscopic signature that can be used to identify the manifestation of such H-bonded ring networks. Our study underscores the implications of the nano-sized ring water clusters, which have the potential to be exploited in a variety of device applications. [ABSTRACT FROM AUTHOR]

In this paper, we present a single nano ring resonator using Annular Photonic Crystal (APC) with ultra-compact size for applications in versatile optical network components. The proposed resonator is designed in the hexagonal lattice, made up of Silicon (Si) planar and annular rods, where the annular rods are filled with Silicon Nitride (Si3N4). Despite being pervasive, the proposed structure operates mostly in the C-band wavelength, providing high resonation, low insertion loss, high contrast ratio, and large bandwidth with low loss comprising a single resonator ring with photonic crystal waveguides. This structure is used to realize several high-performance optical network devices like optical ring resonator, 4 × 2 reversible encoder, 1 × 2 power splitter, and a multiplexer. Several parameters and their performances are optimized for this miniaturized photonic device using Finite Difference Time Domain (FDTD) method. This device works in the quantum regime as a slow light device with a better squeeze factor enabling quantum computing. The proposed nanostructure, having a Quality factor (Q) of 396.05, is highly suitable for optical network applications. [ABSTRACT FROM AUTHOR]

This paper presents the design and optimization of a side-coupled photonic crystal nanobeam (1D PhC) cavity incorporating micro-ring resonators and a bus waveguide for efficient light coupling. The innovative design incorporates a parabolic taper function, ensuring gradual mode-gap modulation and robust light confinement. Through rigorous numerical simulations and optimization of key parameters—including the 1D PhC period, cavity center radius, taper delta radius, number of taper and mirror holes, waveguide width, ring radius, coupling gap distance, and material refractive index—we achieved a remarkable maximum Q factor of 2.5 × 105 at a wavelength of 1693.5 nm. This optimized configuration significantly enhances light-matter interaction, making it promising for applications demanding high-Q resonators. [ABSTRACT FROM AUTHOR]

Recently, Blasiak–Morse–Seelinger introduced symmetric func- tions called Katalan functions, and proved that the K-theoretic k-Schur functions due to Lam–Schilling–Shimozono form a subfamily of the Katalan functions. They conjectured that another subfamily of Katalan functions called closed k-Schur Katalan functions is identified with the Schubert structure sheaves in the K-homology of the affine Grassmannian. Our main result is a proof of this conjecture. We also study a K-theoretic Peterson isomorphism that Ikeda, Iwao, and Maeno constructed, in a nongeometric manner, based on the unipotent solution of the relativistic Toda lattice of Ruijsenaars. We prove that the map sends a Schubert class of the quantum K-theory ring of the flag variety to a closed K-k-Schur Katalan function up to an explicit factor related to a translation element with respect to an antidominant coroot. In fact, we prove this map coincides with a map whose existence was conjectured by Lam, Li, Mihalcea, Shimozono, and proved by Kato, and more recently by Chow and Leung. [ABSTRACT FROM AUTHOR]

A quantum injective frame is a frame whose measurements for density operators can be used as a distinguishing feature in a quantum system, and the frame quantum detection problem demands a characterization of all such frames. Very recently, the quantum detection problem for continuous as well as discrete frames in both finite and infinite dimensional Hilbert spaces received significant attention. The quantum detection problem pertaining to the characterization of informationally complete positive operator-valued measures (POVM) can be split into two cases: The quantum injectivity or state separability problem and the rang analysis or quantum state estimation problem. Building upon this notion, this note is aimed at the quantum detection problem for fusion frames. The injectivity of a family of vectors and a family of closed subspaces is characterized in terms of some operator equations in Hilbert–Schmidt and trace classes. [ABSTRACT FROM AUTHOR]

Optical photonic crystal channel drop filters (CDFs) are widely used due to the sensitivity of individual wavelength among the group of channels in optical communication networks. However, most of the existing filtering scheme still suffer from low transmission efficiency. Here, we propose an eight-channel CDFs with narrow bandwidth and high transmission based on a dual positive hexagonal nested array which is sandwiched between two parallel line defect waveguides. The circular dielectric rods with different radius are arranged in the ring resonant cavity to diminish light leakage and, therefore, increase drop efficiency and quality factor Q. The results show that the drop efficiency and Q factor of the nested cavity CDF can achieve 99% and 5033, and the average values of the cascaded eight-channel CDFs are found up to 92.73%, 3217, respectively, and the channel crosstalk is between − 61.92 and − 14.90 dB. The proposed CDFs offer highly selective spectrum filtering capabilities, showing great potential in high-precision optical sensing and optical communication. [ABSTRACT FROM AUTHOR]

