arXiv subjects

H. Bahlouli

Publications and source records attributed to H. Bahlouli.

At least 19 recordsLinked to original sources

arXiv2026

Single impurity atom embedded in a dipolar two-soliton molecule as a qubit

We consider a single impurity atom trapped in a double well (DW) potential created by a dipolar two-soliton molecule in a quasi-one-dimensional geometry. By solving the eigenvalue problem for the impurity atom in the DW potential, we find that its ground and first excited states are well separated from higher excited states. This allows it to be approximated by a desirable two-level quantum system. Numerical simulations of the Schrödinger equation, governing impurity atom, demonstrate periodic oscillations in the probability of finding the impurity confined either to the ``left" or to the ``right" side of the DW potential. An analytic expression for the coherent oscillations of the population imbalance between the two wells of the DW potential has been derived using the two-mode approximation. Theoretical predictions of the mathematical model are in good agreement with the results of numerical simulations. Potential usage of the developed setup as a physical realization of ``qubit" has been discussed.

cond-mat.quant-gas↗

arXiv2024

Manifestation of superfluidity in atom-number-imbalanced two-component Bose-Einstein condensates

Superfluid and dissipative regimes in the dynamics of a two-component quasi-one-dimensional Bose-Einstein condensate (BEC) with unequal atom numbers in the components have been explored. The system supports localized waves of the symbiotic type owing to the same-species repulsion and cross-species attraction. The minority BEC component moves through the majority component and creates excitations. To quantify the emerging excitations we introduce a time-dependent function called disturbance. Through numerical simulations of the coupled Gross-Pitaevskii equations with periodic boundary conditions, we have revealed a critical velocity of the localized wave, above which a transition from superfluid to dissipative regime occurs, evidenced by a sharp increase in the disturbance function. The factors responsible for the discrepancy between the actual critical velocity and the speed of sound, expected from theoretical arguments, have been discussed.

cond-mat.quant-gas↗

arXiv2023

Two-dimensional symbiotic solitons and quantum droplets in a quasi-one-dimensional optical lattice

Symbiotic solitons (SS) and quantum droplets (QD) are self-trapped localized modes emerging in binary Bose-gas mixtures with intra-component repulsion and inter-component attraction. We have shown that two-dimensional SS can be stabilized against collapse or decay by means of a quasi-one-dimensional optical lattice (OL). Mobility of SSs along the free direction of the potential allows us to explore interactions and collisions of SSs moving in the same channel and neighboring channels of the quasi-1D OL. For the case of equal atom numbers in both components of the binary Bose-Einstein condensate (BEC) we have developed a variational approach that showed the stability of SS. For parameter settings when the SS stays on the verge of collapse instability, we take into account the Lee-Huang-Yang quantum fluctuations (QF) term in the coupled Gross-Pitaevskii equations. Repulsive QF prevents the mean-field collapse and gives rise to the formation of 2D QDs with peculiar properties such as incompressibility and surface tension, which are inherent to liquids. The proposed model of binary BEC loaded in a quasi-1D OL allows us to demonstrate the manifestations of the incompressibility and surface tension of 2D QDs. The formation of QD in imbalanced binary BEC with different numbers of atoms of the components in the presence of a quasi-1D OL has been investigated. The possible application of the proposed model to studies of anisotropic superfluidity is discussed.

cond-mat.quant-gas↗

arXiv2022

Electrostatic multipole contributions to the binding energy of electrons

The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole contribution cos(theta)/r^2. Moreover, the third order effect is due to the electric quadrupole potential, [3*cos^2(theta)-1]/2*r^3. We use the tridiagonal representation approach to give a reasonably accurate account for the combined effects of all these contributions to the binding energy of the electron but with an effective quadrupole interaction. As an application, we obtain the bound states of a valence electron in an atom with both electric dipole and quadrupole moments.

quant-ph↗

arXiv2021

Unidirectional flow of composite bright-bright solitons through asymmetric double potential barriers and wells

We investigate the dynamics of two component bright-bright (BB) solitons through reflectionless double barrier and double well potentials in the framework of a Manakov system governed by the coupled nonlinear Schrödinger equations. The objective is to achieve unidirectional flow and unidirectional segregation/splitting, which may be used in the design of optical data processing devices. We observe how the propagation of composite BB soliton is affected by the presence of interaction coupling between the two components passing through the asymmetric potentials. We consider Gaussian and Rosen-Morse double potential barriers in order to achieve the unidirectional flow. Moreover, we observe a novel phenomenon which we name "\textit{Polarity Reversal}" in the unidirectional flow. In this situation, the polarity of the diode is reversed. To understand the physics underlying these phenomena, we perform a variational calculation where we also achieve unidirectional segregation/splitting using an asymmetric double square potential well. Our comparative study between analytical and numerical analysis lead to an excellent agreement between the two methods.

