Effect of dissipation and reservoir temperature on squeezing exchange and emergence of entanglement between two coupled bosonic modes

Castro, A. S. M. de; Siqueira, R.A.N.; Dodonov, V. V.

doi:10.1016/j.physleta.2007.07.037

Cited by 5 publications

(7 citation statements)

References 71 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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“…The most remarkable feature of formulas (35) and ( 36) is that they do not contain the hyperbolic functions C 2 or S 2 dependent on the argument γ t, in contradistinction to (22) and (23). This fact leads to several important consequences.…”

Section: Photon Distribution Functionsmentioning

confidence: 99%

Parametric excitation of a cavity field mode coupled to a harmonic oscillator detector

Castro¹,

Dodonov²

2013

J. Phys. A: Math. Theor.

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We study the parametric resonance in a system of two coupled quantum harmonic oscillators when the frequency of one of them (describing the field mode) is modulated at exactly twice the unperturbed eigenfrequency (the case of ‘unshifted resonance’). The coordinate–momentum coupling between the two oscillators is chosen in order to simulate the dynamical Casimir effect in a cavity containing a harmonic oscillator detector (LC-contour). Analytical solutions are obtained with the aid of the multiple scales method. For the field mode and detector initially prepared in thermal squeezed states, we calculate the mean numbers of quanta in both modes, as well as the invariant squeezing coefficients, purity and photon distribution functions, analyzing the influence of coupling strength and frequency modulation depth on the dynamics of these quantities. We show that the system goes to strongly squeezed states even for high temperature initial states of the detector. Depending on the relative strength of coupling coefficient and the parametric modulation amplitude, initially separable states go to permanently entangled states or they show periodic appearance and disappearance of entanglement.

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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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Effect of dissipation and reservoir temperature on squeezing exchange and emergence of entanglement between two coupled bosonic modes

Cited by 5 publications

References 71 publications

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Parametric excitation of a cavity field mode coupled to a harmonic oscillator detector

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

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