arXiv subjects

Elhoussine Atmani

Publications and source records attributed to Elhoussine Atmani.

3 recordsLinked to original sources

arXiv2026

Dynamics of quantum entanglement in two time-dependent coupled harmonic oscillators

We investigate the quantum entanglement dynamics of two coupled harmonic oscillators with a time-dependent interaction. Using the Lewis-Riesenfeld invariant method, we derive the exact analytical wave functions without any perturbative or adiabatic approximations and combine this with a phase-space analysis using the Wigner function to provide a complete description of the system's quantum state evolution. We obtain general expression form for the purity and the linear entropy $S_L=1-\mathcal{P}$ for arbitrary excitation numbers $(n,m)$, allows a systematic study of entanglement for a large class of quantum states. We show that the entanglement dynamics is very sensitive to the interplay between the detuning parameters $θ$ and $\vartheta_2$, the frequency parameter $β_0$ and the coupling strength $ε$: the increase of detuning takes the system from slow irregular oscillations to fast and regular periodic behavior, and the stronger coupling systematically enhances both the amplitude and the average value of the linear entropy. Most importantly, for the resonance case $ω_1=ω_2=1$ and strong couplings $ε\approx 0.99$, the system shows robust undamped synchronized periodic oscillations of the linear entropy for all quantum states considered, indicating preserved quantum coherence without saturation. Our findings demonstrate that linear entropy is a sensitive and practical entanglement witness, and we establish explicit analytical relations between the coupling parameters of the system and its entanglement properties, which are directly relevant to quantum information processing and the control of quantum correlations in continuous-variable systems.

quant-ph↗

arXiv2026

Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators

Quantum steering is one of the most intriguing phenomena in quantum mechanics and is essential for understanding correlations in multi-body systems. Despite its importance, analytical results for coupled three-body oscillators remain scarce. In this work, we investigate this phenomenon through a geometrical diagonalization approach, which reduces the degrees of freedom associated with the system's steering properties. Specifically, we derive analytical expressions for quantum steering in all possible directions using the Wigner function framework, as it provides a complete description of the system's quantum state. Our results indicate that excitations significantly enhance quantum steering across the system; this stands in contrast to the ground state $(0,0,0)$, which exhibits no steerable correlations. Furthermore, both the directionality and topology of these correlations are governed by the spatial distribution of the excitations rather than their magnitude. We also observe symmetric steering behavior between oscillators $x$, $y$, and $z$ under equivalent excitation conditions, which can be formalized as $S^{(n,m,l)}_{x\to z}(θ)=S^{(n,m,l)}_{x\to y}(-θ),\quad S^{(n,m,l)}_{z\to x}(θ)=S^{(n,m,l)}_{y\to x}(-θ)$, and $S^{(n,m,l)}_{y\to z}(θ)=S^{(n,m,l)}_{z\to y}(-θ)$. Therefore, we elucidate how excitation levels and mixing angles generate and enhance steering in three coupled harmonic oscillators.

quant-ph↗

arXiv2026

Assessing the entanglement of three coupled harmonic oscillators

Quantum entanglement serves as a key phenomenon in understanding correlations in many-body systems, but analytical results remain scarce for coupled three-body oscillators. In this work, we address this gap by introducing a geometrical diagonalization approach that constrains Euler angles, thereby reducing the degrees of freedom in the entanglement analysis. It consists of deriving analytical expressions for linear entropy and purity under the bipartitions $(x|yz)$, $(y|xz)$, and $(xy|z)$ using the Wigner function framework. Our results indicate that excitations in any oscillator basically enhance the redistribution of correlations across the system. The mixing angle $θ$ governs entanglement intensity, ranging from separability to maximal correlation. Moreover, we reveal the symmetry relations, notably $S_{Ly}[(n,m,l),θ]=S_{Lz}[(n,m,l),-θ]$ and an intrinsic symmetry within $(x|yz)$. Hence, we clarify how excitation levels and mixing angles create and enhance entanglement in the three coupled harmonic oscillators.

quant-ph↗