The quantum entanglement of two connected harmonic oscillators via angular momentum yielding a magnetic coupling [Formula: see text] is discussed in this study. The corresponding Hamiltonian is diagonalized by using three canonical transformations, and then the stationary wave function is obtained. The Schmidt decomposition is used to explicitly determine the modes [Formula: see text], with [Formula: see text], [Formula: see text] and [Formula: see text] being two quantum numbers associated with the two oscillators. We summarize our findings by looking at the effects of anisotropy [Formula: see text], [Formula: see text], asymmetry [Formula: see text], and dynamics on entanglement. (i) With increasing [Formula: see text], the entanglement grows exceedingly large. (ii) The sensitivity to [Formula: see text] is determined by [Formula: see text] and [Formula: see text]. The physical parameters and quantum numbers play a great role in the periodic resuscitation of entanglement.
In this work, we explore the dynamics of entanglement of an isolated quantum system consisting of two time-dependent, coupled harmonic oscillators. Through the use of a numerical method that relies on the estimation of the system's Wigner representation by a specific Gaussian function, we investigate the time evolution of the entanglement entropy after an instant quench in the inherent parameters of the system. Besides, from the comparison of the results obtained from the analytical expression for the time-dependent von Neumann entropy with the numerically computed entropy data, the effectiveness of the numerical method is tested for a variety of angular frequency combinations. Also, we analyze how the entropy of entanglement change as a function of time.
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
SL=1−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
ϑ2, the frequency parameter
β0 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
ω1=ω2=1 and strong couplings
ε≈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.
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 [Formula: see text] can be used to directly cast the covariance matrix [Formula: see text]. 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 nonsymmetric. 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.
The time evolution of a quantum particle’s product of uncertainties in position and momentum is calculated when it is coupled with an external source. We have used a simple toy model where the particle is subject to a harmonic potential and coupled with an equivalent harmonic oscillator via a linear term. It is found that the long-time-averaged product is an increasing function of the coupling strength. It diverges when one of the eigenmodes of the coupled system goes soft, with the singular term twice of that for the stationary state. Generally, there is a jump of finite size for this quantity when a small coupling is turned on, compared to the uncoupled case. Similar behaviors have also been found for the von Neumann entanglement entropy, which is calculated exactly using a covariance matrix formalism. We find that the mode-interference plays an important role in the main features of this work.
The time-dependent Schrödinger equation describing a generalized two-dimensional quantum parametric oscillator in the presence of time-variable external fields is solved using the evolution operator method. For this, the evolution operator is found as a product of exponential operators through the Wei–Norman Lie algebraic approach. Then, the propagator and time-evolution of eigenstates and coherent states are derived explicitly in terms of solutions to the corresponding system of coupled classical equations of motion. In addition, using the evolution operator formalism, we construct linear and quadratic quantum dynamical invariants that provide connection of the present results with those obtained via the Malkin–Man’ko–Trifonov and the Lewis–Riesenfeld approaches. Finally, as an exactly solvable model, we introduce a Cauchy–Euler type quantum oscillator with increasing mass and decreasing frequency in time-dependent magnetic and electric fields. Based on the explicit results for the uncertainties and expectations, squeezing properties of the wave packets and their trajectories in the two-dimensional configuration space are discussed according to the influence of the time-variable parameters and external fields.