arXiv subjects

R. Ahl Laamara

Publications and source records attributed to R. Ahl Laamara.

At least 37 records · Page 2Linked to original sources

arXiv2023

Embedding Integrable Superspin Chain in String Theory

Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its embedding in string theory. Because of the $\mathbb{Z}_{2}$-grading of $ sl(m|n)$, we show that the $\left( m+n\right) !/m!n!$ varieties of superspin chains with underlying super geometries have different cycle homologies. We investigate the algebraic and homological features of these integrable quantum chains and give a link between graded 2-cycles and genus-g Rieman surfaces $Σ_{g}$. Moreover, using homology language, we yield the brane realisation of the $sl(m|n)$ chain in type IIA string and its uplift to M-theory. Other \textrm{aspects} like graded complex surfaces with $sl(m|n)$ singularity as well as super magnons are also described.

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arXiv2023

't Hooft lines of ADE-type and Topological Quivers

We investigate 4D Chern-Simons theory with ADE gauge symmetries in the presence of interacting Wilson and 't Hooft line defects. We analyse the intrinsic properties of these lines' coupling and explicate the building of oscillator-type Lax matrices verifying the RLL integrability equation. We propose gauge quiver diagrams Q$_{G}^{μ}$ encoding the topological data carried by the Lax operators and give several examples where Darboux coordinates are interpreted in terms of topological bi-fundamental matter. We exploit this graphical description $\left( i\right) $ to give new results regarding solutions in representations beyond the fundamentals of $sl_{N}$, $% so_{2N}$ and $e_{6,7}$, and $\left( ii\right) $ to classify the Lax operators for simply laced symmetries in a unified E$_{7}$ CS theory. For quick access, a summary list of the leading topological quivers Q$% _{ADE}^{μ}$ is given in the conclusion section [Figures 29.(a-e), 30.(a-d) and 31.(a-d)].

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arXiv2022

Controlled quantum teleportation between discrete and continuous physical systems

Quantum teleportation of an unknown state basing on the interaction between discrete-valued states (DV) and continuous-valued states (CV) presented a particular challenge in quantum technologies. Here we consider the problem of controlled quantum teleportation of an amplitude-matched CV qubit, encoded by a coherent state of a varied phase as a superposition of the vacuum- and single-photon optical states among two distant partners Alice and Bob, with the consent of controller, Charlie. To achieve this task, we use an hybrid tripartite entangled state (interaction between the discrete and continuous variables states) as the quantum resource where the coherent part belongs to Alice, while the single-photon belongs to Bob and Charlie and the CV qubit is at the disposal of Alice. The discrete-continuous interaction is realized on highly transmissive beam-splitter. We have shown that the perfectly of teleportation fidelity depends on the phase difference between the phase of the state to teleport and the phase of the sender's mode, we found that for a difference which approaches 0 or $π$, near perfect controlled quantum teleportation can be obtained in terms of the fidelity and independently of the amplitude $α$ and the squeezing parameter $ζ$. Experimentally, this proposed scheme has been implemented using linear optical components such as beam splitter, phase shifters and photon counters.

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arXiv2022

Lax Operator and superspin chains from 4D CS gauge theory

We study the properties of interacting line defects in the four-dimensional Chern Simons (CS) gauge theory with invariance given by the $SL\left( m|n\right) $ super-group family. From this theory, we derive the oscillator realisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry. To this end, we investigate the holomorphic property of the bosonic Lax operator $\mathcal{L}$ and build a differential equation $% \mathfrak{D}\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of $\mathcal{L}$ in the framework of\ the CS theory. We generalize this construction to the case of gauge super-groups, and develop a Dynkin super-diagram algorithm to\ deal with the decomposition of the Lie superalgebras. We obtain the generalisation of the Lax operator describing the interaction between the electric Wilson super-lines and the magnetic 't Hooft super-defects. This coupling is given in terms of a mixture of bosonic and fermionic oscillator degrees of freedom in the phase space of magnetically charged 't Hooft super-lines. The purely fermionic realisation of the superspin chain Lax operator is also investigated and it is found to coincide exactly with the $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords: 4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin super-diagrams, Superspin chains and integrability, Super- Lax operator.

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arXiv2021

Neutrino phenomenology in the flavored NMSSM without domain wall problems

We propose a next-to-minimal supersymmetric Standard Model (NMSSM) extended by an $\mathbb{A}_{4}\times \boldsymbol{Z}_{3}$ flavor symmetry and three right-handed neutrinos providing a detailed study of the neutrino sector and a solution to the domain wall problem. In this proposal, neutrino masses are generated through Type I seesaw mechanism while the mixing angles are described by the trimaximal mixing realized using the NMSSM singlet S and only two flavon fields. The phenomenology of neutrino parameters is studied for normal and inverted mass hierarchies. In particular, we numerically evaluated the observables related to neutrino masses and mixing, namely, $\sum m_{i}$, $m_{ee}$, $m_{ν_{e}}$, and $δ_{CP}$ where we find that the ranges of $m_{ee}$ and $m_{ν_{e}}$ are accessible by current and future experiments while the obtained ranges of $\sum m_{i}$ and $δ_{CP}$ lie within the current experimental data. Another attractive feature we discussed in this paper is the circumvention of the domain wall problem induced by the spontaneous breaking of the $\mathbb{A}_{4}\times \boldsymbol{Z}_{3}$ discrete symmetry. We first showed that the domain walls in the charged lepton sector occur at high energy scale leading to unproblematic domain walls, while in the neutrino sector they are inevitable. Then, to solve this problem, we reconsidered the well-known approach that relies on the explicit breaking of the discrete symmetry through the insertion of Planck-suppressed operators induced by supergravity. \keywords{Neutrino physics, Discrete flavor symmetry,Trimaximal mixing, Domain walls}

