Abstract

We combine the scanning temporal ultrafast delay (STUD) technique with spin noise spectroscopy (SNS), which is based upon below band gap Faraday rotation to investigate the full temporal dynamics of stochastically orientated electron spins in slightly n-doped bulk GaAs. The application of STUD-SNS boosts the common technical bandwidth limitation of the electro-optic conversion in cw-SNS into the several hundred GHz regime. Numerical simulations highlight the strengths and examine the limitations of STUD-SNS.

© 2013 OSA

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  1. G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
    [CrossRef]
  2. R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys.29(1), 255–284 (1966).
    [CrossRef]
  3. M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
    [CrossRef]
  4. G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
    [CrossRef]
  5. G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
    [CrossRef] [PubMed]
  6. S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010).
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  10. R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
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    [CrossRef]
  14. S. Starosielec and D. Hägele, “Ultrafast spin noise spectroscopy,” Appl. Phys. Lett.93(5), 051116 (2008).
    [CrossRef]
  15. M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett.94(11), 112105 (2009).
    [CrossRef]
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2012 (1)

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

2010 (5)

M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010).
[CrossRef]

G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
[CrossRef]

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
[CrossRef]

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

2009 (1)

M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett.94(11), 112105 (2009).
[CrossRef]

2008 (2)

S. Starosielec and D. Hägele, “Ultrafast spin noise spectroscopy,” Appl. Phys. Lett.93(5), 051116 (2008).
[CrossRef]

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

2007 (1)

M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum.78(10), 103903 (2007).
[CrossRef] [PubMed]

2004 (1)

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004).
[CrossRef]

2002 (2)

I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B65(20), 205309 (2002).
[CrossRef]

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

1966 (1)

R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys.29(1), 255–284 (1966).
[CrossRef]

1946 (1)

F. Bloch, “Nuclear Induction,” Phys. Rev.70(7-8), 460–474 (1946).
[CrossRef]

Bayer, M.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Bernien, H.

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

Berski, F.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

Bloch, F.

F. Bloch, “Nuclear Induction,” Phys. Rev.70(7-8), 460–474 (1946).
[CrossRef]

Brandt, J.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Crooker, S. A.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Dahbashi, R.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

Das Sarma, S.

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004).
[CrossRef]

Dzhioev, R. I.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Efros, A. L.

I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B65(20), 205309 (2002).
[CrossRef]

Fabian, J.

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004).
[CrossRef]

Gammon, D.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Greilich, A.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Hägele, D.

S. Starosielec and D. Hägele, “Ultrafast spin noise spectroscopy,” Appl. Phys. Lett.93(5), 051116 (2008).
[CrossRef]

Hübner, J.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
[CrossRef]

G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
[CrossRef]

M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett.94(11), 112105 (2009).
[CrossRef]

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum.78(10), 103903 (2007).
[CrossRef] [PubMed]

Jiang, J.

M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010).
[CrossRef]

Katzer, D. S.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Kavokin, K. V.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Korenev, V. L.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Kubo, R.

R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys.29(1), 255–284 (1966).
[CrossRef]

Lazarev, M. V.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Marie, X.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

Meltser, B. Ya.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Merkulov, I. A.

I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B65(20), 205309 (2002).
[CrossRef]

Müller, G.

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

Müller, G. M.

G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
[CrossRef]

G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
[CrossRef]

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

Oestreich, M.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
[CrossRef]

G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
[CrossRef]

M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett.94(11), 112105 (2009).
[CrossRef]

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum.78(10), 103903 (2007).
[CrossRef] [PubMed]

Pierz, K.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

Reuter, D.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Römer, M.

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
[CrossRef]

G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
[CrossRef]

M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett.94(11), 112105 (2009).
[CrossRef]

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum.78(10), 103903 (2007).
[CrossRef] [PubMed]

Rosen, M.

I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B65(20), 205309 (2002).
[CrossRef]

Sandfort, C.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Schuh, D.

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

Schumacher, H. W.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

Starosielec, S.

S. Starosielec and D. Hägele, “Ultrafast spin noise spectroscopy,” Appl. Phys. Lett.93(5), 051116 (2008).
[CrossRef]

Stepanova, M. N.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Wegscheider, W.

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

Weng, M.

M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010).
[CrossRef]

Wieck, A. D.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Wiegand, J.

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

Wu, M.

M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010).
[CrossRef]

Yakovlev, D. R.

S. A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer, “Spin noise of electrons and holes in self-assembled quantum dots,” Phys. Rev. Lett.104(3), 036601 (2010).
[CrossRef] [PubMed]

Zakharchenya, B. P.

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

Žutic, I.

