Dynamics of Quantum Correlation in a Two-qutrit Heisenberg XXZ Model with Heitler-London and Dzyaloshinskii-Moriya Couplings
Brahim Adnane
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorYounes Moqine
Research Laboratory of Physics and Engineers Sciences, Team of Applied Physics and New Technologies, Polydisciplinary Faculty, Sultan Moulay Slimane University, PO Box 592, Béni Mellal, Morocco
Search for more papers by this authorAziz Khribach
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorAbdelghani El Houri
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorCorresponding Author
Rachid Houça
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
LPTHE. Laboratory, Theoretical Physics and High Energy, Faculty of Sciences, Ibn Zohr University, PO Box 8106, Agadir, Morocco
E-mail: [email protected]
Search for more papers by this authorEl Bouâzzaoui Choubabi
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorAbdelhadi Belouad
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorBrahim Adnane
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorYounes Moqine
Research Laboratory of Physics and Engineers Sciences, Team of Applied Physics and New Technologies, Polydisciplinary Faculty, Sultan Moulay Slimane University, PO Box 592, Béni Mellal, Morocco
Search for more papers by this authorAziz Khribach
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorAbdelghani El Houri
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorCorresponding Author
Rachid Houça
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
LPTHE. Laboratory, Theoretical Physics and High Energy, Faculty of Sciences, Ibn Zohr University, PO Box 8106, Agadir, Morocco
E-mail: [email protected]
Search for more papers by this authorEl Bouâzzaoui Choubabi
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorAbdelhadi Belouad
LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
Search for more papers by this authorAbstract
This study investigates the dynamics of quantum coherence and entanglement in the spin-1 Heisenberg XXZ model. Particularly, the effects of the Heitler-London (HL) coupling and the Dzyaloshinskii-Moriya (DM) interaction are examined. By utilizing tools from quantum information theory, the concept of quantum correlated coherence and negativity are explored. The results show intrinsic decoherence leads to a decay of both correlated coherence and negativity. Interestingly, it is found that a small value of the Dzyaloshinskii-Moriya interaction can significantly enhance coherence and entanglement. Various factors influence the system dynamics, including the initial state, anisotropy parameter, and the coupling distance between spins. It is shown that, by fixing the anisotropy parameter, the isotropic Heisenberg models XX and XXX can be easily recovered. Ultimately, the findings highlight that the system maintains a coherent temporal evolution despite decoherence.
Conflict of Interest
The authors declare no conflict of interest.
Open Research
Data Availability Statement
Research data are not shared.
References
- 1K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 2012, 84, 1655.
- 2B. P. Lanyon, M. Barbieri, M. P. Almeida, A. G. White, Phys. Rev. Lett. 2008, 101, 200501.
- 3A. Datta, G. Vidal, Phys. Rev. A 2007, 75, 042310.
10.1103/PhysRevA.75.042310 Google Scholar
- 4W. K. Wootters, Phys. Rev. Lett. 1998, 80, 2245.
- 5S. Luo, Phys. Rev. A 2008, 77, 022301.
- 6H. Ollivier, W. H. Zurek, Phys. Rev. Lett. 2001, 88, 017901.
- 7S. X. Wu, J. Zhang, C. S. Yu, H. S. Song, Phys. Lett. A 2014, 378, 344.
- 8A. K. Ekert, Phys. Rev. Lett. 1991, 67, 661.
- 9C. H. Bennett, G. Brassard, N. D. Mermin, Phys. Rev. Lett. 1992, 68, 557.
- 10C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, J. Smolin, J. Cryptol. 1992, 5, 3.
10.1007/BF00191318 Google Scholar
- 11C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, Phys. Rev. Lett. 1993, 70, 1895.
- 12R. Houça, A. Belouad, E. B. Choubabi, A. Kamal, M. E. Bouziani, J. Magn. Magn. Mater. 2022, 563, 169816.
- 13A. Ekert, R. Jozsa, Rev. Mod. Phys. 1996, 68, 733.
- 14C. H. Bennett, S. J. Wiesner, Phys. Rev. Lett. 1999, 69, 2887.
- 15S. L. Braunstein, H. J. Kimble, Phys. Rev. A 2000, 61, 042302.
- 16C. F. Roos, M. Chwalla, K. Kim, M. Riebe, R. Blatt, Nat. (London) 2006, 443, 316.
- 17S. D. Huver, C. F. Wildfeuer, J. P. Dowling, Phys. Rev. A 2008, 78, 063828.
- 18A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 1935, 47, 777.
- 19E. Schrödinger, Proc. Camb. Phil. Soc. 1935, 31, 555.
- 20J. S. Bell, Phys. Phys. Fiz. 1964, 1, 195.
10.1103/PhysicsPhysiqueFizika.1.195 Google Scholar
- 21G. Vidal, R. F. Werner, Phys. Rev. A 2002, 65, 032314.