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arXiv2019

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg $XY$ model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in the multi-component quantum system [S. Kim et al., Phys. Rev. A. 97, 032326 (2018)]. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg $XY$ model. Two distinct situations are considered. The first one concerns the anisotropic $XY$ model and the second situation concerns the isotropic $XY$ model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.

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arXiv2019

Quantum Fisher information matrix in Heisenberg XY model

The quantum Fisher information matrix provides us with a tool to determine the precision, in any multiparametric estimation protocol, through quantum Cramér-Rao bound. In this work, we study simultaneous and individual estimation strategies using the density matrix vectorization method. Two special Heisenberg $XY$ models are considered. The first one concerns the anisotropic $XY$ model in which the temperature $T$ and the anisotropic parameter $γ$ are estimated. The second situation concerns the isotropic $XY$ model submitted to an external magnetic field $B$ in which the temperature and the magnetic field are estimated. Our results show that the simultaneous strategy of multiple parameters is always advantageous and can provide a better precision than the individual strategy in the multiparameter estimation procedures.

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arXiv2019

Universal evolution of non-classical correlations due to collective spontaneous emission

We explore the spontaneous generation and decay of quantum correlations between two identical atoms coupled to a common Markovian environment in the presence of electromagnetic field modes. For this purpose, we analyze the dynamics of quantum correlations by employing the concurrence, the trace quantum discord and the local quantum uncertainty, for collective Dicke states. It is shown that the collective damping and dipole-dipole interaction plays a key role in enhancing non-classical correlations during the process of intrinsic decoherence. The quantum correlations can be maintained over a long time but for small distance between the two atoms.

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arXiv2018

Non-classical correlations in a two-mode optomechanical system

The pairwise quantum correlations in a tripartite optomechanical system comprising a mechanical mode and two optical modes are analyzed. The Simon criterion is used as a witness of the separability. Whereas, the Gaussian discord is employed to capture the quantumness of correlations. Both entanglement and Gaussian discord are evaluated as functions of the parameters characterizing the environment and the system (temperature, squeezing and optomechanical coupling). We work in the resolved-sideband regime. We show that it is possible to reach simultaneous three bipartite entanglements via the quantum correlations transfer from the squeezed light to the system. While, even without squeezed light, the quantumness of correlations can be captured simultaneously between the three modes for a very wide range of parameters. Specifically, we find that the two optical modes exhibit more quantum correlations in comparison with the entangled mechanical-optical modes. Finally, unlike the two hybrid subsystems, the purely optical one seems more resilient against the environmental destructive effects.

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arXiv2018

Hybrid seesaw neutrino model in SUSY $SU(5)\times \mathbb{A}_{4}$

Motivated by recent results from neutrino experiments, we study the neutrino masses and mixing in the framework of a SUSY $SU(5)\times \mathbb{A}_{4} $ model. The hybrid of Type I and Type II seesaw mechanisms leads to the nonzero value of the reactor angle $θ_{13}\neq 0$ and to the recently disfavored maximal atmospheric angle $θ_{23} \neq45^{\circ}$ by the NOvA experiment. The phenomenological consequences of the model are studied for both normal and inverted mass hierarchies. The obtained ranges for the effective Majorana neutrino mass $m_{ββ}$, the electron neutrino mass $m_{ν_{e}}$, and the $CP$ violating phase $δ_{CP}$ lie within the current experimental allowed ranges where we find that the normal mass hierarchy is favored over the inverted one.

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arXiv2017

Partial Breaking in Rigid Limit of $\mathcal{N}=2$ Gauged Supergravity

Using a new manner to rescale fields in $\mathcal{N}=2$ gauged supergravity with n$_{V}$ vector multiplets and n$_{H}$ hypermultiplets, we develop the explicit derivation of the rigid limit of quaternionic isometry Ward identities agreeing with known results. We show that the rigid limit can be achieved, amongst others, by performing two successive transformations on the covariantly holomorphic sections $V^{M}\left( z,\bar{z}\right) $ of the special Kahler manifold: a particular symplectic change followed by a particular Kahler transformation. We also give a geometric interpretation of the $η_{i}$ parameters used in arXiv:1508.01474 to deal with the expansion of the holomorphic prepotential $\mathcal{F}\left( z\right) $ of the $\mathcal{N}=2$ theory. We give as well a D- brane realisation of gauged quaternionic isometries and an interpretation of the embedding tensor $\vartheta_{M}^{u}$ in terms of type IIA/IIB mirror symmetry. Moreover, we construct explicit metrics for a new family of $4r$- dimensional quaternionic manifolds $\boldsymbol{M}_{QK}^{\left( n_{H}\right) }$ classified by ADE Lie algebras generalising the $SO\left( 1,4\right) /SO\left( 4\right) $ geometry which corresponds to $A_{1}\sim su\left( 2\right) $. The conditions of the partial breaking of $\mathcal{N}=2$ supersymmetry in the rigid limit are also derived for both the observable and the hidden sectors. Other features are also studied.

