arXiv subjects

Radouan Hab-arrih

Publications and source records attributed to Radouan Hab-arrih.

8 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.

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arXiv2023

Implementing quantum Fourier transform using three qubits

Using the circulant symmetry of a Hamiltonian describing three qubits, we realize the quantum Fourier transform. This symmetry allows us to construct a set of eigenvectors independently on the magnitude of physical parameters involved in the Hamiltonian and as a result, the entanglement will be maintained. The realization will be leaned on trapped ions and the gate implementation requires an adiabatic transition from each spin product state to Fourier modes. The fidelity was numerically calculated and the results show important values. Finally, we discuss the acceleration of the gate by using the counter-driving field.

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arXiv2022

Virtual excitations and entanglement dynamics and polygamy in three ultra-strongly coupled systems

The Milburn dynamics of three nonresonant ultra-strongly coupled oscillators are resolved by using symplectic geometry. We look at the Milburn dynamics of virtual excitations and how they affect pairwise entanglement. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, we show that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, we analyze the effects of physical parameters on the redistribution of virtual excitations among the three bi-partitions. As a result, we show the violation of the monogamy of excitations as in quantum discord. This implies that excitations can be considered as signatures of quantum correlations beyond entanglement. Besides, we emphasize that our treatment can be used to model coupled quantum circuits in real situations (with decoherence).

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arXiv2022

Magnetic Field Effect on Dynamics of Entanglement for Time-dependent Harmonic Oscillator

We investigate the dynamics of entanglement, uncertainty and mixedness by solving time dependent Schrödinger equation for two-dimensional harmonic oscillator with time dependent frequency and coupling parameter subject to a static magnetic field. We compute the purities (global/marginal) and then calculate explicitly the linear entropy $S_{L}$ as well as logarithmic negativity $\mathcal{N}$ using the symplectic parametrization of vacuum state. We introduce the spectral decomposition to diagonalize the marginal state and get the expression of von Neumann entropy $S_{von}$ and establish its link with $S_{L}$. We use the Wigner formalism to derive the Heisenberg uncertainties and {show their dependencies on both $S_{L}$ and the coupling parameters $γ_{i}$ $ (i=1,2)$ of the quadrature term $x_{i}p_{i}$.} We graphically study the dynamics of the three features (entanglement, uncertainty, mixedness) and present the similar topology with respect to time. We show the effects of the magnetic field and quenched values of $J(t)$ and $ω_{2}(t)$ on these three dynamics, which lead eventually to control and handle them.

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arXiv2022

Virtual excitations and quantum correlations in ultra-strongly coupled harmonic oscillators under intrinsic decoherence

We study the intrinsic decoherence of coupled harmonic oscillators. The Milburn master equation is solved exactly, and the dynamics of virtual ground state excitations are investigated. The interaction of quantum correlations and virtual excitation was then studied. The following is a summary of our major findings. (i) The damped oscillatory profile of all three quantities is the same. (ii) Ultra-strong coupling combined with huge anisotropy values results in the reemergence of entanglement and steering. (iii) To sustain entanglement and steering, virtual excitations are required. (iv) The quantum correlations are amplified in the quantum synchronous regime. (v) Ultra-strong couplings cause inherent decoherence to be avoided.

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arXiv2021

Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes

This paper surveys the quantum entanglement of two coupled harmonic oscillators via angular momentum generating a magnetic coupling $ω_{c}$. The corresponding Hamiltonian is diagonalized by using three canonical transformations and then the stationary wave function is obtained. Based on the Schmidt decomposition, we explicitly determine the Schmidt modes $λ_{k}$ with $k\in\left\lbrace 0,1,\cdots,n+m\right\rbrace$, $n$ and $m$ being two quantum numbers associated to the two oscillators. By studying the effect of the anisotropy $ R=ω_{1}^{2}/ω_{2}^{2} $, $ω_{c}$, asymmetry $ |n-m| $ and dynamics on the entanglement, we summarize our results as follows. $ (i)- $ The entanglement becomes very large with the increase of $ (n,m) $. $ (ii)- $ The sensistivity to $ω_c$ depends on $ (n,m) $ and $R$. $ (iii)- $ The periodic revival of entanglement strongly depends on the physical parameters and quantum numbers.

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arXiv2021

Dynamics and Redistribution of Entanglement and Coherence in Three Time-Dependent Coupled Harmonic Oscillators

We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix $\mathbb{G}(t)$ can be used to directly cast the covariance matrix $σ(t)$. To quantify the mixedness and entanglement of the state one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully non symmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.

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arXiv2021

Classical Instability Effects on Photon Excitations and Entanglement

The Schrödinger dynamics of photon excitation numbers together with entanglement in two non-resonant time-dependent coupled oscillators is investigated. By considering $ π-$periodically pumped parameters and using suitable transformations, we obtain the coupled Meissner oscillators. Consequently, our analytical study shows two interesting results, which can be summarized as follows. (i): Classical instability of classical analog of quantum oscillators and photon excitation {averages $\left\langle N_{j}\right\rangle $} are strongly correlated. (ii): Photon excitation's and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts. Also it allow to control entanglement by engineering only classical systems where the experiments are less expensive.

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