Skip to main content
SpringerLink
Log in
Book cover

Towards Solid-State Quantum Repeaters pp 25–38Cite as

Quantum Memories: Quantum Dot Spin Qubits

  • Chapter
  • First Online:

  • 783 Accesses

Part of the book series: Springer Theses ((Springer Theses))

Abstract

The quantum bits used in the remainder of this work, are individual electron (Chaps. 3–5 and 7) or hole spins (Chap. 6) in self-assembled quantum dots [1, 2]. Spins, either as direct spin-1/2 particles or as pseudospin-submanifolds of larger systems, are generally considered as good candidate-qubits due to their relatively limited interaction with the environment [3]. In addition, and as we shall show below, the confinement of the spin to quantum dots provides an additional protection of the spin degree of freedom.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Strictly speaking, this is not exactly correct: in view of the band discontinuity, this Hamiltonian is not Hermitian. Several approaches have been developed to cope with this problem, among them the BenDaniel-Duke solution for one-dimensional discontinuities: \(H_{BDD} = \frac{-{\hslash }^{2}} {2} \frac{\partial } {\partial z}( \frac{1} {m_{eff}(z)} \frac{\partial } {\partial z}) + U(z)\) [5].

  2. 2.

    Technically, this is a tensorial quantity. For electrons, with their s-type symmetry, this tensor reduces to a constant times the unit tensor; for holes, however, the tensor is very much anisotropic – see e.g. [18]

  3. 3.

    While we choose a rotating magnetic field for convenience, any uniaxial field could be decomposed into two counter-rotating ones, after which a rotating wave approximation can be invoked to neglect one of them.

  4. 4.

    The description in terms of superpositions of pure heavy-hole eigenstates assumes that the angular momentum along the growth direction, J z , is a good quantum number. In other words, cylindrical symmetry is assumed to be preserved. In view of the differences in confinement distances, this assumption is often but not always justified: strain and large asymmetries in particular quantum dots can lead to inmixing of light holes, which in turn affects the optical selection rules. We refer to Ref. [18] and references therein for more details. For the quantum dots used in the remainder of this work, pre-screening and selection of dots with ‘clean’ selection rules was applied.

  5. 5.

    Given that the decay probabilities are proportional to the matrix elements squared (one can e.g. invoke a Fermi’s golden rule argument [24]), this is actually a statement about the conservation of decay probability: for each excited state, in Voigt, there are two pathways for decay, each with half the probability of the single decay pathway in Faraday. These pathways do interfere, as we will show in Chap. 7.

  6. 6.

    This is, strictly speaking, only valid for slow, adiabatic evolution of the Rabi frequencies Ω1, 2 – we refer to [24, 25] for the necessary caveats.

References

  1. A. Imamoḡlu et al. Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett., 83:4204, 1999.

    Article  ADS  Google Scholar 

  2. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen. Spins in few electron quantum dots. Rev. Mod. Phys., 79:1217, 2007.

    Article  ADS  Google Scholar 

  3. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.

    Google Scholar 

  4. D. Loss and D. P. DiVincenzo. Quantum computation with quantum dots. Phys. Rev. A, 57:120, 1998.

    Article  ADS  Google Scholar 

  5. P. Yu and M. Cardona. Fundamentals of Semiconductors - Physics and Materials Properties (3rd Edition). Springer, 2001.

    Google Scholar 

  6. V. N. Golovach, A. Khaetskii, and D. Loss. Phonon-Induced Decay of the Electron Spin in Quantum Dots. Phys. Rev. Lett., 93:016601, 2004.

    Article  ADS  Google Scholar 

  7. J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven. Single-shot read-out of an individual electron spin in a quantum dot. Nature, 430:431, 2004.

    Article  ADS  Google Scholar 

  8. M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley. Optically programmable electron spin memory using semiconductor quantum dots. Nature, 432:81, 2004.

    Article  ADS  Google Scholar 

  9. E. O. Kane. Band structure of Indium Antimonide. Journal of Physics and Chemistry of Solids, 1:249, 1957.

    Article  ADS  Google Scholar 

  10. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto. Triggered single photons from a quantum dot. Phys. Rev. Lett., 86:1502, 2001.

