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Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler

IN THE CONTEXT OF TIME-INDEPENDENT PARAMETERS IN TWO QUANTUM SYSTEMS: QUANTUM ENTANGLEMENT AND CORRELATIONS WITH NEGATIVITY MEASUREMENT

Rasim Dermez, Yılmaz Tunçer

Published Aug 31, 2020• 2 citations

Abstract

In this paper, we consider two phonons and three-level trapped ion in configuration forming Hilbert 12-space. The negativity and quantum correlations are revealed in trapped ion two phonon states system. Three values of LDP, = 0.006, =0.06 and =0.08 are given. The effects of the time-independent coupling in terms of the system, degree of quantum entanglement are investigated. Therefore, we have found the main optimal times for obtaining the high amount of entanglement with negativity.In this paper, we consider two phonons and three-level trapped ion in configuration forming Hilbert 12-space. The negativity and quantum correlations are revealed in trapped ion two phonon states system. Three values of LDP, = 0.006, =0.06 and =0.08 are given. The effects of the time-independent coupling in terms of the system, degree of quantum entanglement are investigated. Therefore, we have found the main optimal times for obtaining the high amount of entanglement with negativity.

DOI: 10.20290/estubtdb.706641

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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.

The preparation of a wide class of entangled vibrational states involving two or three phononic modes of a three-dimensional trapped ion has been reported in the literature from both theoretical and experimental points of view. Here, the time evolution of such a system from an initial condition wherein two oscillatory modes (M x, M y) are reciprocally entangled and both are disentangled to the third mode (M z) is studied. By coupling one of the entangled oscillators (M x) with the third oscillator (M z), a correlation between the two uncoupled modes (M y, M z) is induced, well visible when the mean value of a suitable operator is considered. A method of measuring the expectation value of a vibrational observable is briefly sketched and then exploited in order to reveal such nonclassical behavior.

In this work, the quantum entanglement and quantum linearity in a trapped ion–phonon system are theoretically explained in terms of the second-order terms of the Lamb–Dicke parameter, η . For the trapped ion–phonon system, the optimum times are 2 and 10 and the optimum probability amplitudes of ions are 0.4 and 0.58, respectively. With the optimum times and amplitudes, it is shown that as η grows, the quality of the entanglement in the trapped ion–phonon system increases. In particular, we have demonstrated the quantum linearity due to second-order terms of η .

In the present study, we determined quantum entanglement in a full trapped ion (TRI)-coherent system and its dependence on the LambDicke parameter (LDP). We investigated the entanglement in view of two elaborated measurements of the family: entropy and fidelity. We selected three values of the deep LDP to demonstrate the benefits of these two critical measures. The findings obtained in this study showed that the maximum value of fidelity for entangled states is quantified approximately to be 0.35, and the long lifetime is also observed with entropy measurement. The findings suggest that three coupling parameters play a significant role in developing quantum entanglement.