arXiv subjects

E. Nahmad-Achar

Publications and source records attributed to E. Nahmad-Achar.

At least 19 recordsLinked to original sources

arXiv2026

Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of 2-Level Matter-Field Systems

Quantum information measures are used to study the quantum phase diagrams of a two-level extended Dicke model, including the particle dipole-dipole interaction, for a finite number of particles. This is treated both with and without the rotating-wave approximation. Differences are noted between these new diagrams and those obtained in the corresponding variational treatment. The standard deviation of the population inversion operator and the correlation of the number of parti- cles occupying the ground and excited levels, carry most of the information of the regions where a phase transition takes place. The correlation coefficient of the number of photons and the number of particles occupying the excited level yields information of the sudden changes in the behavior of the ground state of the composite system.

quant-ph↗

arXiv2025

Geometric properties of qudit systems

We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian systems with known average energy. These geometric characterizations are given in terms of the generalized diagonal Bloch vectors and the invariants of the special unitary group in $n$ dimensions. As examples, Hamiltonians written in terms of linear and quadratic generators of the angular momentum algebra are considered with $J= 1$ and $J=3/2$. For these cases, paths as functions of the temperature are established in the corresponding simplex representations, which show first- and second-order quantum phase transitions, as well as the adiabatic evolution of the interaction strengths (control parameters) of the Hamiltonian models. For the Lipkin-Meshkov-Glick Hamiltonian the quantum phase diagram is explicitly shown for different temperature values in parameter space.

quant-ph↗

arXiv2024

Dynamic violation of Bell's inequalities in the angular momentum representation

A parametrization of density matrices of $d$ dimensions in terms of the raising $J_+$ and lowering $J_-$ angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta $j_1$ and $j_2$ is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the $X$-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel'son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell's inequality.

quant-ph↗

arXiv2023

Storing Quantum Information in a generalised Dicke Model via a Simple Rotation

A method for storing quantum information is presented for $3$-level atomic systems interacting dipolarly with a single radiation field. The method involves performing simple local SU(2) rotations on the Hamiltonian. Under equal detuning, these transformations decouple one of the atomic levels from the electromagnetic field for the $Λ$- and $V$-configurations, yielding two effective $2$-level systems (qubits) plus an isolated atomic level; this allows for the exchange of information between the qubits. This rotation preserves the quantum phase diagram of the system. The method could possibly be used as a means to manipulate quantum information, such as storage and retrieval, or communication via a transmission line.

quant-ph↗

arXiv2023

Wigner Function Analysis of Finite Matter-Radiation Systems

We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of minimum fidelity.

quant-ph↗

arXiv2023

Geometry, quantum correlations, and phase transitions in the $Λ$-atomic configuration

The quantum phase diagram for a finite $3$-level system in the $Λ$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility and entanglement, applied to the reduced density matrix of the matter sector of the system. The quantum phases are explained by emphasizing the spontaneous symmetry breaking along the separatrix. Additionally, a description of the reduced density matrix of one atom in terms of a simplex allows a geometric representation of the entanglement and purity properties of the system. These concepts are calculated for both, the symmetry-adapted variational coherent states and the numerical diagonalisation of the Hamiltonian, and compared. The differences in purity and entanglement obtained in both calculations can be explained and visualised by means of this simplex representation.

quant-ph↗

arXiv2020

Quantum-Optical set-up for the Monty Hall problem

A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined by considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. We also discuss the influence of noise on the game outcome when the parties play through a noisy quantum channel. The experimental set-up can be used to quickly verify the counter-intuitive result of the Monty Hall problem, adding pedagogic value to the proposal.

quant-ph↗

arXiv2019

Optimal basis for the generalized Dicke model

A methodology is devised for building optimal bases for the generalized Dicke model based on the symmetry adapted variational solution to the problem. At order zero, the matter sector is constructed by distributing $N_a$ particles in all the possible two-level subsystems connected with electromagnetic radiation; the next order is obtained when the states of $N_a-1$ particles are added and distributed again into the two-level subsystems; and so on. In the electromagnetic sector, the order zero for each mode is the direct sum of the Fock spaces, truncated to a value of the corresponding constants of motion of each two-level subsystem; by including contributions of the other modes, the next orders are obtained. As an example of the procedure we consider $4$ atoms in the $Ξ$ configuration interacting dipolarly with two modes of electromagnetic radiation. The results may be applied to situations in quantum optics, quantum information, and quantum computing.

quant-ph↗

arXiv2018

Quantum phases of a three-level matter-radiation interaction model using $SU(3)$ coherent states with different cooperation numbers

We use coherent states as trial states for a variational approach to study a system of a finite number of three-level atoms interacting in a dipolar approximation with a one-mode electromagnetic field. The atoms are treated as semi-distinguishable using different cooperation numbers and representations of SU(3). We focus our analysis on the quantum phases of the system as well as the behavior of the most relevant observables near the phase transitions. The results are computed for all three possible configurations ($Ξ$, $Λ$ and $V$) of the three-level atoms.

quant-ph↗

arXiv2017

Dynamic Generation of Light States with Discrete Symmetries

A dynamic procedure is established within the generalised Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group ${\cal C}_n$. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of $3$-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, $\vert ψ\rangle_{M_1}$, and $\vert ψ\rangle_{M_2}$, is considered. It can be generated by the proper selection of the time-of-flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order $n=\vert M_1-M_2\vert$.

