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Chinese Physics B

Comparison of entanglement trapping among different photonic band gap models

Ying-Jie Zhang, Xiu-Qin Yang, Wei Han, Yun‐Jie Xia

Published Sep 1, 2013• 7 citations
Publisher

Abstract

We investigate the roles of different qubit—environment decoherence models on the entanglement trapping of two qubits. By considering three environmental models (the single photonic band gap model, the common photonic band gap model, and the two independent photonic band gaps model), we note that the final values of entanglement trapping are determined by these different models. We also give the conditions of obtaining the larger entanglement trapping by comparing two-qubit entanglement dynamics in different decoherence models. Moreover, the comparison of entanglement trapping between two Bell-like states in the same decoherence model are also carried out.

DOI
10.1088/1674-1056/22/9/090307

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We investigate the roles of different qubit—environment decoherence models on the entanglement trapping of two qubits. By considering three environmental models (the single photonic band gap model, the common photonic band gap model, and the two independent photonic band gaps model), we note that the final values of entanglement trapping are determined by these different models. We also give the conditions of obtaining the larger entanglement trapping by comparing two-qubit entanglement dynamics in different decoherence models. Moreover, the comparison of entanglement trapping between two Bell-like states in the same decoherence model are also carried out.
We study how the environment of photonic band gap (PBG) materials affects entanglement dynamics of qubits. Entanglement between the single qubit and the PBG environment is investigated through the von Neumann entropy while that for two initially entangled qubits in this PBG reservoir is through concurrence. Dynamics of these measurements are solved in use of the fractional calculus which has been shown appropriate for the systems with non-Markovian dynamics. Entropy dynamics of the single qubit system reveals that the coupling with the PBG reservoir prevents decoherence of the qubit through the steady entropy with non-zero value. The effect of PBG reservoir on the concurrence of the two-qubit system leads to the long-time entanglement preservation. The concurrence dynamics shows that unphysical entanglement trapping does not exist in the system with the qubit frequency lying outside the PBG region. Long-time memory effect of the PBG reservoir occurs only for the qubit frequency in the PBG region. Entanglement mechanisms resulting from this long-time memory effect are discussed.
We highlight the direct link between the time-dependent entanglement and single-qubit excited-state population for two independent qubits, each coupled to a zero-temperature bosonic environment. We show that, in environments structured so as to inhibit spontaneous emission, entanglement trapping and thus prevention of entanglement sudden death occur. We explicitly show that, for photonic band-gap materials as environment, high values of entanglement trapping can be achieved. We finally discuss how, under these conditions, coherent quantum operations can be implemented.
Using the pseudomode method, we study the exact entanglement dynamics of two atoms in a common band gap. In order to understand the role played by the common band gap we compare our results with the case of two independent band gap model. We demonstrate that the parameter region at which the entanglement sudden death occurs is smaller than the independent band gap model. Moreover, the atomic entanglement trapping can also be achieved in the common band gap model, and the value of entanglement trapping is larger in the common band gap case than in the independent band gap case.
Establishing three different environment models (i.e., single reservoir model, common reservoir model and independent reservoir model), we investigate the evolutional characteristic of the entangled system initially in Bell-like state by the pseudomode method. Through comparing the entanglement decays under the three different environment models, we find that the entangled Bell-like state cos θ |ee> + sin θ |gg> will be kept in the single reservoir model for a time longer than in the other two models. However, the entanglement decay behavior of Bell-like state cos θ |eg> + sin θ |ge> is dependent on the specific environment model. Meanwhile, the comparison of entanglement decay between the above two Bell-like states at the same environment models is performed.
We study the entanglement trapping of two entangled qubits, each of which is in its own photonic band gap, based on the weak measurement and quantum measurement reversal. An almost maximal entanglement of the two-qubit system can be trapped by using a certain weak measurement strength. Furthermore, we find that the optimal entanglement enhancing is not only dependent on the weak measurement strength but also on the different initial states. The outcomes in our scheme are completely different from that without any measurement on the studied system.