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

Year 2020, , 339 - 352, 25.06.2020
https://doi.org/10.37094/adyujsci.666654

Abstract

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.

Supporting Institution

Afyon Kocatepe Üniversitesi Bilimsel Araştırma Projeleri

Project Number

18-Kariyer.64

Thanks

R. D. thanks in the Foreign Language Support Unit at Afyon Kocatepe University. This work is supported by University of Afyon Kocatepe 18-Kariyer.64 project.

References

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  • [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.
Year 2020, , 339 - 352, 25.06.2020
https://doi.org/10.37094/adyujsci.666654

Abstract

Project Number

18-Kariyer.64

References

  • [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.
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Physics
Journal Section Physics
Authors

Rasim Dermez 0000-0003-0038-801X

Project Number 18-Kariyer.64
Publication Date June 25, 2020
Submission Date February 16, 2020
Acceptance Date May 7, 2020
Published in Issue Year 2020

Cite

APA Dermez, R. (2020). Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime. Adıyaman University Journal of Science, 10(1), 339-352. https://doi.org/10.37094/adyujsci.666654
AMA Dermez R. Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime. ADYU J SCI. June 2020;10(1):339-352. doi:10.37094/adyujsci.666654
Chicago Dermez, Rasim. “Analyzing of Quantum Entanglement With Concurrence in the Deep Lamb-Dicke Regime”. Adıyaman University Journal of Science 10, no. 1 (June 2020): 339-52. https://doi.org/10.37094/adyujsci.666654.
EndNote Dermez R (June 1, 2020) Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime. Adıyaman University Journal of Science 10 1 339–352.
IEEE R. Dermez, “Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime”, ADYU J SCI, vol. 10, no. 1, pp. 339–352, 2020, doi: 10.37094/adyujsci.666654.
ISNAD Dermez, Rasim. “Analyzing of Quantum Entanglement With Concurrence in the Deep Lamb-Dicke Regime”. Adıyaman University Journal of Science 10/1 (June 2020), 339-352. https://doi.org/10.37094/adyujsci.666654.
JAMA Dermez R. Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime. ADYU J SCI. 2020;10:339–352.
MLA Dermez, Rasim. “Analyzing of Quantum Entanglement With Concurrence in the Deep Lamb-Dicke Regime”. Adıyaman University Journal of Science, vol. 10, no. 1, 2020, pp. 339-52, doi:10.37094/adyujsci.666654.
Vancouver Dermez R. Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime. ADYU J SCI. 2020;10(1):339-52.

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