Rasim DERMEZ

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

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.

Keywords:

Trapped ion-coherent system, Interaction Hamiltonians, Probability amplitudes Frequency of harmonic trap,

PDF

___

[1] Bell, J., Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 1987.
[2] Einstein, A., Podolsky, B., Rosen, N., Can quantum-mechanical description of physical reality be considered complete?, Physical Review, 47, 777-780, 1935.
[3] Bohr, N., Can quantum-mechanical description of physical reality be considered complete?, Physical Review, 48, 696-702, 1935.
[4] Schrödinger, E., Die gegenwrtige situation in der quantenmechanik, Naturwissenschaften, 23, 844-849, 1935.
[5] Cirac, J.I., Zoller, P., Quantum computations with cold trapped ions, Physical Review Letters, 74, 4091, 1995.
[6] Landsman, K.A., Wu, Y., Leung, P.H., Zhu, D., Linke, N.M., Brown, K.R., Duan, L.M., Monroe, C., Two-qubit entangling gates within arbitrarily long chains of trapped ions, Physical Review A, 100, 022332, 2019.
[7] Abdel-Aty, M., Qualitative aspects of the entanglement in the three-level model with photonic crystals, Applied Physics B, 81, 193-203, 2005.
[8] Wong-Campos, J.D., Moses, S.A., Johnson, K.G., Monroe, C., Demonstration of two-atom entanglement with ultrafast optical pulses, Physical Review Letters, 119, 230501, 2017.
[9] Wootters, W.K, Entanglement of formation of an arbitrary state of two qubits, Physical Review Letters, 80, 2245, 1998.
[10] Vidal, G., Werner, R.F., Computable measure of entanglement, Physical Review A. 65, 032314, 2002.
[11] Dermez, R., Khalek, S.A., Kara, K. Deveci, B., Gunaydin, G.N., Full-trapped three-level ion in the Lamb-Dicke limit: Analyzing and comparing quantum entanglement measures of two qudits, Journal of Russian Laser Research, 33, 42-51, 2012.
[12] James, D.F.V., Quantum computation and quantum information theory, Applied Physics B, 66, 181-190, 1998.
[13] Monreo, C.D., Meekhof, M., King, B.E., Wineland, D.J., A Schrödinger cat superposition state of an atom, Science, 272, 1131-1136, 1996.
[14] Wei, L.F., Liu, Y., Nori, F., Engineering quantum pure states of a trapped cold ion beyond the Lamb-Dicke limit, Physical Review A, 70, 063801, 2004.
[15] Guo, Y., Du, S., Li, X., Wu, S., Entangled bases with fixed Schmidt number, Journal of Physics A: Mathematical and Theoretical, 48(24), 245301, 2015.
[16] Dermez, R., Müstecaplıoğlu, Ö.E., Long-lived entangled qudits in a trapped three-level ion beyond the Lamb–Dicke limit, Physica Scripta, 71, 015304, 2009.
[17] Nieuwenburg, E., Zilberberg, O., Entanglement spectrum of mixed states, Physical Review A, 98, 012327, 2018.
[18] Neumann, J.V., Mathematical foundations of quantum mechanics, Princeton University Press, N.J., 1995.
[19] Dermez, R., Concurrence and negativity as a family of two measures elaborated for pure qudit states, Journal of Russian Laser Research, 38, 408-415, 2017.
[20] Zheng, S.B., Kuang, L.M., Gao, K.L., Two-mode squeezed states and their superposition in the motion of two trapped ions, Physical Letters A, 300, 427-431, 2002.
[21] Zheng, S.B., Preparation of motional macroscopic quantum-interference states of a trapped ion, Physical Review A, 58, 761, 1998.
[22] Zheng, S.B., Control of motional states of a trapped ion, Physical Letters A, 248, 25-28, 1998.
[23] Müstecaplıoğlu, Ö.E., Motional macroscopic quantum superposition states of a trapped three-level ion, Physical Review A, 68, 023811, 2003.
[24] Sakurai, J.J., Modern Quantum Mechanics, Addison-Wesley Publishing Company, 489p., 1994.
[25] Hill, S., Wooters, W.K., Entanglement of formation of an arbitrary state of two qubits, Physical Review Letters, 80, 2245, 1998.
[26] Dermez, R., Generalized concurrence and negativity in time-dependent C3⊗C5= C15 dimensional ionic–phononic systems, Journal of Russian Laser Research, 37, 572-580, 2016.
[27] Dermez, R., Comparing concurrence and negativity in time-dependent ionic-phononic system with fifteen dimensional density matrix, IOP Publishing Journal of Physics: Conference Series, 766, 012012, 2016.
[28] Anvar, S.J., Ramzan, M., Khan, M.K., Dynamics of entanglement and quantum Fisher information for N-level atomic system under intrinsic decoherence, Quantum Information Process, 16, 142, 2017.
[29] Liao, Q.H., Wu, J.F., Wang, P., Properties of entanglement between the two trapped ions, Indian Journal of Physics, 91(12) 1615, 2017.
[30] Zhang, C.L., Liu, W.W., Generation of W state by combining adiabatic passage and quantum Zeno techniques, Indian Journal of Physics, 93, 67-73, 2019.
[31] Pedemales, L.S., Lizuain, I., Felicetti, S., Romero, G., Lamata L., Solano, E., Quantum Rabi model with trapped ions, Scientific Reports, 5, 15472, 2015.
[32] Filho, R.L.M., Vogel, W., Even and odd coherent states of the motion of trapped ion, Physical Review Letters, 76, 608, 1996.
[33] Khalek, S.A., Quantum Fisher information flow and entanglement in pair coherent states, Optical and Quantum Electronics, 46, 1055-1064, 2014.