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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2020 / Cilt: 10 - Sayı: 1

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

Derin Lamb-Dicke Rejiminde Eş Zamanlılık ile Kuantum Dolanıklığın Analiz Edilmesi

Rasim DERMEZ
Pages
339–352
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Keywords: Trapped ion-coherent system; Interaction Hamiltonians; Probability amplitudes; Frequency of harmonic trap.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The entangled states of three-level of trapped ion and two phonons (into coherent state) in Λ configuration forming a Hilbert space of 12-dimensional (D) are analyzed.
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Key Findings & Data:Four values of Lamb-Dicke parameter (LDP), $nu$ = 0.005, 0.07, 0.08 and 0.09 are investigated by the worths of concurrence.
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Conclusion & Impact:Keywords: Trapped ion-coherent system; Interaction Hamiltonians; Probability amplitudes; Frequency of harmonic trap.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The entangled states of three-level of trapped ion and two phonons (into coherent state) in Λ 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), $nu$ = 0.005, 0.07, 0.08 and 0.09 are investigated by the worths of concurrence. We demonstrate that as $nu$ 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.

Özet

12-boyutlu Hilbert uzayında $wedge$ konfigürasyonunda iki fonon (kohorent durum içinde) ve üç-düzeyli tuzaklanmiş iyon sisteminde dolanık durumlar analiz edildi. Eş zamanlılık;tuzaklanmış iyon-koherent durum sisteminde “bir kuantum ölçümü olarak” düşünüldü. LDP’nin $nu$ = 0.005, 0.07, 0.08 ve 0.09 ile verilen dört değeri için dolanıklığın değerleri araştırıldı. LDP ($nu$) arttıkça, sistemdeki dolanık durumların ani doğumunun arttığı gösterildi. Böylece dolanık durumların oluşturulması LDP ile ayarlanabilir. Anahtar Kelimeler: Tuzaklanmış iyon-koherent sistemi; Etkileşim Hamiltonyenleri; Olasılık genlikleri; Harmonik tuzak frekansı.

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Cite This Article

DERMEZ, R. (2022). Analyzing of Quantum Entanglement with Concurrence in the Deep Lamb-Dicke Regime. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 - Sayı: 1, 339–352. https://ajindex.com/articles/428449

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References (19)

  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 twoatom 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 threelevel 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 threelevel 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 an