Full-trapped three-level ion in the lamb–dicke limit: analyzing and comparing quantum entanglement measures of two qudits

Abstract

Our aim is to investigate the entanglement dynamics and quantum correlations of a full-trapped ion interacting with two time-independent laser beams in view of the Lamb-Dicke parameter. For this purpose, the three probability amplitudes in the trapped ion is taken as 1/3. Concurrence, negativity, and atomic Wehrl entropy of entanglement exhibit a long interacting time. We show that long survival is proved with these quantum measures.

Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime

“…2-6. Negativity and quantum entropy, which are the other elaborated measurements from the measurement family defining the entanglement concept, have also been studied in the literature [6,8,11,18,26,27,29]. We propose the quantum dynamics with concurrence for coupling parameters.…”

“…In the 1935, Erwin Schrödinger acquired the EPR reasoning twice, first in his paper in Naturwissenschaften introducing "Verschrankung", where he advises the Schrödinger cat state, and secondly in a paper for the Cambridge Philosophical Society introducing entanglement [4]. Trapped ions systems are important for the entangled states works [5][6][7][8], concurrence C [9], negativity N [10,11].…”

“…Pure qudit states and quantum correlation of one trapped ion system with respect to C and N are discussed by R. Dermez et al [11]. In the internal states, very small optical wavelength of coupling of vibrational phonons have been achieved.…”

“…C is a useful measurement in quantum optics, especially in trapped ion. We report analytical results of the quantum entanglement for system via C for the deep LD regime and the Hilbert space of 12-D. We focus on the quantum dynamics in concurrence [11,16] with respect to the total and the reduced density matrix. With help of Ref.…”

“…= 1, and two phonons normalization condition is approximately . So, the earliest of ioncoherent state system is given as: (11) here the phonon levels are , and . The new formula of system is given as ( )…”