nlin.PS↗

arXiv2021

Deformed Morse-like potential

We introduce an exactly solvable one-dimensional potential that supports both bound and/or resonance states. This potential is a generalization of the well-known 1D Morse potential where we introduced a deformation that preserves the finite spectrum property. On the other hand, in the limit of zero deformation, the potential reduces to the exponentially confining potential well introduced recently by A. D. Alhaidari. The latter potential supports infinite spectrum which means that the zero deformation limit is a critical point where our system will transition from the finite spectrum limit to the infinite spectrum limit. We solve the corresponding Schrodinger equation and obtain the energy spectrum and the eigenstates using the tridiagonal representation approach.

quant-ph↗

arXiv2020

Series solutions of Bessel-type differential equation in terms of orthogonal polynomials and physical applications

We obtain a class of exact solutions of a Bessel-type differential equation, which is a six-parameter linear ordinary differential equation of the second order with irregular (essential) singularity at the origin. The solutions are obtained using the Tridiagonal Representation Approach (TRA) as bounded series of square integrable functions written in terms of the Bessel polynomial on the real line. The expansion coefficients of the series are orthogonal polynomials in the equation parameters space. We use our findings to obtain solutions of the Schrödinger equation for some novel potential functions.

math.CA↗

arXiv2019

Bound states and the potential parameter spectrum

In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated wavefunctions)? To answer this question, we use the "tridiagonal representation approach" to solve the wave equation at the given energy by expanding the wavefunction in a series of energy-dependent square integrable basis functions in configuration space. The expansion coefficients satisfy a three-term recursion relation, which is solved in terms of orthogonal polynomials. Depending on the selected energy we show that one of the potential parameters must assume a value from within a discrete set called the "potential parameter spectrum" (PPS). This discrete set is obtained from the spectrum of the above polynomials and can be either a finite or an infinite discrete set. Inverting the relation between the energy and the PPS gives the bound state energy spectrum. Therefore, the answer to the above question is affirmative.

math-ph↗

arXiv2019

Electron collimation at van der Waals domain walls in bilayer graphene

We show that a domain wall separating single layer graphene (SLG) and AA-stacked bilayer graphene (AA-BLG) can be used to generate highly collimated electron beams which can be steered by a magnetic field. Such system exists in two distinct configurations, namely, locally delaminated AA-BLG and terminated AA-BLG whose terminal edge-type can be either zigzag or armchair. We investigate the electron scattering using semi-classical dynamics and verify the results independently with wave-packed dynamics simulations. We find that the proposed system supports two distinct types of collimated beams that correspond to the lower and upper cones in AA-BLG. Our computational results also reveal that collimation is robust against the number of layers connected to AA-BLG and terminal edges.

cond-mat.mes-hall↗

arXiv2019

Tridiagonal Representation Approach in Quantum Mechanics

We present an algebraic approach for finding exact solutions of the wave equation. The approach, which is referred to as the Tridiagonal Representation Approach (TRA), is inspired by the J-matrix method and based on the theory of orthogonal polynomials. The class of exactly solvable problems in this approach is larger than the conventional class. All properties of the physical system (energy spectrum of the bound states, phase shift of the scattering states, energy density of states, etc.) are obtained in this approach directly and simply from the properties of the associated orthogonal polynomials.

quant-ph↗

arXiv2018

Weakly bound solitons and two-soliton molecules in dipolar Bose-Einstein condensates

Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross-Pitaevskii equation and good qualitative agreement between them is demonstrated.

cond-mat.quant-gas↗

arXiv2018

Effect of quintic nonlinearity on modulation instability in coupled nonlinear Schroedinger systems

Modulation instability (MI) in continuous media described by a system of two cubic-quintic nonlinear Schrödinger equations (NLSE) has been investigated with a focus on revealing the contribution of the quintic nonlinearity to the development of MI in its linear and nonlinear stages. For the linear stage we derive analytic expression for the MI gain spectrum and compare its predictions with numerical simulations of the governing coupled NLSE. It is found that the quintic nonlinearity significantly enhances the growth rate of MI and alters the features of this well known phenomenon by suppressing its time-periodic character. For the nonlinear stage by employing a localized perturbation to the constant background we find that the quintic nonlinearity notably changes the behavior of MI in the central oscillatory region of the integration domain. In numerical experiments we observe emergence of multiple moving coupled solitons if the parameters are in the domain of MI. Possible applications of the obtained results to mixtures of Bose-Einstein condensates and bimodal light propagation in waveguide arrays are discussed.