We study hulls of constacyclic codes of length n over a finite non-chain ring F q + v F q with respect to the Euclidean and Hermitian inner products, where v 2 = v . Under a special Gray map from F q + v F q to F q 2 , dimensions of hulls of Gary images of constacyclic codes are obtained. Some new quantum error-correcting codes (QECCs) with good parameters are constructed by the quantum construction X method under the Euclidean and Hermitian inner products, respectively. Some of these QECCs are MDS with the minimum distance greater than q 2 , and a few of these QECCs are MDS with the minimum distance equal to q. [ABSTRACT FROM AUTHOR]

The current work focuses on investigating how various external and structural factors can affect the electronic structure and optical properties of a GaAs/Ga1−xAlxAs quantum ring. Specifically, we have studied the effects of spin–orbit interaction (SOI), pressure, temperature, and dimensions on the energy levels, dipole transition matrix elements (DTMEs), susceptibilities, optical absorption coefficients (OACs), refractive index changes (RICs), and group velocity of the quantum ring. These results show that the ground state energy of the system increases with the concentration of aluminum, while increasing temperature and ring size leads to a decrease in DTMEs due to a decrease in wave function overlap. We have also found that the presence of Rashba SOI, pressure, temperature, as well as the ring's size dominate the electronic structure and subsequently affect the OACs and RICs of the system. A significant enhancement of the OACs can be witnessed when the Rashba coefficient and ring size are enlarged. Furthermore, the results represent a red shift with enhanced Rashba coefficient and relaxation time, whereas the growing ring size results in a blue shift in Optical sensitivities. Finally, we have analyzed the dependence of the group velocity of probe light pulses on the ring's size, photon frequency, and incident optical intensity. Our findings suggest that by controlling these parameters appropriately, it may be possible to achieve effective control of light speed, which could have interesting applications in electro-optical quantum communication networks. Overall, this work sheds light on the potential applications of these findings in the design and construction of spin-based devices and may offer new avenues for further research in this field. [ABSTRACT FROM AUTHOR]

Quantum signature has become a hot topic in the current research of digital signature schemes due to its unconditional security. As a special kind of digital signature, ring signatures are frequently employed in practical situations because of their superior anonymity. In this work, we propose a quantum ring signature scheme based on secret sharing that does not use entanglement states. To guarantee the complete security of the participants' secret keys, the idea of secret sharing is incorporated into the quantum key distribution process during the key distribution stage. Each ring member contributes his private key share to the final verification formula through a recursive relationship throughout the signing and verification phases, and the verifier can utilize his private key share along with the user's public key to confirm the ring members' authenticity; The ε -AS2U hash function is used to encrypt the ring signer's identity during the entire signature process, which assures the signer's identity's complete anonymity, effectively protects the signer's privacy, and is more in line with practical requirements. [ABSTRACT FROM AUTHOR]

The temperature characteristics of ring lasers with a diameter of 480 μm of an original design with an active region based on 10 layers of InAs/InGaAs/GaAs quantum dots are studied. The lasers demonstrated a low threshold current density (200 A/cm2 at 20°C), the characteristic temperature of the threshold current in the range of 20–100°C was 68 K, the maximum lasing temperature was as high as 130°C. These values are only slightly inferior to the parameters of the edge-emitting lasers fabricated from the same epitaxial wafer. [ABSTRACT FROM AUTHOR]

We revisit the 3d GLSM computation of the equivariant quantum K-theory ring of the complex Grassmannian from the perspective of line defects. The 3d GLSM onto X = Gr(Nc, nf) is a circle compactification of the 3d N = 2 supersymmetric gauge theory with gauge group U N c k , k + l N c and nf fundamental chiral multiplets, for any choice of the Chern-Simons levels (k, l) in the 'geometric window'. For k = N c − n f 2 and l = −1, the twisted chiral ring generated by the half-BPS lines wrapping the circle has been previously identified with the quantum K-theory ring QKT(X). We identify new half-BPS line defects in the UV gauge theory, dubbed Grothendieck lines, which flow to the structure sheaves of the (equivariant) Schubert varieties of X. They are defined by coupling N = 2 supersymmetric gauged quantum mechanics of quiver type to the 3d GLSM. We explicitly show that the 1d Witten index of the defect worldline reproduces the Chern characters for the Schubert classes, which are written in terms of double Grothendieck polynomials. This gives us a physical realisation of the Schubert-class basis for QKT(X). We then use 3d A-model techniques to explicitly compute QKT(X) as well as other K-theoretic enumerative invariants such as the topological metric. We also consider the 2d/0d limit of our 3d/1d construction, which gives us local defects in the 2d GLSM, the Schubert defects, that realise equivariant quantum cohomology classes. [ABSTRACT FROM AUTHOR]

