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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 6 — Jun. 1, 2010
  • pp: A46–A62

Theory of unitary spin rotation and spin-state tomography for a single electron and two electrons

T. Takagahara  »View Author Affiliations


JOSA B, Vol. 27, Issue 6, pp. A46-A62 (2010)
http://dx.doi.org/10.1364/JOSAB.27.000A46


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Abstract

Electron spins in semiconductor nanostructures are considered as one of the most promising candidates of the building blocks for quantum information processing. Initialization, coherent manipulation, and measurement of a single electron spin have been recently established. Here we explore the possibility to manipulate and measure by optical means the states of two electrons as a single qubit in nanostructures and propose methods of spin-state tomography based on Faraday or Kerr rotation for cases of both a single electron and two electrons, as well as a method of the Bell-state measurement for two electrons.

© 2010 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(270.1670) Quantum optics : Coherent optical effects
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Cold Atoms, Ions, Electrons, and Molecules

History
Original Manuscript: November 19, 2009
Revised Manuscript: January 27, 2010
Manuscript Accepted: January 27, 2010
Published: March 16, 2010

Citation
T. Takagahara, "Theory of unitary spin rotation and spin-state tomography for a single electron and two electrons," J. Opt. Soc. Am. B 27, A46-A62 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-6-A46


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References

  1. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083-4086 (1995). [CrossRef] [PubMed]
  2. D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120-126 (1998). [CrossRef]
  3. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204-4207 (1999). [CrossRef]
  4. C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247-255 (2000). [CrossRef]
  5. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
  6. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).
  7. D. D. Awschalom, D. Loss, and N. Samarth, Semiconductor Spintronics and Quantum Computation (Springer-Verlag, 2002).
  8. T. Takagahara, Quantum Coherence, Correlation and Decoherence in Semiconductor Nanostructures (Academic, Elsevier, 2003).
  9. T. Takagahara, in Proceedings of the International Symposium on Photonics and Spintronics in Semiconductor Nanostructures (PSSN 2003) (Kyoto Institute of Technology, 2003); available online at http://repository.lib.kit.ac.jp/dspace/bitstream/10212/1868/3/PSSN2003.pdf. [PubMed]
  10. X. Li, Y. Wu, D. G. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809-811 (2003). [CrossRef] [PubMed]
  11. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. Vandersypen, “Spins in few-electron quantum dots,” Rev. Mod. Phys. 79, 1217-1265 (2007). [CrossRef]
  12. M. I. Dyakonov, Spin Physics in Semiconductors (Springer-Verlag, 2008). [CrossRef]
  13. F. Henneberger and O. Benson, Semiconductor Quantum Bits (Pan Stanford Publishing, 2009).
  14. R. Hanson, B. Witkamp, L. M. K. Vandersypen, L. H. Willems van Beveren, J. M. Elzerman, and L. P. Kouwenhoven, “Zeeman energy and spin relaxation in a one-electron quantum dot,” Phys. Rev. Lett. 91, 196802 (2003). [CrossRef] [PubMed]
  15. 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 (London) 432, 81-84 (2004). [CrossRef]
  16. 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, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,” Science 309, 2180-2184 (2005). [CrossRef] [PubMed]
  17. 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,” Science 442, 766-771 (2006).
  18. T. Meunier, I. T. Vink, L. H. Willems van Beveren, K. J. Tielrooij, R. Hanson, F. H. L. Koppens, H. P. Tranitz, M. Wegscheider, L. P. Kouwenhoven, and L. M. K. Vandersypen, “Experimental signature of phonon-mediated spin relaxation in a two-electron quantum dot,” Phys. Rev. Lett. 98, 126601 (2007). [CrossRef] [PubMed]
  19. H. Kosaka, A. A. Kiselev, F. A. Baron, K. W. Kim, and E. Yablonovitch, “Electron g factor engineering in III-V semiconductors for quantum communications,” Electron. Lett. 37, 464-465 (2001). [CrossRef]
  20. R. Vrijen and E. Yablonovitch, “A spin-coherent semiconductor photo-detector for quantum communication,” Physica E (Amsterdam) 10, 569-575 (2001). [CrossRef]
  21. E. Yablonovitch, H. W. Jiang, H. Kosaka, H. D. Robinson, D. S. Rao, and T. Szkopek, “Optoelectronic quantum telecommunications based on spins in semiconductors,” Proc. IEEE 91, 761-780 (2003). [CrossRef]
  22. H. Kosaka and E. Yablonovitch, “Quantum media converter from a photon qubit to an electron-spin qubit for quantum repeaters,” in Ref. , pp. 63-70.
  23. M. Atatüre, J. Dreiser, A. Badolato, A. Hogele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,” Science 312, 551-553 (2006). [CrossRef] [PubMed]