    Article  ADS  Google Scholar 

  11. C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto. Indistinguishible photons from a single-photon device. Nature, 419:594, 2002.

    Article  ADS  Google Scholar 

  12. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu. A quantum dot single-photon turnstile device. Science, 290:2282, 2000.

    Article  ADS  Google Scholar 

  13. M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto. Efficient source of single photons: A single quantum dot in a micropost microcavity. Phys. Rev. Lett., 89:233602, 2002.

    Article  ADS  Google Scholar 

  14. E. Moreau, I. Robert, L. Manin, V. Thierry-Mieg, J. M. Gérard, and I. Abram. A single-mode solid-state source of single photons based on isolated quantum dots in a micropillar. Physica E, 13:418, 2002.

    Article  ADS  Google Scholar 

  15. J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom. Picosecond coherent optical manipulation of a single electron spin in a quantum dot. Science, 320:349, 2008.

    Article  ADS  Google Scholar 

  16. D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto. Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature, 456:218, 2008.

    Article  ADS  Google Scholar 

  17. D. Press, K. De Greve, P. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto. Ultrafast optical spin echo in a single quantum dot. Nat. Photonics, 4:367, 2010.

    Article  ADS  Google Scholar 

  18. M. Bayer et al. Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots. Phys. Rev. B, 65:195315, 2002.

    Article  ADS  Google Scholar 

  19. A. Greilich et al. Nuclei-induced frequency focusing of electron spin coherence. Science, 317(4):1896, 2007.

    Google Scholar 

  20. W. A. Coish and D. Loss. Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics. Phys. Rev. B, 70:195340, 2004.

    Article  ADS  Google Scholar 

  21. W. M. Witzel and S. Das Sarma. Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment. Phys. Rev. B, 74:035322, 2006.

    Article  ADS  Google Scholar 

  22. 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. Driven coherent oscillations of a single electron spin in a quantum dot. Nature, 442, 766.

    Google Scholar 

  23. K. C. Nowack, F. H. L. Koppens, Yu. V. Nazarov, and L. M. K. Vandersypen. Coherent Control of a Single Electron Spin with Electric Fields. Science, 318:1430, 2007.

    Article  ADS  Google Scholar 

  24. M. O. Scully and M. S. Zubairy. Quantum optics. Cambridge University Press, 1997.

    Google Scholar 

  25. A. Messiah. Quantum mechanics. Dover, 1999.

    Google Scholar 

  26. K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto. Coherent Population Trapping of Electron Spins in a High-Purity n-Type GaAs Semiconductor. Phys. Rev. Lett., 95:187405, 2005.

    Article  ADS  Google Scholar 

  27. X. Xu et al. Optically controlled locking of the nuclear field via coherent dark-state spectroscopy. Nature, 459(4):1105, 2009.

    Google Scholar 

  28. M. Fleischauer, A. Imamoglu, and J. P. Marangos. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys., 77:633, 2005.

    Article  ADS  Google Scholar 

  29. S. M. Clark, K-M. C. Fu, T. D. Ladd, and Y. Yamamoto. Quantum computers based on electron spins controlled by ultrafast off-resonant single optical pulses. Phys. Rev. Lett., 99:040501, 2007.

    Google Scholar 

  30. C. E. Pryor and M. E. Flatté. Predicted ultrafast single-qubit operations in semiconductor quantum dots. Appl. Phys. Lett., 88:233108, 2006.

    Article  ADS  Google Scholar 

  31. K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto. Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit. Nat. Phys., 7:872, 2011.

    Article  Google Scholar 

  32. K.-M. C. Fu et al. Ultrafast control of donor-bound electron spins with single detuned optical pulses. Nat. Phys., 4:780, 2008.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, MA, USA

    Kristiaan De Greve

Authors
  1. Kristiaan De Greve
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this chapter

Cite this chapter

De Greve, K. (2013). Quantum Memories: Quantum Dot Spin Qubits. In: Towards Solid-State Quantum Repeaters. Springer Theses. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00074-9_2

Download citation

Publish with us

Policies and ethics

Search

Navigation