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arXiv:0906.1830 · Physical Review A

Entanglement generation between distant atoms by Lyapunov control

Xiaoting Wang, S. G. Schirmer

Published Oct 6, 2009• 66 citations
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Abstract

We show how to apply Lyapunov control design to the problem of entanglement creation between two atoms in distant cavities connected by optical fibers. The Lyapunov control design is optimal in the sense that the distance from the target state decreases monotonically and exponentially, and the concurrence increases accordingly. This method is far more robust than simple geometric schemes.

DOI
10.1103/physreva.80.042305

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We show how to apply Lyapunov control design to the problem of entanglement creation between two atoms in distant cavities connected by optical fibers. The Lyapunov control design is optimal in the sense that the distance from the target state decreases monotonically and exponentially, and the concurrence increases accordingly. This method is far more robust than simple geometric schemes.
"We present a model to generate atomic entanglement with atoms located at distant cavities. It consists of two cavities connected by an optical fiber, where each cavity interacts with a single two-level atom. For certain atom-cavity and cavity-fiber coupling parameters, we find a wide time plateau for the concurrence between the atoms. An increase of the atom-cavity detuning, gives rise to a linear increase of the width of the plateau, but at the same time, when losses are included in the model, it also decreases the value of the concurrence and increases the response time to reach the maximum."
Based on Lyapunov control theory in closed and open systems, we propose a scheme to generate W state of many distant atoms in the cavity-fiber-cavity system. In the closed system, the W state is generated successfully even when the coupling strength between the cavity and fiber is extremely weak. In the presence of atomic spontaneous emission or cavity and fiber decay, the photon-measurement and quantum feedback approaches are proposed to improve the fidelity, which enable efficient generation of high-fidelity W state in the case of large dissipation. Furthermore, the time-optimal Lyapunov control is investigated to shorten the evolution time and improve the fidelity in open systems.
We present a model to generate atomic entanglement with atoms located at distant cavities. It consists of two cavities connected by an optical fibre, where each cavity interacts with a single two-level atom. For certain atom–cavity and cavity–fibre coupling parameters, we find a wide time plateau for the concurrence between the atoms. An increase of the atom–cavity detuning gives rise to a linear increase of the width of the plateau, but at the same time, when losses are included in the model, it also decreases the value of the concurrence and increases the response time to reach the maximum.
A scheme is proposed for the deterministic generation of three-dimensional entanglement of two distant atoms separately trapped in two optical cavities connected by an optical fiber. Employing adiabatic passage along dark states, the atoms are always in ground states, in particular, the fiber mode remains in the vacuum state due to the quantum destructive interference, and the population of the cavities being excited can be negligible under certain conditions. In this sense, our scheme constructs an effective way to avoid the atomic spontaneous emission and the decays of fiber and cavities.
The generation of atomic entanglement is discussed in a system that atoms are trapped in separate cavities which are connected via optical fibres. Two distant atoms can be projected to Bell-state by synchronized turning off of the local laser fields and then performing a single quantum measurement by a distant controller. The distinct advantage of this scheme is that it works in a regime where Δ ≈ κ ≫ g, which makes the scheme insensitive to cavity strong leakage. Moreover, the fidelity is not affected by atomic spontaneous emission.