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Chinese Physics B

Entanglement and decoherence of coupled superconductor qubits in a non-Markovian environment

Yinghua Ji, Juju Hu

Published Jun 1, 2010• 22 citations
Publisher

Abstract

The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entanglement sudden death (ESD) always happens in the thermal reservoir, where its appearance strongly depends on the environment. In particular, ESD of the qubits occurs more easily for the non-Markovian process than for the Markovian one.

DOI
10.1088/1674-1056/19/6/060304

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The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entanglement sudden death (ESD) always happens in the thermal reservoir, where its appearance strongly depends on the environment. In particular, ESD of the qubits occurs more easily for the non-Markovian process than for the Markovian one.
The evolution of entangled decoherence of coupling superconducting qubits in non-Markovian environment is investigated in detail using concurrence function.The results show that,for coupling superconducting qubit under different entangled initial states,because of the role of memory feedback due to environmental effect,the entanglement of coupling superconducting qubits under a thermal bath always tends to zero monotonically.Further results also showed that,the sudden death of entanglement will soon occur in non-Markovian process,stronger the dissipation,faster the death of entanglement.But in Markovian process,it tends to death of entanglement slowly.
We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters like the temperature and the ratio rrr between ω0ω_0ω0​ the characteristic frequency of the quantum system of interest, and ωcω_cωc​ the cut-off frequency of Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-markovian entanglement concurrence Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) at temperature kBT=0k_BT=0kB​T=0 is different from the kBT>0k_BT>0kB​T>0 case. We find that "entanglement sudden death" (ESD) depends on the initial state when kBT=0k_BT=0kB​T=0, otherwise the concurrence always disappear at finite time when kBT>0k_BT>0kB​T>0, which means that ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.
environment on the entanglement dynamics in non-Markov process. Our results show that the entanglement degree is strongly related with the initial quantum state and the coupling between the qubits and the environment. The interaction between the qubits and the environment suppresses the decay of the entanglement. The sudden death of entanglement (ESD) can be prevented only by using and controlling targeted the interaction model between the different qubits and the environment. We also find the dissipation phenomenon always exists when the qubits system is initially in the maximally entangled mixed states.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
The entanglement evolution of a pair of two-level systems is studied in this paper. The two systems without mutual interaction are independently coupled to different two-band non-Markovian environments. By comparing our results to others in the literature, we find that taking one of the Bell states as the initial state, certain non-Markovian effect protects the entanglement in short time scale, while on long time scale it leads to the entanglement sudden death (ESD), which never occurs for this initial state in the Markovian case. Finally, by analyzing the parameters in our model, a relation between disentanglement and decoherence is established and discussed.