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004).
[CrossRef]

Appl. Phys. Lett. (3)

R. Dahbashi, J. Hübner, F. Berski, J. Wiegand, X. Marie, K. Pierz, H. W. Schumacher, and M. Oestreich, “Heavy-hole spin dephasing in (InGa)As quantum dots,” Appl. Phys. Lett.100(3), 031906 (2012).
[CrossRef]

S. Starosielec and D. Hägele, “Ultrafast spin noise spectroscopy,” Appl. Phys. Lett.93(5), 051116 (2008).
[CrossRef]

M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett.94(11), 112105 (2009).
[CrossRef]

Phys. Rep. (1)

M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010).
[CrossRef]

Phys. Rev. (1)

F. Bloch, “Nuclear Induction,” Phys. Rev.70(7-8), 460–474 (1946).
[CrossRef]

Phys. Rev. B (4)

I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B65(20), 205309 (2002).
[CrossRef]

R. I. Dzhioev, K. V. Kavokin, V. L. Korenev, M. V. Lazarev, B. Ya. Meltser, M. N. Stepanova, B. P. Zakharchenya, D. Gammon, and D. S. Katzer, “Low-temperature spin relaxation in n-type GaAs,” Phys. Rev. B66(24), 245204 (2002).
[CrossRef]

M. Römer, H. Bernien, G. Müller, D. Schuh, J. Hübner, and M. Oestreich, “Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition,” Phys. Rev. B81(7), 075216 (2010).
[CrossRef]

G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B81(12), 121202 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

G. M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics,” Phys. Rev. Lett.101(20), 206601 (2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Physica E (1)

G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E43(2), 569–587 (2010).
[CrossRef]

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[CrossRef]

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M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum.78(10), 103903 (2007).
[CrossRef] [PubMed]

Other (2)

F. Berski, H. Kuhn, J. G. Lonnemann, J. Hübner, and M. Oestreich, “Ultrahigh Bandwidth Spin Noise Spectroscopy: Detection of large g-factor fluctuations in highly n-doped GaAs,” arXiv:1207.0081v1.

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Figures (4)

Fig. 1
Fig. 1

Experimental set-up: The outputs of two degenerate ultrafast ps-laser oscillators are joined in a single mode, polarization maintaining optical fiber. A fast photodiode picks up the temporal evolution of Δt . The linear polarized fiber output is focused to a spot diameter of about 40 µm onto the sample which is mounted in a low temperature magneto-optical cryostat. The average power is 8 mW at a wavelength of 825 nm. The polarization axis of the transmitted linear probe light is analyzed by a polarization bridge. The difference signal is electrically amplified and sent to a PC for digitalization and further data processing.

Fig. 2
Fig. 2

STUD spin noise principle. The left column shows the continuously varying pulse delay Δt together with an exemplary spin Larmor precession. The second column displays the Faraday rotation θ F sampled by each individual pulse leading to the detected Faraday rotation signal shown in the third column. In this example the detuning frequency is Δf32kHz .

Fig. 3
Fig. 3

(a) Illustrated is the SN autocorrelation at finite magnetic field for a full cycle of pulse pair delays. Δt periodically changes between its minimal and maximal value. The first and last sections contain the equivalent autocorrelation signal, whilst the two middle sections only contain photon shot noise. (b) Depicted is the dependence of the integrated spin noise power on the effective spin dephasing time as a result of a full numerical simulation of the experiments (dots) in units of the complete spin noise power for τ c . The red line follows the analytical model assuming a pseudo-Voigt type weighted distribution (see text). The parameter η denotes the relative weight of in- (η=0) and homogenous contribution (η=1) .

Fig. 4
Fig. 4

(a) Experimental result of STUD-SNS. Shown is an excerpt of the measured spectral noise power density of n-doped bulk GaAs at low temperatures (4 K) for different transverse magnetic field strengths, i.e., Larmor frequencies. The difference frequency Δf is 39kHz. The spin coherence time of τ c 1ns is determined by the spectral resolution of the setup and is in accordance with previously measured values of τ c for this sample [3]. The measurement time for a single spectrum is 30 min. (b) Numerical simulations of the spin noise spectra. All spectra are vertically shifted for clarity.

Equations (3)

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S B (t)= t b 1 /2 t+ b 1 /2 n= [ δ( t f r 1 n)+δ( t ( f r +Δf) 1 n) ]×[ θ F ( t )+σ( t ) ] d t .
{ S B (nΔt)} 2 θ F ( t i =0) θ F ( t i =0+nΔt)+const.
P SNS ( τ c (η)) P signal SNS | τ c = 0 T r /4 g(Δt, τ c (η),η) dΔt P signal SNS T r /4 T r /2 g(Δt, τ c (η),η) dΔt P background SNS .

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