Abstract

Spin-photon interactions such as the Faraday effect provide techniques for measuring coherent spin dynamics in semiconductors. In contrast to typical ultrafast pulsed laser techniques, which measure spin dynamics in the time domain with an intense, spectrally broad probe pulse, we demonstrate a frequency-domain spin-photon resonance effect using modulated continuous-wave lasers which enables measurement of GHz-scale coherent spin dynamics in semiconductors with minimal spectral linewidth. This technique permits high-resolution spectroscopic measurements not possible with ultrafast methods. We have employed this effect to observe coherent spin dynamics in CdSe nanocrystals using standard diode lasers. By fitting the results to the expected model, we extract electron g-factors, and spin coherence and dephasing times in agreement with time-domain measurements.

© 2012 OSA

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  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(4), 1217–1265 (2007).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  17. 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,” Science320(5874), 349–352 (2008).
    [CrossRef] [PubMed]

2012 (1)

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

2008 (1)

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,” Science320(5874), 349–352 (2008).
[CrossRef] [PubMed]

2007 (2)

P. Irvin, P. S. Fodor, and J. Levy, “Gigahertz optical spin transceiver,” Opt. Express15(18), 11756–11762 (2007).
[CrossRef] [PubMed]

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(4), 1217–1265 (2007).
[CrossRef]

2006 (1)

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

2005 (3)

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, “Spin noise spectroscopy in GaAs,” Phys. Rev. Lett.95(21), 216603 (2005).
[CrossRef] [PubMed]

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

2004 (1)

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature431(7004), 49–52 (2004).
[CrossRef] [PubMed]

2003 (1)

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

2002 (1)

J. A. Gupta, D. D. Awschalom, A. L. Efros, and A. V. Rodina, “Spin dynamics in semiconductor nanocrystals,” Phys. Rev. B66(12), 125307 (2002).
[CrossRef]

2000 (1)

J. M. Kikkawa and D. D. Awschalom, “All-optical magnetic resonance in semiconductors,” Science287(5452), 473–476 (2000).
[CrossRef] [PubMed]

1998 (1)

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett.80(19), 4313–4316 (1998).
[CrossRef]

1988 (1)

M. Combescot and R. Combescot, “Excitonic Stark shift: A coupling to “semivirtual” biexcitons,” Phys. Rev. Lett.61(1), 117–120 (1988).
[CrossRef] [PubMed]

Alen, B.

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

Atatüre, M.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Awschalom, D. D.

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,” Science320(5874), 349–352 (2008).
[CrossRef] [PubMed]

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

J. A. Gupta, D. D. Awschalom, A. L. Efros, and A. V. Rodina, “Spin dynamics in semiconductor nanocrystals,” Phys. Rev. B66(12), 125307 (2002).
[CrossRef]

J. M. Kikkawa and D. D. Awschalom, “All-optical magnetic resonance in semiconductors,” Science287(5452), 473–476 (2000).
[CrossRef] [PubMed]

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett.80(19), 4313–4316 (1998).
[CrossRef]

Badolato, A.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Balatsky, A. V.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature431(7004), 49–52 (2004).
[CrossRef] [PubMed]

Bartl, M. H.

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

Bayer, M.

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

Berezovsky, J.

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,” Science320(5874), 349–352 (2008).
[CrossRef] [PubMed]

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

Bickel, F.

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

Coldren, L. A.

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,” Science320(5874), 349–352 (2008).
[CrossRef] [PubMed]

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

Combescot, M.

M. Combescot and R. Combescot, “Excitonic Stark shift: A coupling to “semivirtual” biexcitons,” Phys. Rev. Lett.61(1), 117–120 (1988).
[CrossRef] [PubMed]

Combescot, R.

M. Combescot and R. Combescot, “Excitonic Stark shift: A coupling to “semivirtual” biexcitons,” Phys. Rev. Lett.61(1), 117–120 (1988).
[CrossRef] [PubMed]

Crooker, S. A.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature431(7004), 49–52 (2004).
[CrossRef] [PubMed]

Dreiser, J.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Efros, A. L.

J. A. Gupta, D. D. Awschalom, A. L. Efros, and A. V. Rodina, “Spin dynamics in semiconductor nanocrystals,” Phys. Rev. B66(12), 125307 (2002).
[CrossRef]

Fodor, P. S.

Gerardot, B. D.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Glazov, M. M.

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

Gupta, J. A.

J. A. Gupta, D. D. Awschalom, A. L. Efros, and A. V. Rodina, “Spin dynamics in semiconductor nanocrystals,” Phys. Rev. B66(12), 125307 (2002).
[CrossRef]

Gywat, O.

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

Hägele, D.

M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, “Spin noise spectroscopy in GaAs,” Phys. Rev. Lett.95(21), 216603 (2005).
[CrossRef] [PubMed]

Hanson, R.

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(4), 1217–1265 (2007).
[CrossRef]

Haug, R. J.

M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, “Spin noise spectroscopy in GaAs,” Phys. Rev. Lett.95(21), 216603 (2005).
[CrossRef] [PubMed]

Högele, A.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Hu, E. L.

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

Imamoglu, A.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Irvin, P.

Karrai, K.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

Kikkawa, J. M.

