Geometric Phase for Analytically Solvable Driven Time-Dependent Two-Level Quantum Systems

• Authors: I. Mendaš , N. Burić , D. Popović , S. Prvanović , M. Radonjić
• Languages of publication: EN

Abstracts

EN

Geometric phase for novel analytical solutions (Barnes and Das Sarma) of time-dependent two-level quantum systems is discussed, specifically for a general single-axis driving term, which is represented by a function J(t) in the Hamiltonian, and its corresponding evolution operator. It is demonstrated how general results for corresponding phases (total, dynamic and geometric) can be obtained. Using a specific case, it was found that over time in which the driving field is appreciably different from zero, the corresponding geometric phase changes (in the specific example by Δ β ≈ 0.8 radians) thus enabling detection. The results are relevant to qubit control and to quantum computing applications.

Keywords

EN

03.65.Aa; 03.65.Vf; 07.05.Dz

Discipline

• 03.65.Vf: Phases: geometric; dynamic or topological
• 03.65.Aa: Quantum systems with finite Hilbert space
• 07.05.Dz: Control systems

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 3
• Pages: 670-673

Dates

published

2014-08

received

2013-05-11

(unknown)

2014-04-16

(unknown)

2014-05-23

Contributors

author

I. Mendaš

• Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

author

N. Burić

• Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

author

D. Popović

• Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

author

S. Prvanović

• Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

author

M. Radonjić

• Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

References

• [1] L. Landau, Phys. Z. Sov. 2, 46 (1932)
• [2] C. Zener, Proc. R. Soc. A 137, 696 (1932), doi: 10.1098/rspa.1932.0165
• [3] I. Rabi, Phys. Rev. 51, 652 (1937), doi: 10.1103/PhysRev.51.652
• [4] E.T. Jaynes, F.W. Cummings, Proc. IEEE 51, 89 (1963), doi: 10.1109/PROC.1963.1664
• [5] S.L. McCall, E.L. Hahn, Phys. Rev. 183, 457 (1969), doi: 10.1103/PhysRev.183.457
• [6] S.E. Economou, L.J. Sham, Y. Wu, D.G. Steel, Phys. Rev. B 74, 205415 (2006), doi: 10.1103/PhysRevB.74.205415
• [7] A. Greilich, S.E. Economou, S. Spatzek, D.R. Yakovlev, D. Reuter, A.D. Wieck, T.L. Reineckee, M. Bayer, Nature Phys. 5, 262 (2009), doi: 10.1038/nphys1226
• [8] E. Poem, O. Kenneth, Y. Kodriano, Y. Benny, S. Khatsevich, J.E. Avron, D. Gershoni, Phys. Rev. Lett. 107, 087401 (2011), doi: 10.1103/PhysRevLett.107.087401
• [9] P.K. Jha, Y.V. Rostovtsev, Phys. Rev. A 81, 033827 (2010), doi: 10.1103/PhysRevA.81.033827
• [10] A. Gangopadhyay, M. Dzero, V. Galitski, Phys. Rev. B 82, 024303 (2010), doi: 10.1103/PhysRevB.82.024303
• [11] Q. Xie, W. Hai, Phys. Rev. A 82, 032117 (2010), doi: 10.1103/PhysRevA.82.032117
• [12] E. Barnes, S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012), doi: 10.1103/PhysRevLett.109.060401
• [13] M.V. Berry, Proc. R. Soc. Lond. A 392, 45 (1984), doi: 10.1098/rspa.1984.0023
• [14] M.V. Berry, J. Phys. A, Math. Gen. 18, 15 (1985), doi: 10.1088/0305-4470/18/1/012
• [15] Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987), doi: 10.1103/PhysRevLett.58.1593
• [16] J. Samuel, R. Bhandari, Phys. Rev. Lett. 60, 2339 (1988), doi: 10.1103/PhysRevLett.60.2339
• [17] S. Pancharatnam, Proc. Indian Acad. Sci. A 44, 247 (1956)
• [18] Collected Works of S. Pancharatnam, Oxford University Press, London 1975
• [19] D.M. Tong, J.L. Chen, J.F. Du, Chin. Phys. Lett. 20, 793 (2003), doi: 10.1088/0256-307X/20/6/304
• [20] I. Mendaš, Phys. Rev. A 55, 1514 (1997), doi: 10.1103/PhysRevA.55.1514
• [21] I. Mendaš, Phys. Rev. A 67, 044101 (2003), doi: 10.1103/PhysRevA.67.044101
• [22] M.A. Bouchene, M. Abdel-Aty, Phys. Rev. A 79, 055402 (2009), doi: 10.1103/PhysRevA.79.055402
• [23] E. Sjöqvist, A.K. Pati, A. Ekert, J.S. Anandan, M. Ericsson, D.K.L. Oi, V. Vedral, Phys. Rev. Lett. 85, 2845 (2000), doi: 10.1103/PhysRevLett.85.2845
• [24] A. Ekert, M. Ericsson, P. Hayden, H. Inamori, J.A. Jones, D.K.L. Oi, V. Vedral, J. Mod. Opt. 47, 2501 (2000), doi: 10.1080/09500340008232177
• [25] J.A. Jones, V. Vedral, A. Ekert, G. Castagnoli, Nature 403, 869 (2000), doi: 10.1038/35002528
• [26] M. Johansson, E. Sjöqvist, I. Mauritz Andersson, M. Ericsson, B. Hessmo, K. Singh, D.M. Tong, Phys. Rev. A 86, 062322 (2012), doi: 10.1103/PhysRevA.86.062322
• [27] S. Filipp, J. Klepp, Y. Hasegawa, C. Plonka-Spehr, U. Schmidt, P. Geltenbort, H. Rauch, Phys. Rev. Lett. 102, 030404 (2009), doi: 10.1103/PhysRevLett.102.030404

Identifiers

DOI

10.12693/APhysPolA.126.670