Geometric phase for two-partite qutrit-like entangled coherent state

Document Type : Full length research Paper

Authors

1 University of Mohaghegh Ardabili. Ardabil. Iran

2 Department of Physics, University of Mohaghegh Ardabili, Ardabil, P.O. Box 179, Iran.

3 University of Mohaghegh Ardabili

Abstract

Coherent states, most close state to the classical states, have special role in quantum optics. In this paper, the geometric phase of the two-partite qutri-like entangled coherent state undergoing a unitary and cyclic evolution is calculated. Using the concurrence measure,the degree of entanglement of the state before and after the evolution is calculated and compared with the geometric phase.We show that the geometric phase and concurrence,as a function of the time evolution parameter, are inversely change, in the sense that the increase of one is accompanied by a decrease of the other.Finally, we suggest an experimental realization to the production of the two-mode entangled coherent state based on the interferometry scheme.

Keywords

Main Subjects

References

[1] M.V. Berry, Quantal phase factors accompanying adiabatic changes, Proceedings of the Royal Society of London, A, Mathematical and Physical Sciences 392 (1984) 45-57. https://doi.org/10.1098/rspa.1984.0023
[2] F. Wilczek, A. Zee, Appearance of gauge structure in simple dynamical systems, Physical Review Letters 52 (1984) 2111–2114. https://doi.org/10.1103/PhysRevLett.52.2111
[3] Y. Aharonov, J. Anandan, Phase change during a cyclic quantum evolution, Physical Review Letters 58 (1987) 1593. https://doi.org/10.1103/PhysRevLett.58.1593
[4] A. Uhlmann, Parallel transport and quantum holonomy along density operators, Reports on Mathematical Physics 24 (1986) 229-240. https://doi.org/10.1016/0034-4877(86) 90055-8
[5] E. Sjöqvist, Geometric phase for entangled spin pairs, Physical Review A 62 (2000) 022109. https://doi.org/10.1103/PhysRevA.62.022109
[6] J. Samuel, R. Bhandari, General setting for berry's phase, Physical Review Letters 60 (1988) 2339. https://doi.org/10.1103/PhysRevLett.60.2339
[7] A. Carollo, I. Fuentes-Guridi, M.F. Santos, V. Vedral, Geometric phase in open systems, Physical review letters 90 (2003) 160402. https://doi.org/10.1103/PhysRevLett.90.160402
[8] R.S. Whitney, Y. Gefen, Berry phase in a nonisolated system, Physical review letters 90 (2003) 190402. https://doi.org/10.1103/PhysRevLett.90.190402
[9] D. Tong, E. Sjöqvist, L.C. Kwek, C.H. Oh, Kinematic approach to the mixed state geometric phase in nonunitary evolution, Physical review letters 93 (2004) 080405. https://doi.org/10.1103/PhysRevLett.93.080405
[10] P. Zanardi, M. Rasetti, Holonomic quantum computation, Physics Letters A 264 (1999) 94-99.        https://doi.org/10.1016/S0375-9601(99) 00803-8
[11] J.A. Jones, V. Vedral, A. Ekert, G. Castagnoli, Geometric quantum computation using nuclear magnetic resonance, Nature 403 (2000) 869-871. https://doi.org/10.1038/35002528
[12] S.-L. Zhu, Z. Wang, Implementation of universal quantum gates based on nonadiabatic geometric phases, Physical review letters 89 (2002) 097902. https://doi.org/10.1103/PhysRevLett.89.097902
[13] V. Vedral, Geometric phases and topological quantum computation, International Journal of Quantum Information 1 (2003) 1-23. https://doi.org/10.1142/S0219749903000024
[14] E. Rowell, Z. Wang, Mathematics of topological quantum computing, Bulletin of the American Mathematical Society 55 (2018) 183-238.                        https://doi.org/10.1090/bull/1605
[15] S. Tiwari, Geometric phase in optics: Quantal or classical?, Journal of Modern Optics 39 (1992) 1097-1105. https://doi.org/10.1080/09500349214551101