Quantum cascade lasers (QCLs) have emerged as promising candidates for generating chip-scale frequency combs in mid-infrared and terahertz wavelengths. In this work, we demonstrate frequency comb formation in ring terahertz QCLs using the injection of light from a distributed feedback (DFB) laser. The DFB design frequency is chosen to match the modes of the ring cavity (near 3.3 THz), and light from the DFB is injected into the ring QCL via a bus waveguide. By controlling the power and frequency of the optical injection, we show that combs can be selectively formed and controlled in the ring cavity. Numerical modeling suggests that this comb is primarily frequency-modulated in character, with the injection serving to trigger comb formation. We also show that the ring can be used as a filter to control the output of the DFB QCL, potentially being of interest in terahertz photonic integrated circuits. Our work demonstrates that waveguide couplers are a compelling approach for injecting and extracting radiation from ring terahertz combs and offer exciting possibilities for the generation of new comb states in terahertz, such as frequency-modulated waves, solitons, and more. [ABSTRACT FROM AUTHOR]

Within the effective mass approximation framework, the electronic and optical properties of GaAs-based two-dimensional eccentric quantum rings subjected to a transverse magnetic field with an inclination θ-angle to the x-axis are investigated using a two-dimensional diagonalisation method. The results show that the electron energy spectra in concentric quantum rings reveal transparency to the action of magnetic field orientation, contrary to their optical properties, which turn out to be anisotropic with this later. In addition, the eccentricity preserves the absorption coefficient spectra for y-polarisation for all orientations of the magnetic field qualitatively, while those of x-polarisation are significantly modified by eccentricity and magnetic field. Specific peak transitions occurring at specific magnetic field values and θ-angle can be used as a signature of magnetic field orientation and eccentricity. [ABSTRACT FROM AUTHOR]

We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [N. Gnan and E. Zaccarelli, Nat. Phys. 15, 683 (2019)] where an inner Hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced by opposite forces, and (iii) a semi-flexible model where an angular potential between adjacent monomers induces strong particle deformations. By analyzing the dynamics of the three models, we find that in all cases, there exists a direct link between the system fragility and particle asphericity. Among the three, only the first model displays anomalous dynamics in the form of a super-diffusive behavior of the mean-squared displacement and of a compressed exponential relaxation of the density auto-correlation function. We show that this is due to the combination of internal elasticity and the out-of-equilibrium force self-generated by each ring, both of which are necessary ingredients to induce such a peculiar behavior often observed in experiments of colloidal gels. These findings reinforce the role of particle deformation, connected to internal elasticity, in driving the dynamical response of dense soft particles. [ABSTRACT FROM AUTHOR]

Several proposals are available to get selective spin transmission through different nano-junctions and in all the cases the regulation is done either by applying a magnetic field or by tuning spin–orbit (SO) coupling. In the present work, we explore a separate scheme where the spin-dependent transport is regulated externally by irradiating a quantum ring that bridges the contact electrodes. This is a new proposal of generating spin selective transmission through a nano-junction, to the best of our knowledge. A high degree of spin polarization along with its phase alteration can be achieved by suitably adjusting the irradiation, circumventing the regulation of magnetic field and/or SO coupling. The effect of irradiation is included through the well-known Floquet-Bloch ansatz, where all the spin-dependent transport phenomena are worked out using Green's function formalism following the Landauer–Büttiker prescription within a tight-binding framework. Precise dependencies of light irradiation, SO coupling, magnetic flux threaded by the ring, interface sensitivity, system temperature, and impurities on spin polarization are critically investigated. Our analysis may give a new platform for spin selective electron transmission and make it applicable to other complex nano-structured materials also. We strongly believe that the present proposal can be examined in a suitable laboratory. [ABSTRACT FROM AUTHOR]

