## Rapid scanning of spin noise with two free running ultrafast oscillators |

Optics Express, Vol. 21, Issue 5, pp. 5872-5878 (2013)

http://dx.doi.org/10.1364/OE.21.005872

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### 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

## 1. Introduction

1. G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E **43**(2), 569–587 (2010). [CrossRef]

*without*driving the system out of equilibrium [2

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. B **81**(7), 075216 (2010). [CrossRef]

7. 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]

4. G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B **81**(12), 121202 (2010). [CrossRef]

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

### Spin noise in semiconductors

12. F. Bloch, “Nuclear Induction,” Phys. Rev. **70**(7-8), 460–474 (1946). [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. B **81**(7), 075216 (2010). [CrossRef]

9. I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B **65**(20), 205309 (2002). [CrossRef]

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. B **66**(24), 245204 (2002). [CrossRef]

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

## 2. Technique

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

*amplitude*corresponding to the fluctuation envelope of the spin dynamic.

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

4. G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B **81**(12), 121202 (2010). [CrossRef]

## 3. Measurement results

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

## 4. Conclusion

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

## Acknowledgment

## References and links

1. | G. M. Müller, M. Oestreich, M. Römer, and J. Hübner, “Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges,” Physica E |

2. | R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. |

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. B |

4. | G. M. Müller, M. Römer, J. Hübner, and M. Oestreich, “Gigahertz spin noise spectroscopy in n-doped bulk GaAs,” Phys. Rev. B |

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. |

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. |

7. | 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. |

8. | M. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep. |

9. | I. A. Merkulov, A. L. Efros, and M. Rosen, “Electron spin relaxation by nuclei in semiconductor quantum dots,” Phys. Rev. B |

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. B |

11. | F. Meier and B. P. Zakharchenya, eds., |

12. | F. Bloch, “Nuclear Induction,” Phys. Rev. |

13. | I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. |

14. | S. Starosielec and D. Hägele, “Ultrafast spin noise spectroscopy,” Appl. Phys. Lett. |

15. | M. Römer, J. Hübner, and M. Oestreich, “Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy,” Appl. Phys. Lett. |

16. | M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum. |

17. | 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. |

**OCIS Codes**

(000.2170) General : Equipment and techniques

(320.7150) Ultrafast optics : Ultrafast spectroscopy

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: December 19, 2012

Revised Manuscript: February 4, 2013

Manuscript Accepted: February 20, 2013

Published: March 1, 2013

**Citation**

Jens Hübner, Jan Gerrit Lonnemann, Petrissa Zell, Hendrik Kuhn, Fabian Berski, and Michael Oestreich, "Rapid scanning of spin noise with two free running ultrafast oscillators," Opt. Express **21**, 5872-5878 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5872

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### References

- 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]
- R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys.29(1), 255–284 (1966). [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]
- 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]
- 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]
- 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. Wu, J. Jiang, and M. Weng, “Spin dynamics in semiconductors,” Phys. Rep.493(2-4), 61–236 (2010). [CrossRef]
- 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]
- F. Meier and B. P. Zakharchenya, eds., Optical Orientation (North-Holland, 1984).
- F. Bloch, “Nuclear Induction,” Phys. Rev.70(7-8), 460–474 (1946). [CrossRef]
- I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004). [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]
- M. Römer, J. Hübner, and M. Oestreich, “Spin noise spectroscopy in semiconductors,” Rev. Sci. Instrum.78(10), 103903 (2007). [CrossRef] [PubMed]
- 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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