Decoherence of spin qubits due to a nearby charge fluctuator in gate-defined double dots

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 4, 2010, Pages

  Ramon, Guy ^a   Hu, Xuedong ^b  

^a SANTA CLARA UNIVERSITY   (United States)

^b UNIVERSITY AT BUFFALO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954828730     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.045304     Document Type: Article

References (64)

1. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Rev. Mod. Phys. 79, 1217 (2007). 10.1103/RevModPhys.79.1217 (Pubitemid 47534150)
2. M. Ciorga, A. S. Sachrajda, P. Hawrylak, C. Gould, P. Zawadzki, S. Jullian, Y. Feng, and Z. Wasilewski, Phys. Rev. B 61, R16315 (2000). 10.1103/PhysRevB.61.R16315
3. R. Hanson, L. H. Willems van Beveren, I. T. Vink, J. M. Elzerman, W. J. M. Naber, F. H. L. Koppens, L. P. Kouwenhoven, and L. M. K. Vandersypen, Phys. Rev. Lett. 94, 196802 (2005). 10.1103/PhysRevLett.94.196802 (Pubitemid 41492993)
4. J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Science 309, 2180 (2005). 10.1126/science.1116955 (Pubitemid 41396061)
5. S. Amasha, K. MacLean, I. P. Radu, D. M. Zumbuhl, M. A. Kastner, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 100, 046803 (2008). 10.1103/PhysRevLett.100.046803 (Pubitemid 351191342)
6. Amir Yacoby (private communication).
7. K. Ono, D. G. Austing, Y. Tokura, and S. Tarucha, Science 297, 1313 (2002). 10.1126/science.1070958 (Pubitemid 34918615)
8. J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, Nature (London) 430, 431 (2004). 10.1038/nature02693 (Pubitemid 38987899)
9. L. DiCarlo, H. J. Lynch, A. C. Johnson, L. I. Childress, K. Crockett, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 92, 226801 (2004). 10.1103/PhysRevLett.92.226801
10. F. H. L. Koppens, C. Buizert, K. J. Tielrooij, I. T. Vink, K. C. Nowack, T. Meunier, L. P. Kouwenhoven, and L. M. K. Vandersypen, Nature (London) 442, 766 (2006). 10.1038/nature05065 (Pubitemid 44261899)
11. K. C. Nowack, F. H. L. Koppens, Yu. V. Nazarov, and L. M. K. Vandersypen, Science 318, 1430 (2007). 10.1126/science.1148092 (Pubitemid 350208949)
12. V. N. Golovach, A. V. Khaetskii, and D. Loss, Phys. Rev. Lett. 93, 016601 (2004). 10.1103/PhysRevLett.93.016601
13. I. A. Merkulov, Al. L. Efros, and M. Rosen, Phys. Rev. B 65, 205309 (2002). 10.1103/PhysRevB.65.205309
14. A. C. Johnson, J. R. Petta, J. M. Taylor, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Nature (London) 435, 925 (2005). 10.1038/nature03815 (Pubitemid 40896314)
15. F. H. L. Koppens, J. A. Folk, J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, I. T. Vink, H. P. Tranitz, W. Wegscheider, L. P. Kouwenhoven, and L. M. K. Vandersypen, Science 309, 1346 (2005). 10.1126/science.1113719 (Pubitemid 41209357)
16. A. Greilich, A. Shabaev, D. R. Yacovlev, Al. L. Efros, I. A. Yugova, D. Reuter, A. D. Wielck, and M. Bayer, Science 317, 1896 (2007). 10.1126/science.1146850 (Pubitemid 47509430)
17. J. Baugh, Y. Kitamura, K. Ono, and S. Tarucha, Phys. Rev. Lett. 99, 096804 (2007). 10.1103/PhysRevLett.99.096804 (Pubitemid 47358530)
18. X. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, Nature (London) 459, 1105 (2009). 10.1038/nature08120