  24. C. Emary, X. Xu, D. G. Steel, S. Saikin, and L. J. Sham, “Fast initialization of the spin state of an electron in a quantum dot in the Voigt configuration,” Phys. Rev. Lett. 98, 047401 (2007). [CrossRef] [PubMed]
  25. X. Xu, Y. Wu, B. Sun, Q. Huang, J. Cheng, D. G. Steel, A. S. Bracker, D. Gammon, C. Emary, and L. J. Sham, “Fast spin state initialization in a singly charged InAs-GaAs quantum dot by optical cooling,” Phys. Rev. Lett. 99, 097401 (2007). [CrossRef] [PubMed]
  26. 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, 1430-1433 (2007). [CrossRef] [PubMed]
  27. P. Chen, C. Piermarocchi, L. J. Sham, D. Gammon, and D. G. Steel, “Theory of quantum optical control of a single spin in a quantum dot,” Phys. Rev. B 69, 075320 (2004). [CrossRef]
  28. M. V. G. Dutt, J. Cheng, B. Li, X. Xu, Xiaoqin Li, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, S. E. Economou, R. B. Liu, and L. J. Sham, “Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots,” Phys. Rev. Lett. 94, 227403 (2005). [CrossRef] [PubMed]
  29. S. E. Economou and L. J. Sham, Y. Wu, and D. G. Steel, “Proposal for optical U(1) rotations of electron spin trapped in a quantum dot,” Phys. Rev. B 74, 205415 (2006). [CrossRef]
  30. Y. Wu, E. D. Kim, X. Xu, J. Cheng, D. G. Steel, A. S. Bracker, D. Gammon, S. E. Economou, and L. J. Sham, “Selective optical control of electron spin coherence in singly charged GaAs-Al0.3Ga0.7As quantum dots,” Phys. Rev. Lett. 99, 097402 (2007). [CrossRef] [PubMed]
  31. S. E. Economou and T. L. Reinecke, “Theory of fast optical spin rotation in a quantum dot based on geometric phases and trapped states,” Phys. Rev. Lett. 99, 217401 (2007). [CrossRef]
  32. 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, 349-352 (2008). [CrossRef] [PubMed]
  33. D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature (London) 456, 218-221 (2008). [CrossRef]
  34. A. M. Tyryshkin, S. A. Lyon, A. V. Astashkin, and A. M. Raitsimring, “Electron spin relaxation times of phosphorus donors in silicon,” Phys. Rev. B 68, 193207 (2003). [CrossRef]
  35. M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312-1316 (2007). [CrossRef]
  36. J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and S. A. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature (London) 455, 1085-1088 (2008). [CrossRef]
  37. H. Kosaka, H. Shigyou, Y. Mitsumori, Y. Rikitake, H. Imamura, T. Kutsuwa, K. Arai, and K. Edamatsu, “Coherent transfer of light polarization to electron spins in a semiconductor,” Phys. Rev. Lett. 100, 096602 (2008). [CrossRef] [PubMed]
  38. H. Kosaka, T. Inagaki, Y. Rikitake, H. Imamura, Y. Mitsumori, and K. Edamatsu, “Spin state tomography of optically injected electrons in a semiconductor,” Nature (London) 457, 702-705 (2009). [CrossRef]
  39. N. Rosen and C. Zener, “Double Stern-Gerlach experiment and related collision phenomena,” Phys. Rev. 40, 502-507 (1932). [CrossRef]
  40. A. Bambini and P. R. Berman, “Analytic solutions to the two-state problem for a class of coupling potentials,” Phys. Rev. A 23, 2496-2501 (1981). [CrossRef]
  41. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1972).
  42. A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nat. Phys. 5, 262-266 (2009). [CrossRef]
  43. O. Cakir and T. Takagahara, “Quantum dynamics in electron-nuclei coupled spin system in quantum dots: Bunching, revival, and quantum correlation in electron-spin measurements,” Phys. Rev. B 77, 115304 (2008). [CrossRef]
  44. J. Berezovsky, M. H. Mikkelsen, O. Gywat, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Nondestructive optical measurements of a single electron spin in a quantum dot,” Science 314, 1916-1920 (2006). [CrossRef] [PubMed]
  45. M. Atature, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3, 101-106 (2007). [CrossRef]
  46. A. A. Kiselev, K. W. Kim, and E. Yablonovitch, “In-plane light-hole g factor in strained cubic heterostructures,” Phys. Rev. B 64, 125303 (2001). [CrossRef]
  47. R. B. Dingle, “Some magnetic properties of metals. I. general introduction, and properties of large systems of electrons,” Proc. R. Soc. London 211, 500-516 (1952). [CrossRef]
  48. R. B. Dingle, “Some magnetic properties of metals. III. diamagnetic resonance,” Proc. R. Soc. London 212, 38-47 (1952). [CrossRef]
  49. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]
  50. T. Takagahara and O. Cakir, “Theoretical aspects of quantum state transfer, correlation measurement and electron-nuclei coupled dynamics in quantum dots,” J. Nanophotonics 1, 011593 (2007). [CrossRef]
  51. J. M. Taylor, C. M. Marcus, and M. D. Lukin, “Long-lived memory for mesoscopic quantum bits,” Phys. Rev. Lett. 90, 206803 (2003). [CrossRef] [PubMed]
  52. O. Cakir and T. Takagahara, “Proposals of nuclear spin quantum memory in group-IV elemental and II-VI semiconductors,” Phys. Rev. B 80, 155323 (2009). [CrossRef]

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