Sudden death and sudden birth of entanglement in common structured reservoirs

Mazzola, Laura; Maniscalco, Sabrina; Piilo, Jyrki; Suominen, Kalle-Antti; Garraway, B. M.

doi:10.1103/physreva.79.042302

Cited by 280 publications

(315 citation statements)

References 29 publications

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“…The SV and SR effects in such systems have different character than studied here. Mazzola et al [51] observed the oscillations in short times, which disappear after some finite time and are related to the non-Markovian character of the reservoirs. In contrast, in the examples presented here, the periodic behavior of the nonclassicality witnesses persists as being related to the unitary evolution of the states.…”

Section: Periodic Sudden Vanishing Of Nonclassicality Witnesses Fmentioning

confidence: 99%

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Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

et al. 2011

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Analyses of phenomena exhibiting finite-time decay of quantum entanglement have recently attracted considerable attention. Such decay is often referred to as sudden vanishing (or sudden death) of entanglement, which can be followed by its sudden reappearance (or sudden rebirth). We analyze various finite-time decays (for dissipative systems) and analogous periodic vanishings (for unitary systems) of nonclassical correlations as described by violations of classical inequalities and the corresponding nonclassicality witnesses (or quantumness witnesses), which are not necessarily entanglement witnesses. We show that these sudden vanishings are universal phenomena and can be observed: (i) not only for two-or multi-mode but also for single-mode nonclassical fields, (ii) not solely for dissipative systems, and (iii) at evolution times which are usually different from those of sudden vanishings and reappearances of quantum entanglement.

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Section: Periodic Sudden Vanishing Of Nonclassicality Witnesses Fmentioning

confidence: 99%

“…V, should not be confused with the oscillations of the entanglement measures in systems interacting with non-Markovian reservoirs (see, e.g., Ref. [51]). The SV and SR effects in such systems have different character than studied here.…”

Section: Periodic Sudden Vanishing Of Nonclassicality Witnesses Fmentioning

confidence: 99%

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

et al. 2011

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“…Cavities provide a well-defined mode spectrum and a relatively loss-free environment such that the atom-field interactions can have anomalously large coupling strengths, leading to reversible, non-Markovian type dynamics of the system. As a consequence, the already dead entanglement can revive even if in the equivalent free-space situation no revival is predicted [11,12,23,[27][28][29][30][31][32][33]. However, calculations based on deriving the master equation for the reduced density operator of two atoms, both placed inside a cavity, frequently assume a large distance between the atoms such that there is no direct interaction between them.…”

Section: Introductionmentioning

confidence: 99%

“…This effect, known as sudden death of entanglement (SDE), has been studied in a numerous number of papers [2,[11][12][13][14][15], and has recently been observed in experiments involving photons [16,17] and atoms [18]. Furthermore, theoretical treatment of the coupling of sub-systems to a common (non-local) environment has predicted that the already destroyed entanglement could suddenly revive [19][20][21][22][23] or initially separable systems could become entangled after a finite time, the phenomenon known as sudden birth of entanglement (SBE).…”

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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“…In non-Markovian (NM) case, S is coherently interacting with a finite part of B over a finite time. From different theoretical efforts [4][5][6][7][8][9][10] we distill a central question: how can we divide the environment B into the memory M and detector D? Part M is continuously entangled with S but the compound S+M becomes a Markovian open system, as we shall argue.…”

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confidence: 99%

Non-Markovian open quantum systems: Input-output fields, memory, and monitoring

Diósi

2012

Phys. Rev. A

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Principles of monitoring non-Markovian open quantum systems are analyzed. We use the field representation of the environment (Gardiner and Collet, 1985) for the separation of its memory and detector part, respectively. We claim the system-plus-memory compound becomes Markovian, the detector part is tractable by standard Markovian monitoring. Because of non-Markovianity, only the mixed state of the system can be predicted, the pure state of the system can be retrodicted. We present the corresponding non-Markovian stochastic Schrödinger equation.PACS numbers: 03.65. Yz, 42.50.Lc In a seminal paper [1] Gardiner and Collett used quantum white-noise and the related Markovian quantum field to represent the dynamics of a quantum oscillator bath in the Markovian (memory-less) limit. This allowed the construction of exact stochastic differential equations to describe the influence of the bath B on the embedded (i.e.: open) quantum system S, the reaction of S on B, and the time-continuous monitoring of S. The theory became standard in quantum optics [2] and in many fields where a quantum system is open to natural or designed environmental influence [3]. If the memory of B cannot be ignored for S then Markovian tools become jeopardized. In non-Markovian (NM) case, S is coherently interacting with a finite part of B over a finite time. From different theoretical efforts [4-10] we distill a central question: how can we divide the environment B into the memory M and detector D? Part M is continuously entangled with S but the compound S+M becomes a Markovian open system, as we shall argue. Part D contains information on S and can be continuously disentangled, i.e.: monitored, without changing the dynamics of S.As a matter of fact, the Markovian field representation [1] of B is capable to account for memory effects and leads to a natural separation between M and D. The local Markov field interacts with S in a finite range: this part makes the memory M. The output field carries away information on S, it makes the detector D. Markovian field, non-Markovian coupling. The composite S+B dynamics is based on the total HamiltonianwhereĤ S is the Hamiltonian of S, the bath Hamiltonian isĤ B = ωb † ωbω dω andĤ SB = iŝ κ ωb † ω dω+h.c. is their interaction, whereŝ is a S-operator that couples to the Bmodes. Hereb ω are boson annihilation operators for the ω-frequency modes of B, satisfying. B can be called Markovian because of the flat spectrum. Memory effects are fully encoded in the coupling κ ω . If the coupling is frequency-independent, κ ω = const, then S is Markovian open system, otherwise it has a memory. We are interested in the latter case, i.e., in NM open systems. We assume that S and B are initially uncorrelated. Let, for simplicity's, the initial B-state be the vacuum |0 defined byb ω |0 = 0 for all ω.We switch for an abstract field representation [1-3]. The bath fieldb(z) is defined bŷwhere z is a real 1-dimensional spatial coordinate. For convenience, we set the velocity of propagation to 1. The canonical commutation r...

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Sudden death and sudden birth of entanglement in common structured reservoirs

Cited by 280 publications

References 29 publications

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

Effect of retardation on the dynamics of entanglement between atoms

Non-Markovian open quantum systems: Input-output fields, memory, and monitoring

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