19. W. A. Coish and D. Loss, Phys. Rev. B 72, 125337 (2005). 10.1103/PhysRevB.72.125337 (Pubitemid 43028894)
20. D. Klauser, W. A. Coish, and D. Loss, Phys. Rev. B 73, 205302 (2006). 10.1103/PhysRevB.73.205302
21. W. Yao, R. B. Liu, and L. J. Sham, Phys. Rev. Lett. 98, 077602 (2007). 10.1103/PhysRevLett.98.077602
22. W. Yang and R-B. Liu, Phys. Rev. B 78, 085315 (2008) 10.1103/PhysRevB.78. 085315
23. W. Yang and R-B. Liu, Phys. Rev. B 79, 115320 (2009). 10.1103/PhysRevB.79.115320
24. W. M. Witzel, and S. Das Sarma, Phys. Rev. B 76, 241303 (R) (2007). 10.1103/PhysRevB.76.241303
25. L. Cywiński, W. M. Witzel, and S. Das Sarma, Phys. Rev. B 79, 245314 (2009). 10.1103/PhysRevB.79.245314
26. C. Deng and X. Hu, Phys. Rev. B 72, 165333 (2005) 10.1103/PhysRevB.72. 165333
27. C. Deng and X. Hu, Phys. Rev. B 73, 241303 (R) (2006). 10.1103/PhysRevB.73.241303 (Pubitemid 43849233)
28. L. Jiang, M. V. G. Dutt, E. Togan, L. Childress, P. Cappellaro, J. M. Taylor, and M. D. Lukin, Phys. Rev. Lett. 100, 073001 (2008). 10.1103/PhysRevLett.100.073001 (Pubitemid 351393604)
29. G. Burkard, D. Loss, and D. P. DiVincenzo, Phys. Rev. B 59, 2070 (1999). 10.1103/PhysRevB.59.2070
30. S. Das Sarma, R. de Sousa, X. Hu, and B. Koiller, Solid State Commun. 133, 737 (2005). 10.1016/j.ssc.2004.12.037 (Pubitemid 40276677)
31. G. Ramon and X. Hu, Phys. Rev. B 75, 161301 (R) (2007). 10.1103/PhysRevB.75.161301
32. J. R. Petta, J. M. Taylor, A. C. Johnson, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 100, 067601 (2008). 10.1103/PhysRevLett.100.067601 (Pubitemid 351391470)
33. D. J. Reilly, J. M. Taylor, J. R. Petta, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Science 321, 817 (2008). 10.1126/science.1159221
34. S. Foletti, H. Bluhm, D. Mahalu, V. Umansky, and A. Yacoby, Nat. Phys. 5, 903 (2009). 10.1038/nphys1424
35. X. Hu and S. Das Sarma, Phys. Rev. Lett. 96, 100501 (2006). 10.1103/PhysRevLett.96.100501
36. D. Culcer, X. Hu, and S. Das Sarma, Appl. Phys. Lett. 95, 073102 (2009). 10.1063/1.3194778
37. M. Pioro-Ladrière, John H. Davies, A. R. Long, A. S. Sachrajda, L. Gaudreau, P. Zawadzki, J. Lapointe, J. Gupta, Z. Wasilewski, and S. Studenikin, Phys. Rev. B 72, 115331 (2005). 10.1103/PhysRevB.72.115331 (Pubitemid 43029123)
38. S. W. Jung, T. Fujisawa, Y. Hirayama, and Y. H. Jeong, Appl. Phys. Lett. 85, 768 (2004). 10.1063/1.1777802
39. D. Taubert, M. Pioro-Ladrière, D. Schröer, D. Harbusch, A. S. Sachrajda, and S. Ludwig, Phys. Rev. Lett. 100, 176805 (2008). 10.1103/PhysRevLett.100.176805 (Pubitemid 351624647)
40. J. M. Taylor, H.-A. Engel, W. Dür, A. Yacoby, C. M. Marcus, P. Zoller, and M. D. Lukin, Nat. Phys. 1, 177 (2005). 10.1038/nphys174
41. I. Puerto Gimenez, C.-Y. Hsieh, M. Korkusinski, and P. Hawrylak, Phys. Rev. B 79, 205311 (2009). 10.1103/PhysRevB.79.205311
42. K. Roszak and P. Machnikowski, Phys. Rev. B 80, 195315 (2009). 10.1103/PhysRevB.80.195315
43. X. Hu, arXiv:0903.1080 (unpublished).
44. O. Astafiev, Yu. A. Pashkin, Y. Nakamura, T. Yamamoto, and J. S. Tsai, Phys. Rev. Lett. 93, 267007 (2004) 10.1103/PhysRevLett.93.267007
45. O. Astafiev, Yu. A. Pashkin, Y. Nakamura, T. Yamamoto, and J. S. Tsai, Phys. Rev. Lett. 96, 137001 (2006). 10.1103/PhysRevLett.96.137001
