Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field

Anastopoulos, Charis; Shresta, Sanjiv; Hu, B. L.

doi:10.1007/s11128-009-0137-6

Cited by 40 publications

(42 citation statements)

References 49 publications

(148 reference statements)

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“…[38] for two qubits in a common electromagnetic field). This is what one might anticipate would happen for our model in the more general cases.…”

Section: Dynamics Of Entanglement: An Examplementioning

confidence: 99%

“…Doing a level reduction scheme for both oscillators and viewing the harmonic oscillator bath as a field would reduce our 2HO QBM model to that of two qubits interacting either directly or indirectly through a common field. An example of the latter situation is studied in [38]. One can use the exact master equations here under appropriate simplifications to describe the nonMarkovian dynamics of such systems.…”

Section: B Decoherence and Disentanglementmentioning

confidence: 99%

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Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

2008

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In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N , harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations and dissipation of mesoscopic objects towards the construction of a theoretical framework for macroscopic quantum phenomena.

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“…[38] for two qubits in a common electromagnetic field). This is what one might anticipate would happen for our model in the more general cases.…”

Section: Dynamics Of Entanglement: An Examplementioning

confidence: 99%

Section: B Decoherence and Disentanglementmentioning

confidence: 99%

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

2008

Self Cite

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show abstract

“…For example, qubits have great advantages in certain computational tasks compared to classical bits because of quantum coherence and quantum entanglement. However, for an open quantum system, mutual effects due to the coupling between the system and environment are inevitable and result in very complex reduced dynamics including dissipation, fluctuation, decoherence and disentanglement [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion

Shu

Zhao

Jing

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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In this paper, we use the quantum state diffusion (QSD) equation to implement the Uhrig dynamical decoupling (UDD) to a three-level quantum system coupled to a non-Markovian reservoir comprising of infinite numbers of degrees of freedom. For this purpose, we first reformulate the nonMarkovian QSD to incorporate the effect of the external control fields. With this stochastic QSD approach, we demonstrate that an unknown state of the three-level quantum system can be universally protected against both colored phase and amplitude noises when the control-pulse sequences and control operators are properly designed. The advantage of using non-Markovian quantum state diffusion equations is that the control dynamics of open quantum systems can be treated exactly without using Trotter product formula and be efficiently simulated even when the environment comprise of infinite numbers of degrees of freedom. We also show how the control efficacy depends on the environment memory time and the designed time points of applied control pulses.

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“…In particular those explicitly taking into account the distance between the particles are of relevance [39][40][41]. In these works it was shown that for certain initial states, the distance between the qubits can qualitatively change the entanglement dynamics.…”

Section: Introductionmentioning

confidence: 99%

Effect of retardation on the dynamics of entanglement between atoms

2012

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The role of retardation in the entanglement dynamics of two distant atoms interacting with a multi-mode field of a ring cavity is discussed. The retardation is associated with a finite time required for light to travel between the atoms located at a finite distance and between the atoms and the cavity boundaries. We explore features in the concurrence indicative of retardation and show how these features evolve depending on the initial state of the system, distance between the atoms and the number of modes to which the atoms are coupled. In particular, we consider the short-time and the long time dynamics for both the multi-and sub-wavelength distances between the atoms. It is found that the retardation effects can qualitatively modify the entanglement dynamics of the atoms not only at multi-but also at sub-wavelength distances. We follow the temporal evolution of the concurrence and find that at short times of the evolution the retardation induces periodic sudden changes of entanglement. To analyze where the entanglement lies in the space spanned by the state vectors of the system, we introduce the collective Dicke states of the atomic system that explicitly account for the sudden changes as a periodic excitation of the atomic system to the maximally entangled symmetric state. At long times, the retardation gives rise to periodic beats in the concurrence that resemble the phenomenon of collapses and revivals in the JaynesCummings model. In addition, we identify parameter values and initial conditions at which the atoms remain separable or are entangled without retardation during the entire evolution time, but exhibit the phenomena of sudden birth and sudden death of entanglement when the retardation is included.

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Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field

Cited by 40 publications

References 49 publications

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion

Effect of retardation on the dynamics of entanglement between atoms

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