Optical absorption spectra of GaSb/GaAs quantum-ring-with-dot structures (QRDSs) are calculated using Fermi's golden rule by which the electronic states involved in the optical transitions are obtained from the eight-band k ⋅ p method. The absorption spectra of multi-stacked QRDS layers show that the interband and intraband transitions are favorable to intermediate band solar cells (IBSCs). A drift-diffusion model with rate equations for a solar cell containing multi-stacked QRDS layers is formulated based on the absorption spectra. The external quantum efficiency (EQE) determined by the model with the AM1.5 solar spectrum and additional infrared light demonstrates that the confined hole states in the quantum ring (QR) parts of the QRDSs effectively function as an IB. The more efficient two-step photon absorption indicated by the enhancement of the EQE also suggests the potential of QRDSs for the IBSCs. [ABSTRACT FROM AUTHOR]

In this paper, slow light features of an engineered photonic crystal waveguide are presented. The combined effect of lattice shift, lattice twist and introduction of ring-like holes (rings) in the innermost rows on the slow light features is studied. The rings are introduced in the first and second innermost rows of the waveguide. Slow light is characterized by calculating group index, second and fourth-order dispersions, and delay-bandwidth products. MIT Photonic Bands software is used for simulation. With rings in the innermost rows, a flat band of 17.71 nm is observed with a group index value of 12.72 and a flat band of 40.16 nm with a group index of 7.77. The normalized delay bandwidth product (NDBP) is observed as 0.1378 in the first structure and 0.1874 in the second structure with the proposed effects. These values are nearly 4.3 times higher in comparison with the NDBP value of the base structure (0.0436) and approximately 2 times higher than the engineered structure (0.0927). These structures are useful in slow light applications. [ABSTRACT FROM AUTHOR]

We present the study of the SiGe quantum ring (QR) modeled by an anharmonic axially symmetric potential with a centrifugal core in the effective mass approximation. We show how the femtosecond laser pulses (FLPs) can be used efficiently for controlling the induced current and magnetic field. We have compared the strength of induced currents and magnetic fields with and without pulsed laser which shows a substantial change. The spin-orbit interaction (SOI) and Zeeman energy show a massive impact on the generation and enhancement of these induced current and magnetic fields. These induced currents and magnetic fields have many applications in interdisciplinary areas. We have shown that the SOI presence with the FLP fields while competing with the confinement strength lowers the strength of the induced current and field. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically studied a 3D structure of GaAs/Al0.3Ga0.7As triple concentric quantum rings submitted to the combined action of a non-resonant intense laser and a static electric field. The 3D model was built using the cross-sectional profile of the structure that corresponds to a realistic experimental case of triple rings with different heights and widths. The electric field and the laser field have opposite influence on the energy levels, decreasing or increasing all studied levels, respectively. Linear or quadratic Stark effect can be seen in specific ranges of electric field values, depending on the anisotropy induced by the intense laser field, for given fields orientations. The observed anti-crossings are explained by wave-functions delocalisation from one ring to another or by symmetry exchange between the wave-functions of the inner ring. For the most deformed potential created by perpendicular orientation of electric field and intense laser polarisation, very large absorption peaks, blue-shifts, red-shifts or an oscillatory behaviour in peaks energy and amplitude are obtained in a controllable way by proper manipulation of the fields. This can be helpful for the tunability and optical features improvement of THz detectors or solar cells. [ABSTRACT FROM AUTHOR]

In this paper, we study the optical properties of a two-dimensional quantum ring with a diluted magnetic semiconductors structure. The Volcano model was chosen as the confinement potential of a quantum system. For interband optical transitions, the behavior of the absorption coefficient of a quantum ring as a function of the incident photon energy is numerically studied as a function of various values of such parameters as temperature, magnetic field, ring radius, and inner ring radius. In addition, the change in the threshold frequency as a function of the magnetic field and temperature for an interband optical transition is numerically studied. According to the results obtained, the considered parameters change the optical properties of the quantum ring. [ABSTRACT FROM AUTHOR]