46. J. M. Martinis, K. B. Cooper, R. McDermott, M. Steffen, M. Ansmann, K. D. Osborn, K. Cicak, S. Oh, D. P. Pappas, R. W. Simmonds, and C. C. Yu, Phys. Rev. Lett. 95, 210503 (2005). 10.1103/PhysRevLett.95.210503 (Pubitemid 41777027)
47. A. Shnirman, G. Schön, I. Martin, and Y. Makhlin, Phys. Rev. Lett. 94, 127002 (2005). 10.1103/PhysRevLett.94.127002 (Pubitemid 40620571)
48. E. Paladino, M. Sassetti, G. Falci, and U. Weiss, Phys. Rev. B 77, 041303 (R) (2008). 10.1103/PhysRevB.77.041303
49. J. Bergli, Y. M. Galperin, and B. L. Altshuler, New J. Phys. 11, 025002 (2009). 10.1088/1367-2630/11/2/025002
50. E. Paladino, L. Faoro, G. Falci, and R. Fazio, Phys. Rev. Lett. 88, 228304 (2002). 10.1103/PhysRevLett.88.228304
51. L. Faoro, J. Bergli, B. L. Altshuler, and Y. M. Galperin, Phys. Rev. Lett. 95, 046805 (2005). 10.1103/PhysRevLett.95.046805 (Pubitemid 41506236)
52. We excluded a constant term that does not play any role in the system dynamics.
53. Guy Ramon and Xuedong Hu, arXiv:0909.4116 (unpublished).
54. We do not expect that a choice of a spheical symmetric TLS wavefunction will induce any qualitative change in our results.
55. When tunneling between the TLS centers is introduced the TLS eigenstates become (L ± R) / √ 2 (for ω T = 0) and contributions from off-diagonal TLS states become appreciable. The qubit-TLS coupling then produces additional terms in the interaction Hamiltonian (Eq.) of the form σ x T ⊗- σ z Q, σ x T ⊗- I Q. Assuming the TLS is unbiased there is no TLS dipole term and the leading contribution comes from the TLS quadrupole term, which is calculated to be very small for the TLS tunneling values assumed in this paper.
56. See, e.g., J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap..
57. J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 93, 186802 (2004). 10.1103/PhysRevLett.93.186802
58. R. Hanson and G. Burkard, Phys. Rev. Lett. 98, 050502 (2007). 10.1103/PhysRevLett.98.050502 (Pubitemid 46198306)
59. We have verified that switching times ≲ 1ns, comparable to experimentally used bias sweep times, do not contribute appreciably to gate errors in most cases, and in any case can be corrected by a careful pulse design. To isolate the effects of qubit-TLS coupling we have nevertheless considered very short switching times (∼ 1ps).
60. Throughout most of the parameter ranges presented in Figure 7, t T > Γ thus the TLS is not overdamped exclugin a direct coupling of its reservoir to the qubit.
61. Higher order contributions to β in the multipole expansion may have an opposite sign to that of the leading term. Typically, their magnitude will be comparable at shorter distances (R ≲ 25 nm), where the expansion converges slowly and yet higher order contributions are needed for an accurate estimate of the coupling.
62. The geometry depicted in Fig. yields β / γ ∼ 1 and thus yields considerably larger gate errors and dephsing as compared with the parallel-axis geometry.
63. In refering to the double dot bias we adopt the convention of zero bias at the anticrossing point.
64. Notice that while the qubit holds two electrons, its charge density corresponds to single-particle operators. The two-particle qubit states are considered at a later stage, when evaluating the Coulomb matrix elements, Eq.