- 22A. Miranowicz, A. Grudka, J. Opt. B Quant. Semiclass. Opt. 2004, 6, 542.
- 23M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 1996, 1, 223.
10.1016/0375-9601(95)00904-3 Google Scholar
- 24X. Wang, H. B. Li, Z. Sun, Y. Q. Li, J. Phys. A Math. Gen. 2005, 38, 8703.
10.1088/0305-4470/38/40/014 Google Scholar
- 25X. Wang, S. J. Gu, J. Phys. A Math. Gen. 2007, 40, 10759.
10.1088/1751-8113/40/35/003 Google Scholar
- 26Z. Xi, Y. Li, H. Fan, Sci. Rep. 2015, 5, 10922.
- 27M. L. Hu, X. Hu, J. Wang, Y. Peng, Y. R. Zhang, H. Fan, Phys. Rep. 2018, 762, 1.
- 28D. Girolami, Phys. Rev. Lett. 2014, 113, 170401.
- 29J. Goold, M. Huber, A. Riera, L. Del Rio, P. Skrzypczyk, J. Phys. A Math. Theor. 2016, 49, 143001.
- 30M. H. M. Passos, P. C. Obando, W. F. Balthazar, F. M. Paula, J. A. O. Huguenin, M. S. Sarandy, Opt. Lett. 2019, 44, 2478.
- 31G. J. Milburn, Phys. Lett. A 1991, 44, 5401.
- 32B. Adnane, Y. Moqine, A. Khribach, A. E. Houri, R. Houça, E. B. Choubabi, A. Belouad, Opt. Quantum Electron. 2024, 56, 936.
10.1007/s11082-024-06852-3 Google Scholar
- 33L. Zheng, G. F. Zhang, Eur. Phys. J. D 2017, 71, 288.
10.1140/epjd/e2017-80408-y Google Scholar
- 34T. Baumgratz, M. Cramer, M. B. Plenio, Phys. Rev. Lett. 2014, 113, 140401.
- 35A. Streltsov, G. Adesso, M. B. Plenio, Rev. Mod. Phys. 2017, 89, 041003.
- 36C. Cruz, M. F. Anka, Europhys. Lett. 2020, 130, 30006.
- 37T. Moriya, Phys. Rev. 1960, 120, 91.
- 38T. Moriya, Phys. Rev. Lett. 1960, 4, 228.
- 39M. Oumennana, A. U. Rahman, M. Mansour, Appl. Phys. B 2022, 128, 162.
- 40A. Ait Chlih, N. Habiballah, M. Nassik, Quantum Inf. Process. 2021, 20, 1.
10.1007/s11128-021-03030-2 Google Scholar
- 41H. Xiao-Mian, L. Jin-Ming, Chin. Phys. B. 2009, 18, 411.
- 42R. Houça, E. B. Choubabi, M. E. Bouziani, A. Belouad, A. Kamal, Quantum Inf. Process. 2022, 21, 200.
10.1007/s11128-022-03544-3 Google Scholar
- 43B. Adnane, Y. Moqine, R. Houça, A. Belouad, E. B. Choubabi, Quantum Inf. Process. 2023, 22, 225.
10.1007/s11128-023-03974-7 Google Scholar
- 44B. Adnane, Y. Moqine, R. Houça, A. Belouad, E. B. Choubabi, Phys. Scr. 2024, 99, 015106.
10.1088/1402-4896/ad11c4 Google Scholar
- 45Y. Moqine, B. Adnane, R. Houça, A. Belouad, S. Belhouideg, J. Low Temp. Phys. 2023, 213, 171.
- 46Y. Moqine, B. Adnane, R. Houça, A. Belouad, S. Belhouideg, Int. J. Quantum Inf. 2023, 21, 2340007.
10.1142/S0219749923400075 Google Scholar
- 47W. Heitler, F. London, Z. Physik 1927, 44, 455.
- 48P. K. Misra, Academic Press, 2012, 409.
- 49Y. Khedif, S. Haddadi, M. Daoud, H. Dolatkhah, M. R. Pourkarimi, Quantum Inf. Process. 2022, 21, 235.
10.1007/s11128-022-03565-y Google Scholar
- 50D. L. Cooper, Valence Bond Theory, Elsevier, 2002.
- 51K. C. Tan, H. Kwon, C. Y. Park, H. Jeong, Phys. Rev. A 2016, 94, 022329.
- 52M. L. Hu, H. Fan, Phys. Rev. A 2017, 95, 052106.
- 53W. Wu, Doctoral thesis, University of London, 2007.
- 54Y. Fu, W. Liu, X. Ye, Y. Wang, C. Zhang, C. K. Duan, X. Rong, J. Du, Phys. Rev. Lett. 2022, 129, 100501.
- 55S. Rana, P. Parashar, M. Lewenstein, Phys. Rev. A 2016, 93, 012110.
