Generalized Concurrence and Negativity in Time-Dependent C3 ⊗ C5 = C15 Dimensional Ionic–Phononic Systems

Abstract

We investigate the entanglement of a trapped three-level ion interacting with two vibrational phonons, which form a fifteen-dimensional Hilbert space. We reveal analytic formulas describing both the concurrence and negativity. We show that, in such a system, a higher degree of entanglement with a concurrence of 0.999 and a negativity of 0.499 can be attained at a specific time of 16.9 fs. Derived expressions of concurrence and negativity include first-order terms in the interaction picture. Finally, an explicit solution for first-order terms shows that the amount of concurrence can be tuned between 0 and 1.0, while the amount of negativity changes between 0 and 0.5.