nlin.PS↗

arXiv2018

Band gap engineering in AA-stacked bilayer graphene

We demonstrate that AA-stacked bilayer graphene (AA-BLG) encapsulated by dielectric materials can possess an energy gap due to the induced mass term. Using the four-band continuum model, we evaluate transmission and reflection probabilities along with the respective conductance. Considering interlayer mass-term difference opens a gap in the energy spectrum and also couples the two Dirac cones. This cone coupling induces an inter-cone transport that is asymmetric with respect to the normal incidence in the presence of asymmetric mass-term. The energy spectrum of the gapped AA-BLG exhibits electron-hole asymmetry that is reflected in the associated intra- and inter-cone channels. We also find that even though Klein tunneling exists in gated and biased AA-BLG, it is precluded by the interlayer mass-term difference and instead Febry-Pérot resonances appear.

cond-mat.mes-hall↗

arXiv2018

Electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment

We make a multipole expansion of the atomic/molecular electrostatic charge distribution as seen by the valence electron up to the quadrupole term. The Tridiagonal Representation Approach (TRA) is used to obtain an exact bound state solution associated with an effective quadrupole moment and assuming that the electron-molecule interaction is screened by suborbital electrons. We show that the number of states available for binding the electron is finite forcing an energy jump in its transition to the continuum that could be detected experimentally in some favorable settings. We expect that our solution gives an alternative, viable and simple description of the binding of valence electron(s) in atoms/molecules with electric dipole and quadrupole moments. We also ascertain that our model implies that a pure quadrupole-bound anion cannot exist in such a charge-screening environment.

quant-ph↗

arXiv2018

Exact solvability of two new 3D and 1D nonrelativistic potentials within the TRA framework

This work is concerned about introducing two new 1D and 3D confined potentials and present their solutions using the Tridiagonal Representation Approach (TRA). The wavefunction is written as a series in terms of square integrable basis functions which are expressed in terms of Jacobi polynomials. Moreover, the expansion coefficients are written in terms of new orthogonal polynomials that were introduced recently by Alhaidari, the analytical properties of these polynomials are yet to be derived. Moreover, we have computed the numerical eigen-energies for both potentials by considering specific choices of the potential parameters.

math-ph↗

arXiv2018

Confined states in graphene quantum blisters

Bilayer graphene samples may exhibit regions where the two layers are locally delaminated forming a so-called quantum blister in the graphene sheet. Electron and hole states can be confined in this graphene quantum blisters (GQB) by applying a global electrostatic bias. We scrutinize the electronic properties of these confined states under the variation of interlayer bias, coupling, and blister's size. The spectra display strong anti-crossings due to the coupling of the confined states on upper and lower layers inside the blister. These spectra are layer localized where the respective confined states reside on either layer or equally distributed. For finite angular momentum, this layer localization can be at the edge of the blister and corresponds to degenerate modes of opposite momenta. Furthermore, the energy levels in GQB exhibit electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we demonstrate that confinement in GQB persists even in the presence of a variation in the inter-layer coupling.

cond-mat.mes-hall↗

arXiv2018

Substrate effects on transport properties of a biased AA-stacked bilayer graphene

The important experimental advances in graphene fabrication and its peculiar transport properties motivated researchers to utilize graphene as a potential basis for the next generation of fast and smart electronic devices. In this article, we investigate the influence of a potential substrate on the transport properties of a biased AA-stacked n-p-n bilayer graphene junction (AA-BLG). Using the Dirac Hamiltonian with the transfer matrix approach we obtain the transmission probabilities and thus the respective conductance. In the presence of the induced mass-term, the energy spectrum and the intra-cone transmission drastically change while the inter-cone transmission remains zero. On the other hand, the bias slightly alters the energy spectrum but it significantly affects the transport properties due to its ability to switch on the inter-cone transmission. In addition, we find that Klein tunneling is attenuated in the presence of the induced mass-term which can improve the carriers confinement in such configurations. Our findings provide possible experimental measurements to determine the interlayer coupling and the induced mass terms in graphene bilayer based on conductance and band structure measurements.

cond-mat.mes-hall↗

arXiv2018

Graphene quantum blisters: a tunable system to confine charge carriers

Due to Klein tunneling, electrostatic confinement of electrons in graphene is not possible. This hinders the use of graphene for quantum dot applications. Only through quasi-bound states with finite lifetime has one achieved to confine charge carriers. Here we propose that bilayer graphene with a local region of decoupled graphene layers is able to generate bound states under the application of an electrostatic gate. The discrete energy levels in such a quantum blister correspond to localized electron and hole states in the top and bottom layers. We find that this layer localization and the energy spectrum itself are tunable by a global electrostatic gate and that the latter also coincides with the electronic modes in a graphene disk. Curiously, states with energy close to the continuum exist primarily in the classically forbidden region outside the domain defining the blister. The results are robust against variations in size and shape of the blister which shows that it is a versatile system to achieve tunable electrostatic confinement in graphene.

cond-mat.mes-hall↗