Generation of Entanglement in Qutrit Spin Coherent States by Nonlinear Hamiltonian

Document Type : Original Research Articles

Authors
Azita Naji
N. Shadman
Department of Physics, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran
10.22059/jsciences.2022.325672.1007653
Abstract
We study entanglement in coherent spin states and several superpositions of multi-qutrit coherent states evolved under the one-axis counter-twisting Hamiltonian in the presence and absence of a magnetic field. Considering a non-entangled multi-qutrit spin coherent state as an initial one, it is found that the entanglement is instigated with an oscillatory behavior in time; however, its average is a decreasing function of the magnetic field. Also, we observe that under this Hamiltonian, the two-qutrit superposed state retains its maximum entanglement with no change, while, the negativity for the three-qutrit superposed state oscillates in time and its average increases in the presence of the magnetic field.
Keywords
Entanglement
Qutrit
Coherent states
One-axis counter-twisting Hamiltonian
  1. Bell On the Einstein-Podolsky-Rosen paradox. Physics. 1964;1: 195-200.
  2. Einstein A, Podolosky A and Rosen N. Can quantum-mechanical description of physical reality be considered complete? Rev. 1935;47: 777-780.
  3. Aspect A, Grangier P and Roger Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev. Lett. 1981;47: 460-463.
  4. Berrada K, Abdel Khalek S and Raymond Ooi CH. Quantum metrology with entangled Spin-coherent states of two modes. Rev. A 2012;86: 033823
  5. Zhang GF and Li SS. Entanglement in a spin-one spin chain. Solid State Commun. 2006;138: 17-21.
  6. Zhu GQ, Zhao X and Li Entanglement of two-qutrit system. Eur. Phys. J. B. 2005;44: 359-364.
  7. Xiao X and Li Protecting qutrit-qutrit entanglement by weak measurement and reversal. Eur. Phys. J. D. 2013;67: 204.
  8. Xiao X. Protecting qubit-qutrit entanglement from amplitude damping decoherence via weak measurement and reversal. Physica Scripta 2014;89(6): 065102.
  9. Strakhov AA and Manko Virtual correlations in single qutrit. Advances in Mathematical Physics. 2016;2016: 7213197.
  • Kurzynski P, Kolodziejski A, Laskowski W and Markiewicz M. Three-dimensional visualisation of a qutrit. Rev. A 2016;93: 062126.
  • Naji A, Jafarpour M and Sammak F. Spin squeezing and entanglement in superposition of nonlinear spin coherent states. J. Phys. Commun 2018;2: 055001.
  • Naji A and Jafarpour M. Squeezing and entanglement in multi-qutrit systems. Quant. Info. Process. 2013;12: 2917-2933.
  • Radcliffe Some properties of coherent spin states. J. Phys. A: Gen. Phys. 1971;4: 313.
  • Kitagawa M and Ueda M. Squeezed spin states. Phys. Rev. A. 1993;47(6): 5138-5143.
  • Wang X and Sanders BC. Spin squeezing and pairwise entanglement for symmetric multiqubit states. Phys. Rev. A. 2003;68: 012101.
  • Sanders BC. Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement. J. Phys. Rev. A. 1989;40: 2417.
  • Imamoglu A, Awschalom D, Burkard G, Divincenzo DP, Loss D, Sherwin M, et al. Quantum information processing using quantum dot spins and cavity QED. Rev. Lett. 1999;83: 4204.
  • Zheng One-step synthesis of multiatom Greenberger-Horn-Zeilinger states. Phys. Rev. Lett. 2001;87: 230404.
  • Poulsen U, Molmer K. Positive-P simulations of spin squeezing in a two-component Bose condensate. Phys. Rev. A. 2001;64:
  • Sorensen A, Duan LM, Cirac JI and Zoller P. Many-particle entanglement with Bose-Einstein condensates. Nature 2001;409: 63-66.
  • Molmer K, Sorensen A. Multi-particle entanglement of hot trapped ions. Rev. Lett. 1999;82: 1835-1838.
  • Vidal CM, Werner R. A computable measure of entanglement. Phys. Rev. A 2002;65: 032314.
  1. Rungta P, Caves CM. I-concurrence and tangle for isotropic states. Phys. Rev. A 2003;67: 012307.
Journal of Sciences, Islamic Republic of Iran
Volume 32, Issue 4
Autumn 2021
Pages 359-365