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Physica Scripta

Long-lived entangled qudits in a trapped three-level ion beyond the Lamb–Dicke limit

Rasim Dermez, Özgür Esat Müstecaplıoğlu

Published Dec 22, 2008• 15 citations
Publisher

Abstract

Higher dimensional quantum entanglement in a trapped three-level ion interacting with two laser beams in Λ scheme is investigated beyond the Lamb–Dicke limit. It is shown that higher dimensional entanglement can be established in a single step, with a tunable dimensionality and duration via the Lamb–Dicke parameter.
DOI
10.1088/0031-8949/79/01/015304

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The entangled states of three-level of trapped ion and two phonons (into coherent state) in Lambda configuration forming a Hilbert space of 12-dimensional (D) are analyzed. The concurrence is considered "such as a quantum measure" in trapped ion-coherent state system. Four values of Lamb-Dicke parameter (LDP), eta=0.005, 0.07, 0.08$ and $0.09 are investigated by the worths of concurrence. We demonstrate that as eta is increased, sudden birth of entangled states in the system is increased. Thus, establishing of entangled states can be tuned by LDP.
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.