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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Generalized Donkor model with induced dipole-dipole forbidden transitions using Maple

Camilo Jaramillo Correa

Published May 1, 2012• 0 citations
Publisher

Abstract

The idea of this work was to generalize the Donkor model (Quantum Information and Computation IX, edited by Eric Donkor, Andrew R. Pirich, Howard E. Brandt, Proc. of SPIE Vol. 8057) about the application of induced dipole-dipole forbidden transitions to quantum computation. Using computer algebra we were able to reproduce the original Donkor model. Then we applied some modifications to this model and obtained the respective solutions. It is expected that this model has applications for quantum computation.

DOI
10.1117/12.918407

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The idea of this work was to generalize the Donkor model (Quantum Information and Computation IX, edited by Eric Donkor, Andrew R. Pirich, Howard E. Brandt, Proc. of SPIE Vol. 8057) about the application of induced dipole-dipole forbidden transitions to quantum computation. Using computer algebra we were able to reproduce the original Donkor model. Then we applied some modifications to this model and obtained the respective solutions. It is expected that this model has applications for quantum computation.
We calculate electric susceptibility of a laser-dressed atomic medium.The model adopted in this work refers to the experiment with cold 85 Rb atoms, where the states F′ = 1, 2, 3 of the hyperfine manifold 5P 3/2 (F′) are strongly coupled with the ground state 5S 1/2 (F = 2), and the coupling is probed by a weak probing field from the other ground-state component 5S 1/2 (F = 3).We present a five-level model in which the states F = 2, 3 and F′ = 1, 2, 3 are taken into account, while the noncoupled state F′ = 4 is neglected.The model is used as a starting point to reproduce spectral features observed in the absorption of probe light passing through a cold sample of 85 Rb atoms in a magneto-optical trap.Basing on numerical solutions of this model, we have also studied in detail the impact on the probe spectra from the presence of the state F′ = 1 to which probing is forbidden by electric-dipole transition, but coupling is allowed [see, e.g., Proc. of SPIE 8770 (2013) 87700Q].
In this paper we discuss the prospects of quantum information processing involving forbidden transitions in the inner shell of the rare-earth elements. We shall derive the selection rule for such transitions and investigate the prospects for rare-earth based quantum information procession that employ dipole-dipole forbidden transitions. The long decoherence time, degree of entanglement, lossless interconnectivity of these transitions will be model and their impact on quantum information processing will be examined.
The main goal of this paper is to apply the Yang-Baxter-Rowell equation in topological quantum computation, using the symbolic computational software Maple. Initially, using Maple, I reproduced the Dye classification of the 4x4 unitary solutions of the Yang-Baxter equation. Then, also using Maple, I reproduced the solutions given by Rebecca Chen to the Yang-Baxter-Rowell equation. Finally, the obtained solutions were applied to the problem of topological quantum categorification of the chromatic polynomial for graphs. It was claimed that the Yang-Baxter-Rowell operators, considered as quantum gates, can be incorporated in quantum circuit models and quantum games, such as the Grover algorithm and the game Battle of the Sexes. It is expected that a future investigation can provide a more complete classification of the solution to the Yang-Baxter-Rowell equation and its possible applications on topological quantum computation.