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Indian Journal of Physics

Quantifying of quantum entanglement in Schrödinger cat states with the trapped ion-coherent system for the deep Lamb-Dick regime

Rasim Dermez

Published Mar 5, 2020• 7 citations
Publisher
DOI
10.1007/s12648-020-01697-4

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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.
In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrödinger-cat states.
The fidelity of the generated Schrodinger Cat state (SCS) of a single trapped ion in the Lamb–Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb–Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb–Dike approximation in laser–ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb–Dicke parameters.