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.
Numerical experiments with a nonlinear (λχ4) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ > 0), a threshold is reached at λ = λc when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. © 1997 John Wiley & Sons, Inc.
The dynamics of systems consisting of coupled quantum–classical oscillators is numerically investigated. It is shown that, under certain conditions, the quantum oscillator exhibits chaos. When the mass of the classical oscillator increases, the chaos will be suppressed; if the energy of the system and/or the coupling strength between the two oscillators increases, chaotic behaviour of the system appears. This result will be helpful to understand the probability of the emergence of quantum chaos and may be applied to explain the spectra of complex atoms qualitatively.
Abstract We analyze the response of a single anharmonic diatomic molecule to a monochromatic time dependent electric field ω(t) and evaluate the temporal evolution of the dipole moment, phase space trajectories, and several transition probabilities as a function of the intensity of the field. We define deformed boson operators A† = f( )a†, A = af( ) in terms of the usual harmonic oscillator creation and annihilation operators a, a†, = a†a and choose the number operator function f( ) such that the energy spectrum of a harmonic oscillator‐type Hamiltonian written in terms of the deformed operators yields an energy spectrum similar to that of a Morse potential. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Abstract We have obtained a microscopic expression for entropy in terms of ℋ︁ function based on nonunitary Λ transformation that leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of ℋ︁, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment we emphasize the importance of precollisional and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the influence of spatial configuration of the system on the initial correlations in terms of the ℋ︁ function in a three‐dimensional situation. In a subsequent paper we discuss a model including virtual transitions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004