[16] E.J. Galvez, Applications of geometric phase in optics, Recent Research Developments in Optics 2 (2002) 165-182.
[17] A. Morpurgo, J. Heida, T. Klapwijk, B. Van Wees, G. Borghs, Ensemble-average spectrum of aharonov-bohm conductance oscillations: evidence for spin-orbit-induced berry's phase, Physical review letters 80 (1998) 1050.
[18] Q. Niu, X. Wang, L. Kleinman, W.-M. Liu, D. Nicholson, G. Stocks, Adiabatic dynamics of local spin moments in itinerant magnets, Physical review letters 83 (1999) 207. https://doi.org/10.1103/PhysRevLett.83.207
[19] A.C. Carollo, J.K. Pachos, Geometric phases and criticality in spin-chain systems, Physical review letters 95 (2005) 157203. https://doi.org/10.1103/PhysRevLett.95.157203
[20] S.-L. Zhu, Scaling of geometric phases close to the quantum phase transition in the x y spin chain, Physical review letters 96 (2006) 077206. https://doi.org/10.1103/PhysRevLett.96.077206
[21] G. Najarbashi, B. Seifi, Quantum phase transition in the dzyaloshinskii-moriya interaction with inhomogeneous magnetic field: Geometric approach, Quantum Information Processing 16 (2017) 1-16.
[22] V. Vedral, Geometric phases and topological quantum computation, International Journal of Quantum Information 1 (2002) 1-23. https://doi.org/10.1142/S0219749903000024
[23] E. Sjöqvist, A new phase in quantum computation, Department of quantum chemistry, Sweden 1 (2008). https://doi.org/10.1103/Physics.1.35
[24] A. Ekert, M. Ericsson, P. Hayden, H. Inamori, J.A. Joens, D.K.L. Oi, V. Vedral, Geometric quantum Computation, Journal of Modern Optics 47 (2000) 2501-2513. https://doi.org/10.1080/09500340008232177
[25] E. Sjöqvist, Geometric phases in quantum information, International Journal of Quantum Chemistry 115 (2015) 1311-1326. https://doi.org/10.1002/qua.24941
[26] D. Tong, L. Kwek, C. Oh, Geometric phase for entangled states of two spin-1/2 particles in rotating magnetic field, Journal of Physics A: Mathematical and General 36 (2003) 1149. https://doi.org/10.1088/0305-4470/36/4/320
[27] D. Tong, E. Sjöqvist, L. Kwek, C. Oh, M. Ericsson, Relation between geometric phases of entangled bipartite systems and their subsystems, Physical Review A 68 (2003) 022106. https://doi.org/10.1103/PhysRevA.68.022106
[28] E. Schrödinger, Der stetige übergang von der mikro-zur makromechanik, Naturwissenschaften 14 (1926) 664-666. https://doi.org/10.1007/BF01507634
[29] S. Chaturvedi, M. Sriram, V. Srinivasan, Berry's phase for coherent states, Journal of Physics A: Mathematical and General 20 (1987) 1071. https://doi.org/10.1007/BF02742688
[30] A.K. Pati, Geometric aspects of noncyclic quantum evolutions, Physical Review A 52 (1995) 2576. https://doi.org/10.1103/PhysRevA.52.2576
[31] D.-B. Yang, Y. Chen, F.-L. Zhang, J.-L. Chen, Geometric phases for nonlinear coherent and squeezed states, Journal of Physics B: Atomic, Molecular and Optical Physics 44 (2011) 075502.         https://doi.org/10.1088/0953-4075/44/7/ 075502
[32] A. Ekert, Quantum cryptography based on Bell's theorem, Physical Review Letters 67 (1991) 661. https://doi.org/10.1103/PhysRevLett.67.661
[33] C.H. Bennett, H.G. Brassard, C. Crepeau, R. Jozsa, A. Peres,
W.K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Physical Review Letters 70 (1993) 1895. https://doi.org/10.1103/PhysRevLett.70.1895
[34] G. Najarbashi, S. Mirzaei, Comparison of qubit and qutrit like entangled squeezed and coherent states of light, Optics Communications 377 (2016) 33-40.‏ https://doi.org/10.1016/j.optcom.2016.04.068
