Abstract.
The Landau-Zener (LZ) transition probability of a two-level crossing in a single quantum dot driven by a two-state auto-correlated (TSAC) noise is studied. The model used isolates a central electron spin (CES) system bathed with TSAC noise and an anti-ferromagnetic spin bath. This model turnes into the LZ formalism in the limit of weak-excitation magnetic field. The effects of noise and of the coupling with the spin chain, on the LZ-transition probability are studied. In the weak coupling regime of the CES with the bath, it is seen that the TSAC noise effect can be compared with that of a deterministic sinusoidal oscillating function. In the strong coupling regime this effect decreases and alters the noise process on the LZ-transition probability.
Similar content being viewed by others
References
F. Bloch, Phys. Rev. 70, 460 (1946)
Y. Xiao-Zhong, G. Hsi-Sheng, Z. Ka-Di, New J. Phys. 9, 219 (2007)
M. Tchoffo, G.C. Fouokeng et al., World J. Condens. Matter Phys. 2, 246 (2012)
M. Tchoffo, G.C. Fouokeng, L.C. Fai, M.E. Ateuafack, J. Quantum Inf. Sci. 3, 10 (2013)
Y. Xiao-Zhong, Hsi-Sheng Goan, Ka-Di Zhu, Phys. Rev. B 75, 045331 (2007)
H. Ribeiro, J.R. Petta, Guido Burkard, Phys. Rev. B 82, 115445 (2010)
K.C. Nowack, F.H.L. Koppens, Yu.V. Nazarov, L.M.K. Vandersypen, Science 318, 1430 (2007)
J. Schliemann, A. Khaetskii, D. Loss, J. Phys. Condens. Matter 15, R1809 (2003)
S. Foletti, H. Bluhm, D. Mahalu, V. Umansky, A. Yacoby, Nat. Phys. 5, 903 (2009)
K. Saito, M. Wubs, S. Kohler, Y. Kayanuma, P. Hänggi, Phys. Rev. B 75, 214308 (2007)
W.D. Oliver, Y. Yu, J.C. Lee, K.K. Berggren, L.S. Levitov, T.P. Orlando, Science 310, 1653 (2005)
M. Sillanpaa, T. Lehtinen, A. Paila, Y. Makhlin, P. Hakonen, Phys. Rev. Lett. 96, 187002 (2006)
J. Ankerhold, H. Grabert, Phys. Rev. Lett. 91, 016803 (2003)
K. Saito, Y. Kayanuma, Phys. Rev. B 70, 201304(R) (2004)
G.C. Fouokeng, M. Tchoffo et al., Adv. Condens. Matter Phys. 2014, 526205 (2014)
F. Bloch, Z. Phys. A 52, 555 (1929)
L.D. Landau, Phys. Z. Sowjetunion 2, 46 (1932)
R. McDermott, IEEE Trans. Appl. Superconduct. 19, 1 (2009)
B. Rosam, K. Leo et al., Phys. Rev. B 68, 125301 (2003)
P. Abumov, D.W.L. Sprung, Phys. Rev. B 75, 165421 (2007)
A. Zenesini et al., New J. Phys. 10, 053038 (2008)
K. Rapedius, C. Elsen, D. Witthaut, S. Wimberger, H.J. Korsch, Phys. Rev. A 82, 063601 (2010)
R. Hanson et D.D. Awschalom, Nature 453, (2008)
J. Clarke, F.K. Wilhelm, Nature 453, (2008)
T.D. Ladd, F. Jelezko et al., Nature 464, (2010)
P.W. Anderson, J. Phys. Soc. Jpn. 9, (1954)
R. Kubo, J. Phys. Soc. Jpn. 9, (1954)
P.R. Berman, et R.G. Brewer, Phys. Rev. A 32, 5 (1985)
R.F. Loring, et S. Mukame, Chem. Phys. Lett. 114, (1985)
E. Shimshoni, A. Stern, Phys. Rev. B 47, 9523 (1992)
M. Wubs, K. Saito, S. Kohler, P. Hanggi, Y. Kayanuma, Phys. Rev. Lett. 97, 200404 (2006)
V.L. Pokrovsky, S. Scheidl, Phys. Rev. B 70, 014416 (2004)
S.N. Shevchenko, S. Ashhab, Franco Nori, Phys. Rep. 492, (2010)
J.I. Vestgården, J. Bergli, Y.M. Galperin, Phys. Rev. B 77, 014514 (2008)
I.I. Rabi, Phys. Rev. 51, 652 (1937)
R. Hanson, D.D. Awschalom, Nature (London) 453, 1043 (2008)
A. Abragam, Principles of Nuclear Magnetism (Oxford University Press, New York, 1961)
N. Rosen, C. Zener, Phys. Rev. 40, 502 (1932)
F.T. Hioe, C.E. Carroll, Phys. Rev. A 32, 1541 (1985)
E.C.G. Stuckelberg, Helv. Phys. Acta 5, 369 (1932)
P. Hanggi, P. Jung, Adv. Chem. Phys. 39, 239 (1995)
W. Yang, R.B. Liu, Phys. Rev. B 78, 085315 (2008)
D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio, Phys. Rev. A 75, 032333 (2007)
C. Zener, Proc. Roy. Soc. London A 137, 696 (1932)
E. Majorana, Nuovo Cimento 9, 43 (1932)
A.V. Shytov, D.A. Ivanov, M.V. Feigelman, Eur. Phys. J. B 36, 263 (2003)
F. Di Giacomo, E.E. Nikitin, Phys. Usp. 48, 515 (2005)
N.V. Vitanov, Phys. Rev. A 59, 2 (1999)
A. Ishkhanyan, J. Javanainenand, H. Nakamura, J. Phys. A: Math. Gen. 38, 3505 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fouokeng, G., Tchoffo, M., Ateuafack, M. et al. Dynamics of a central electron spin coupled to an anti-ferromagnetic spin bath driven by a variable magnetic field in the Landau-Zener scenario. Eur. Phys. J. Plus 129, 151 (2014). https://doi.org/10.1140/epjp/i2014-14151-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2014-14151-x