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arXiv2016

Type II seesaw supersymmetric neutrino model for $θ_{13}\neq0$

Using the type II seesaw approach and properties of discrete flavor symmetry group representations, we build a supersymmetric $A_{4}\times A_{3}$\ neutrino model with $θ_{13}\neq0$. After describing the basis of this model--which is beyond the minimal supersymmetric Standard Model--with a superfield spectrum containing flavons in $A_{4}\times A_{3}$\ representations, we first generate the tribimaximal neutrino mixing which is known to be in agreement with the mixing angles $θ_{12}$ and $θ_{23}$. Then, we give the scalar potential of the theory where the $A_{3}$ discrete subsymmetry is used to avoid the so-called sequestering problem. We \textrm{next} study the deviation from the tribimaximal mixing matrix which is produced by perturbing the neutrino mass matrix with a nontrivial $A_{4}$ singlet. Normal and inverted mass hierarchies are discussed numerically. We also study the breaking of $A_{4}$\ down to $Z_{3}$\ in the charged lepton sector, and use the branching ratio of the decay $τ\rightarrow μμe$--which is allowed by the residual symmetry $Z_{3}$--to get estimations on the mass of one of the flavons and the cutoff scale $Λ$ of the model.

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arXiv2016

On Discrete Gauge Symmetries in Trinification Model

Given the important role of discrete gauge symmetries in viable models, we discuss these symmetries in intersecting D6-brane trinification model where the ZN symmetry is investigated and its identification is shown.

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arXiv2016

MSSM-like from $SU_{5}\times D_{4}$ Models

Using finite discrete group characters and symmetry breaking by hyperflux as well as constraints on top- quark family, we study minimal low energy effective theory following from SU$_{5}\times D_{4}$ models embedded in F-theory with non abelian flux. Matter curves spectrum of the models is obtained from SU$_{5}\times S_{5}$ theory with monodromy $S_{5}$ by performing two breakings; first from symmetric group $S_{5}$ to $S_{4}$ subsymmetry; and next to dihedral $D_{4}$ subgroup. As a consequence, and depending on the ways of decomposing triplets of $S_{4}$, we end with three types of $D_{4}$- models. Explicit constructions of these theories are given and a MSSM- like spectrum is derived.

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arXiv2015

Hilbert-Schmidt measure of pairwise quantum discord for three-qubit $X$ states

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit $X$ states. They include three-qubit states of ${\rm W}$, ${\rm GHZ}$ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.

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arXiv2015

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schrödinger cat states

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schrödinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three and four qubit systems. In the second scheme, the subsystem comprising the $(k-1)$ qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.

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arXiv2015

$\mathcal{N}=2$ Supersymmetry Partial Breaking and Tadpole Anomaly

We consider the $U(1) ^{n}$ extension of the effective $\mathcal{N}=2$ supersymmetric $U(1) \times U(1) $ model of $arXiv:1204.2141$; and study the explicit relationship between partial breaking of $\mathcal{N}=2$ supersymmetry constraint and D3 brane tadpole anomaly of type IIB string on Calabi-Yau threefolds in presence of H$^{RR}$ and H$^{NS}$ fluxes. We also comment on supersymmetry breaking in the particular $\mathcal{N}=2$ $U(1) $ Maxwell theory; and study its interpretation in connection with the tadpole anomaly with extra localized flux sources.

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arXiv2015

Building SO$_{10}$- models with $\mathbb{D}_{4}$ symmetry

Using characters of finite group representations and monodromy of matter curves in F-GUT, we complete partial results in literature by building SO$% _{10}$ models with dihedral $\mathbb{D}_{4}$ discrete symmetry. We first revisit the $\mathbb{S}_{4}$-and $\mathbb{S}_{3}$-models from the discrete group character view, then we extend the construction to $\mathbb{D}_{4}$.\ We find that there are three types of $SO_{10}\times \mathbb{D}_{4}$ models depending on the ways the $\mathbb{S}_{4}$-triplets break down in terms of irreducible $\mathbb{D}_{4}$- representations: $\left(α \right) $ as $\boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,+}};$ or $\left(β\right) \boldsymbol{\ 1}_{_{+,+}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,-}};$ or also $\left(γ\right) $ $\mathbf{1}_{_{+,-}}\oplus \mathbf{2}_{_{0,0}}$. Superpotentials and other features are also given.

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