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Computers & Mathematics with Applications

Dynamics of two-level ions in a laser beam

Luis G. Reyna, JORGE R. SOBEHART

Published Feb 1, 1993• 6 citations
Publisher
DOI
10.1016/0898-1221(93)90141-h

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Dynamics of the laser-cooling of a trapped ion

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Abstract In this work, the absorption spectrum of a two-level ion in a linear Paul trap is investigated, the ion is supposed to be driven by two orthogonal laser beams, the one along the axial of the trap acts as the control light beam, the other as probe beam. When the frequency of the control laser is tuned to the first red sideband of the ionic transition, the coupling between the internal states of the ion and vibrational mode turns out to be a Jaynes–Cummings (JC) Hamiltonian, which together with the coupling between the probe beam and the two-level ion constructs a Λ -type three-level structure. In this case the transparency window may appear in the absorption spectrum of the probe light, which is induced by the ionic vibration and is very similar to the cavity induced transparency (Rice and Brecha 1996 Opt. Commun . 126 230–5). On the other hand, when the frequency of the control laser is tuned to the first blue sideband of the ionic transition, the two-level ion and vibrational mode are governed by an anti-Jaynes–Cummings (anti-JC) Hamiltonian, the total system including the probe beam forms a V -type three-level structure. And the Autler–Townes splitting in the absorption spectrum is found.
We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., the bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e., the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.