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arXiv:1101.3674 · Journal of Physics B Atomic Molecular and Optical Physics

Robustness of spatial Penning-trap modes against environment-assisted entanglement

M Genkin, A Eisfeld

Published Jan 17, 2011• 5 citations
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Abstract

The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.

DOI
10.1088/0953-4075/44/3/035502

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The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.
The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.
We study the time evolution of a charged particle in a Penning trap in the framework of open quantum systems. The interaction with the environment is taken into account by imposing Lindblad operators which are linear in the canonical variables. For the special case of a proton in an asymmetric Penning trap, we compare the dynamics with earlier results obtained from the unitary time-dependent Schrödinger equation. A possibility of estimating the spatial decoherence time of the system is discussed, and approximate decoherence time scales are given for different ions.
We investigate the generation of entanglement between the axial degrees of freedom of electrons confined in separated locations in planar Penning traps. We show that there are two different sources of entanglement: one is related with the mechanism of switching on and off the electrical coupling between the two electrons, and the other is due to the two-quanta-transition term of the coupling interaction. We show that the degree of entanglement can be controlled by adjusting the strength of the coupling between the traps and the time of interaction. We show that the coupled electrons behave as a temporal active interferometer.
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.