[34] G. Najarbashi, S. Mirzaei, Noise effects on entangled coherent state generated via atom-field interaction and beam splitter, International Journal of Theoretical Physics 55 (2016) 2311-2323.                         https://doi.org/10.1007/s10773-015-2869-7
[35] G. Najarbashi, S. Mirzaei, Entanglement of multi-qudit states constructed by linearly independent coherent states: Balanced case, International Journal of Theoretical Physics 55 (2016) 1336-1353. https://doi.org/10.1007/s10773-015-2775-z
[36] B. Mojaveri, A. Dehghani, R. Jafarzadeh Bahrbeig, Enhancing entanglement of entangled coherent states via a f-deformed photon-addition operation, The European Physical Journal Plus 134 (2019) 1-8. https://doi.org/10.1140/epjp/i2019-12823-7
[37] A. Dehghani, B. Mojaveri, A.A. Alenabi, Photon added qutrit like entangled coherent states of light, Journal of Research on Many-body Systems 11 (2022) 37-50. https://doi.org/10.22055/JRMBS.2021.17268
[38] A. Dehghani, B. Mojaveri, M. Aryaie, A.A. Alenabi, Superposition of two-mode “Near” coherent states: non-classicality and entanglement, Quantum Information Processing 18 (2019) 1-16.     https://doi.org/10.1007/s11128-019-2216-7
[39] X. Wu, S.P. Jia, C.L. Cai, L.M. Kuang, Witnessing entanglement via the geometric phase in a impurity-doped Bose-Einstein condensate, (2021). https://doi.org/10.48550/arXiv.2106.00224
[40] S.J. Akhtarshenas, Concurrence vectors in arbitrary multipartite quantum systems, Journal of Physics A: Mathematical and General 38 (2005) 6777.              https://doi.org/10.1088/0305-4470/38/30/011
[41] B. Yurke, S.L. McCall, J.R. Klauder, Su (2) and su (1, 1) interferometers, Physical Review A 33 (1986) 4033. https://doi.org/10.1103/PhysRevA.33.4033
[42] R. Demkowicz-Dobrza_nski, M. Jarzyna, J. Ko lody_nski, Quantum limits in optical interferometry, Progress in Optics 60 (2015) 345-435. https://doi.org/10.1016/bs.po.2015.02.003
[43] S. Mirzaei, G. Najarbashi, One-mode wigner quasi-probability distribution function for entangled coherent states generated by beam splitter and cavity QED, Reports on Mathematical Physics 83 (2019) 1-20. https://doi.org/10.1016/S0034-4877(19) 30020 -5
[44] A. Messina, B. Militello, A. Napoli, Generation of Glauber coherent state superpositions via unitary transformations. Proceedings of Institute of Mathematics of NAS of Ukraine 50. No. Part 2. (2004).
[45] A.P. Lund, et al., Conditional production of superpositions of coherent states with inefficient photon detection, Physical Review A 70 (2004) 020101. https://doi.org/10.1103/PhysRevA.70.020101
[46] H. Jeong, A.P. Lund, T.C. Ralph, Production of superpositions of coherent states in traveling optical fields with inefficient photon detection, Physical Review A 72 (2005) 013801. https://doi.org/10.1103/PhysRevA.72.013801
[47] S. Glancy, H.M. de Vasconcelos, Methods for producing optical coherent state superpositions, JOSA B 25 (2008) 712-733. https://doi.org/10.1364/JOSAB.25.000712
[48] H. Takahashi, et al., Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction, Physical review letters 101 (2008) 233605. https://doi.org/10.1103/PhysRevLett.101.233605
[49] T. Gerrits, et al., Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum, Physical Review A 82 (2010) 031802. https://doi.org/10.1103/PhysRevA.82.031802
Journal of Research on Many-body Systems
Volume 12, Issue 3 - Serial Number 34
autumn 2022
December 2022
Pages 51-64

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History

  • Receive Date: 17 January 2022
  • Revise Date: 20 April 2022
  • Accept Date: 20 July 2022

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