We investigate the electronic properties of a semiconductor quantum ring with an elliptical shape and non-uniform height, allowing for distributed quantum-dot-like bulges along its perimeter. The adiabatic approximation and the finite element method are combined to calculate the allowed electron states in the structure under the effective mass approximation, considering the contributions from Rashba and Dresselahaus spin–orbit interactions and the Zeeman effect in the presence of an applied magnetic field. We discuss the features of the calculated spectra for two different ring geometries: a symmetric one with four dot-like bulges, and an asymmetric one with three hilled protuberances. The information about those states allows us to evaluate the linear optical absorption response associated with interlevel transitions between the ground and lowest excited states. This phenomenon takes place at resonant energies of only a few milielectronvolts. It is observed that spin–orbit interactions tend to quench this response under zero-field conditions in the case of symmetric confinement. [ABSTRACT FROM AUTHOR]

We theoretically investigate the properties of an electron energy spectrum in a double GaAs-Al0.3Ga0.7As quantum ring by using the effective mass and adiabatic approximations, together with a realistic description of the confining potential profile, which is assumed to be deformed due to the application of an intense nonresonant laser field. The effects of the applied magnetic field and spin-orbit interaction are included. We discuss the features of the lowest confined energy levels under a variation of magnetic field strengths and intense laser parameters. The influence of this external probe on the linear optical absorption response associated with interlevel transitions is analyzed by considering both the presence and absence of spin-orbit effects. [ABSTRACT FROM AUTHOR]

Epitaxially grown semiconductor quantum dots (QDs) and quantum rings (QRs) have been demonstrated to be excellent sources of single photons and entangled photon pairs enabling applications within quantum photonics. The emerging field of QD-based nanophotonics requires the deterministic integration of single or multiple QD structures into photonic architectures. However, the natural inhomogeneity and spatial randomness of self-assembled QDs limit their potential, and the reliable formation of homogeneous and ordered QDs during epitaxy still presents a challenge. Here, we demonstrate the fabrication of regular arrays of single III–V QDs and QRs using molecular beam epitaxy assisted by in situ direct laser interference patterning. Both droplet epitaxy (DE) GaAs/AlGaAs QDs and QRs and Stranski–Krastanov (SK) InAs/GaAs QDs are presented. The resulting QD structures exhibit high uniformity and good optical quality, in which a record-narrow photoluminescence linewidth of ∼17 meV from patterned GaAs QD arrays is achieved. Such QD and QR arrays fabricated through this novel optical technique constitute a next-generation platform for functional nanophotonic devices and act as useful building blocks for the future quantum revolution.

We establish a noncommutative generalisation of the Borel–Weil theorem for the Heckenberger–Kolb calculi of the irreducible quantum flag manifolds |${\mathcal {O}}_q(G/L_S)$|⁠ , generalising previous work for the quantum Grassmannians |${\mathcal {O}}_q(\textrm {Gr}_{n,m})$|⁠. As a direct consequence we get a novel noncommutative differential geometric presentation of the quantum coordinate rings |$S_q[G/L_S]$| of the irreducible quantum flag manifolds. The proof is formulated in terms of quantum principal bundles, and the recently introduced notion of a principal pair, and uses the Heckenberger and Kolb first-order differential calculus for the quantum Possion homogeneous spaces |${\mathcal {O}}_q(G/L^{\,\textrm {s}}_S)$|⁠. [ABSTRACT FROM AUTHOR]

In this paper, the optical properties of two-dimensional coupled concentric double quantum rings with a parabolic confinement potential are studied theoretically. The optical absorption coefficient for the transition from the ground state to the first excited state is calculated. The effects of inter-ring coupling, internal or external ring width variation, and on-center donor and acceptor impurities are investigated. The peak value of the absorption coefficient decreases when the width of the internal ring is decreased, but reducing the width of the external ring causes the absorption coefficient to first increase and then decrease. In addition, concentric double quantum rings with a wider internal (external) ring absorb the photons with higher (lower) energies. An increment of the inter-ring coupling causes the concentric double quantum rings to absorb photons with higher energies. Although the on-center impurity reduces the magnitude of the absorption coefficient, the decrement is considerable for the donor impurity rather than the acceptor impurity. It is shown that the peak value position of the absorption coefficient has an obvious blue-shift (red-shift) in the presence of donor (acceptor) impurity. [ABSTRACT FROM AUTHOR]

The article discusses the generation of terahertz optical solitons using dispersion-compensated antenna-coupled planarized ring Quantum Cascade Lasers (QCL). The researchers address the challenges of achieving solitons in terahertz ring QCLs, including dispersion compensation and power extraction. They propose a double waveguide structure and a planarization technique to overcome these challenges.