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arXiv:quant-ph/0408139

Control of entanglement with multipulse application

Chikako Uchiyama, Masaki Aihara

Published Aug 23, 2004• 0 citations
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Abstract

We show that the multipulse application can suppress the degradation of the quantum entanglement with focusing on the concurrence, the degree of entanglement. By evaluating the time evolution of concurrence with a linearly interacting spin-boson model under pulse application, we find that the effectiveness of the multipulse control depends on the non-Markovian nature of the reservoir.

DOI
10.48550/arxiv.quant-ph/0408139

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We show that the multipulse application can suppress the degradation of the quantum entanglement with focusing on the concurrence, the degree of entanglement. By evaluating the time evolution of concurrence with a linearly interacting spin-boson model under pulse application, we find that the effectiveness of the multipulse control depends on the non-Markovian nature of the reservoir.
We present a strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir. We discuss the applicability of this strategy by studying the dependence of the decoherence suppression on the shape of the coupling spectral density. We find that the effectiveness of this strategy arises from the non-Markovian nature of dynamical motion of the reservoir.
We present a general formulation to suppress pure dephasing by multipulse control. The formula is free from a specific form of interaction and is expressed in terms of the correlation function of an arbitrary system-reservoir interaction. We first apply the formula to a phenomenological two-level model where the correlation function of the interaction decays exponentially. In this case, we show analytically that the pure dephasing time is effectively lengthened by the multipulse control. Secondly, we apply the formula to the spin-boson model where a spin interacts nonlinearly with a boson reservoir. We find the multipulse control works well when the pulse interval is sufficiently shorter than the correlation time of the system-reservoir interaction. Moreover, in this case, the pure dephasing can also be suppressed by adjusting the pulse interval to the period of dynamical motion of the reservoir.
Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies. In this regard, we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent (Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field. Then, we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure. It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency, the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies (central detuning) in both non-Markovian and Markovian reservoirs. While the central detuning has a constructive role, the detuning between the qubit and the classical field (laser detuning) affects negatively on the entanglement protection. The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir. We demonstrate that, in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.
We study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that are individually coupled to non-Markovian reservoirs. This coupling ensures that the dynamical equations of the atoms can be treated independently. The non-Markovian reservoirs are described by a model which leads to an exact non-Markovian master equation of the Nakajima-Zwanzig form [J. Salo, S. M. Barnett, and S. Stenholm, Optics Commun. 259, 772 (2006)]. We consider the evolution of the entanglement of a two-atom state that is initially completely entangled, quantified by its concurrence. Collapses and revivals in the concurrence, induced by the memory effects of the reservoir, govern the dynamics of the entangled quantum system. These collapses and revivals in the concurrence are a strong manifestation of the non-Markovian reservoir.
Quantum entanglement is studied NMR multipulse spin locking, when a system of spins coupled by the dipole–dipole interaction in a strong magnetic field is irradiated by a sequence of resonant high-frequency φ\varphi φ -pulses with the same time delay 2τ2\tau 2τ between successive pulses. For times t∼T2t \sim {{T}_{2}}t∼T2​ ( T2≈ωloc−1{{T}_{2}} \approx \omega _{{{\text{loc}}}}^{{ - 1}}T2​≈ωloc−1​ , ωloc{{\omega }_{{{\text{loc}}}}}ωloc​ is determined by the dipole–dipole interaction), quasi-equilibrium with a structure depending on the relation between the pulsed field ω1=φ/2τ{{\omega }_{1}} = \varphi {\text{/}}2\tau ω1​=φ/2τ and ωloc{{\omega }_{{{\text{loc}}}}}ωloc​ is established in the system. For ω1⪅ωloc{{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}ω1​⪅ωloc​ , a one-temperature quasi-equilibrium state arises, while a quasi-equilibrium with the dipole and Zeeman temperatures appears for ω1≫ωloc{{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}ω1​≫ωloc​ . The temperature dependence of entanglement is investigated for ω1⪅ωloc{{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}ω1​⪅ωloc​ . For ω1≫ωloc{{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}ω1​≫ωloc​ , the further evolution of the system is determined by the Provotorov equations and leads to the equalization of the dipole and Zeeman temperatures. It is shown that the entanglement is absent in this case.