quant-ph↗

arXiv2017

Characterization of the quantum phase transition in a two-mode Dicke model for different cooperation numbers

We show how the use of variational states to approximate the ground state of a system can be employed to study a multi-mode Dicke model. One of the main contributions of this work is the introduction of a not very commonly used quantity, the cooperation number, and the study of its influence on the behavior of the system, paying particular attention to the quantum phase transitions and the accuracy of the used approximations. We also show how these phase transitions affect the dependence of the expectation values of some of the observables relevant to the system and the entropy of entanglement with respect to the energy difference between atomic states and the coupling strength between matter and radiation, thus characterizing the transitions in different ways.

quant-ph↗

arXiv2016

Variational Study of $λ$- and $N$-Atomic Configurations Interacting with an Electromagnetic Field of $2$ Modes

A study of the $λ$- and $N$-atomic configurations under dipolar interaction with $2$ modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both configurations exhibit normal and collective (super-radiant) regimes. While the latter in the $λ$-configuration divides itself into $2$ subregions, corresponding to each of the modes, that in the $N$-configuration may be divided into $2$ or $3$ subregions depending on whether the field modes divide the atomic system into $2$ separate subsystems or not. Our variational procedure compares well with the exact quantum solution. The properties of the relevant field and matter observables are obtained.

quant-ph↗

arXiv2016

Parametrisation in electrostatic DPD Dynamics and Applications

A brief overview of mesoscopic modelling via dissipative particle dynamics is presented, with emphasis on the appropriate parametrisation and how to calculate the relevant parameters for given realistic systems. The dependence on concentration and temperature of the interaction parameters is also considered, as well as some applications.

physics.chem-ph↗

arXiv2016

Multiscale Modeling of the effect of Pressure on the Interfacial Tension and other Cohesion Parameters in Binary Mixtures

We study and predict the interfacial tension, solubility parameters and Flory-Huggins parameters of binary mixtures as functions of pressure and temperature, using multiscale numerical simulation. A mesoscopic approach is proposed for simulating the pressure dependence of the interfacial tension for binary mixtures, at different temperatures, using classical Dissipative Particle Dynamics (DPD). The thermodynamic properties of real systems are reproduced via the parametrization of the repulsive interaction parameters as functions of pressure and temperature via Molecular Dynamics simulations. Using this methodology, we calculate and analyze the cohesive density energy and the solubility parameters of different species obtaining excellent agreement with reported experimental behavior. The pressure- and temperature-dependent Flory-Huggins and repulsive DPD interaction parameters for binary mixtures are also obtained and validated against experimental data. This multiscale methodology offers the benefit of being applicable for any species and under difficult or non-feasible experimental conditions, at a relatively low computational cost.

physics.chem-ph↗

arXiv2015

Symmetry Adapted Coherent States for Three-Level Atoms Interacting with One-Mode Radiation

We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of Na three- level atoms interacting with a one-mode quantised electromagnetic field, with and without the rotating wave approximation, which preserves the symmetry presented by the Hamiltonian. These provide us with the possibility of finding analytical solutions for the ground and first excited states. We study the properties of these solutions for the V-configuration in the double resonance condition, and calculate the expectation values of the number of photons, the atomic populations, the total number of excitations, and their corresponding fluctuations. We also calculate the photon number distribution and the linear entropy of the reduced density matrix to estimate the entanglement between matter and radiation. For the first time, we exhibit analytical expressions for all of these quantities, as well as an analytical description for the phase diagram in parameter space, which distinguishes the normal and collective regions, and which gives us all the quantum phase transitions of the ground state from one region to the other as we vary the interaction parameters (the matter-field coupling constants) of the model, in functional form.

quant-ph↗

arXiv2014

A triple point in 3-level systems

The energy spectrum of a 3-level atomic system in the $Ξ$-configuration is studied. This configuration presents a triple point independently of the number of atoms, which remains in the thermo- dynamic limit. This means that in a vicinity of this point any quantum fluctuation will drastically change the composition of the ground state of the system. We study the expectation values of the atomic population of each level, the number of photons, and the probability distribution of photons at the triple point.

quant-ph↗

arXiv2014

Scaling properties in the adsorption of ionic polymeric surfactants on generic nanoparticles of metallic oxides by mesoscopic simulation

We study the scaling of adsorption isotherms of polyacrylic dispersants on generic surfaces of metallic oxides $XnOm$ as a function of the number of monomeric units, using Electrostatic Dissipative Particle Dynamics simulations. The simulations show how the scaling properties in these systems emerge and how the isotherms rescale to a universal curve, reproducing reported experimental results. The critical exponent for these systems is also obtained, in perfect agreement with the scaling theory of deGennes. Some important applications are mentioned.

physics.chem-ph↗

arXiv2013

Fidelity, susceptibility and critical exponents in the Dicke model

We calculate numerically the fidelity and its susceptibility for the ground state of the Dicke model. A minimum in the fidelity identifies the critical value of the interaction where a quantum phase crossover, the precursor of a phase transition for finite number of atoms N, takes place. The evolution of these observables is studied as a function of N, and their critical exponents evaluated. Using the critical exponents the universal curve for the specific susceptibility is recovered. An estimate to the precision to which the ground state wave function is numerically calculated is given, and found to have its lowest value, for a fixed truncation, in a vicinity of the critical coupling.

quant-ph↗