Time evolution of entanglement in a cavity at finite temperature

Figueiredo, Eberval Gadelha; Linhares, C. A.; Malbouisson, A. P. C.; Malbouisson, J. M. C.

doi:10.1016/j.physa.2016.06.128

Cited by 4 publications

(4 citation statements)

References 38 publications

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“…In a recent paper [27], Fock-like eigenstates of a Lindbladian are constructed using Lie algebras induced by the master equation for a linear chain of coupled harmonic oscillators. The special case of two coupled oscillators presents a family of models that has been the subject of intense studies [28][29][30][31][32][33][34][35][36][37] dealing with the dynamics of entanglement in open continuous-variable systems (see, e.g., [38] for a review).…”

Section: Introductionmentioning

confidence: 99%

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Kiselev

Ali

Rybin

2021

Entropy

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In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.

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Section: Introductionmentioning

confidence: 99%

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Kiselev

Ali

Rybin

2021

Entropy

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“…As far as correlations are concerned, there is an extensive body of the literature dealing with dynamics of entanglement in open continuous-variable systems such as two coupled oscillators [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] (see also Refs. [ 44 , 45 ] for reviews).…”

Section: Introductionmentioning

confidence: 99%

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

Kiselev

Ali

Rybin

2022

Entropy

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We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert–Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

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“…[16] as a method to account, in a non perturbative way, for the oscillator radiation process in free space. In subsequent works the concept was used to study the spontaneous emission of atoms in small cavities [17], the quantum Brownian motion [19,20], the thermalization process [21,22,29], the time evolution of bipartite systems [23][24][25], the entanglement of biatomic systems [27,28,30] and other related issues [31][32][33][34][35]. For a clear explanation see reference [32].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous decay in arbitrary cavity size

Flores-Hidalgo¹,

Silva²,

Rojas³

2017

Preprint

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We consider a complete study of the influence of the cavity size on the spontaneous decay of an atom excited state, roughly approximated by a harmonic oscillator. We confine the oscillator-field system in a spherical cavity of radius R, perfectly reflective, and work in the formalism of dressed coordinates and states, which allows to perform non-perturbative calculations for the probability of the atom to decay spontaneously from the first excited state to the ground state. In free space, R → ∞, we obtain known exact results an for sufficiently small R we have developed a power expansion calculation in this parameter. Furthermore, for arbitrary cavity size radius, we developed numerical computations and showed complete agreement with the exact one for R → ∞ and the power expansion results for small cavities, in this way showing the robustness of our results. We have found that in general the spontaneous decay of an excited state of the atom increases with the cavity size radius and vice versa. For sufficiently small cavities the atom practically does not suffers spontaneous decay, whereas for large cavities the spontaneous decay approaches the free-space R → ∞ value. On the other hand, for some particular values of the cavity radius, in which the cavity is in resonance with the natural frequency of the atom, the spontaneous decay transition probability is increased compared to the free-space case. Finally, we showed how the probability spontaneous decay go from an oscillatory time behaviour, for finite cavity radius, to an almost exponential decay, for free space.

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Time evolution of entanglement in a cavity at finite temperature

Cited by 4 publications

References 38 publications

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

Spontaneous decay in arbitrary cavity size

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