J. M. Kikkawa and D. D. Awschalom, “All-optical magnetic resonance in semiconductors,” Science287(5452), 473–476 (2000).
[CrossRef] [PubMed]

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett.80(19), 4313–4316 (1998).
[CrossRef]

Kouwenhoven, L. P.

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(4), 1217–1265 (2007).
[CrossRef]

Kroner, M.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Levy, J.

Mikkelsen, M. H.

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,” Science320(5874), 349–352 (2008).
[CrossRef] [PubMed]

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

Oestreich, M.

M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, “Spin noise spectroscopy in GaAs,” Phys. Rev. Lett.95(21), 216603 (2005).
[CrossRef] [PubMed]

Petroff, P. M.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

Petta, J. R.

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(4), 1217–1265 (2007).
[CrossRef]

Poggio, M.

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

Rickel, D. G.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature431(7004), 49–52 (2004).
[CrossRef] [PubMed]

Rodina, A. V.

J. A. Gupta, D. D. Awschalom, A. L. Efros, and A. V. Rodina, “Spin dynamics in semiconductor nanocrystals,” Phys. Rev. B66(12), 125307 (2002).
[CrossRef]

Römer, M.

M. Oestreich, M. Römer, R. J. Haug, and D. Hägele, “Spin noise spectroscopy in GaAs,” Phys. Rev. Lett.95(21), 216603 (2005).
[CrossRef] [PubMed]

Seidl, S.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Smith, D. L.

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature431(7004), 49–52 (2004).
[CrossRef] [PubMed]

Sokolova, A. A.

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

Stern, N. P.

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

Stoltz, N. G.

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,” Science320(5874), 349–352 (2008).
[CrossRef] [PubMed]

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

Stucky, G. D.

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

Tarucha, S.

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(4), 1217–1265 (2007).
[CrossRef]

Vandersypen, L. M. K.

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(4), 1217–1265 (2007).
[CrossRef]

Warburton, R. J.

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

Yakovlev, D. R.

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

Yugova, I. A.

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

Appl. Phys. Lett. (2)

B. Alen, F. Bickel, K. Karrai, R. J. Warburton, and P. M. Petroff, “Stark-shift modulation absorption spectroscopy of single quantum dots,” Appl. Phys. Lett.83(11), 2235–2237 (2003).
[CrossRef]

A. Högele, M. Kroner, S. Seidl, K. Karrai, M. Atatüre, J. Dreiser, A. Imamoglu, R. J. Warburton, A. Badolato, B. D. Gerardot, and P. M. Petroff, “Spin-selective optical absorption of singly charged excitons in a quantum dot,” Appl. Phys. Lett.86(22), 221905 (2005).
[CrossRef]

Nature (1)

S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature431(7004), 49–52 (2004).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (3)

J. A. Gupta, D. D. Awschalom, A. L. Efros, and A. V. Rodina, “Spin dynamics in semiconductor nanocrystals,” Phys. Rev. B66(12), 125307 (2002).
[CrossRef]

I. A. Yugova, M. M. Glazov, D. R. Yakovlev, A. A. Sokolova, and M. Bayer, “Coherent spin dynamics of electrons and holes in semiconductor quantum wells and quantum dots under periodical optical excitation: resonant spin amplification versus spin mode locking,” Phys. Rev. B85(12), 125304 (2012).
[CrossRef]

N. P. Stern, M. Poggio, M. H. Bartl, E. L. Hu, G. D. Stucky, and D. D. Awschalom, “Spin dynamics in electrochemically charged CdSe quantum dots,” Phys. Rev. B72(16), 161303 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

M. Combescot and R. Combescot, “Excitonic Stark shift: A coupling to “semivirtual” biexcitons,” Phys. Rev. Lett.61(1), 117–120 (1988).
[CrossRef] [PubMed]

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett.80(19), 4313–4316 (1998).
[CrossRef]

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Rev. Mod. Phys. (1)

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(4), 1217–1265 (2007).
[CrossRef]

Science (3)

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,” Science314(5807), 1916–1920 (2006).
[CrossRef] [PubMed]

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,” Science320(5874), 349–352 (2008).
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[CrossRef] [PubMed]

Other (3)

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D. D. Awschalom, D. Loss, and N. Samarth, eds., Semiconductor Spintronics and Quantum Computation. NanoScience and Technology (Springer-Verlag, Berlin, 2002).

O. Gywat, H. Krenner, and J. Berezovsky, Spins in Optically Active Quantum Dots (Wiley-VCH, 2010).

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Figures (4)

Fig. 1
Fig. 1

Calculated FTSR spectra. Column (i) displays time-domain spin dynamics sz(B,t). Columns (ii)-(iv) show FTSR spectra with B fixed (B1 = 70 mT, B2 = 140 mT, B3 = 210 mT) and Ω varied (ii), with Ω fixed (Ω1 = 7.5 GHz, Ω2 = 15 GHz, Ω3 = 22.5 GHz) and B varied (iii), and with Ω fixed and B varied with a non-harmonic pump/probe modulation (iv). The vertical scale in columns (iii) and (iv) are set with the central peak off-scale to more clearly show the satellite peaks. (a) Spin dynamics with a single precession frequency, and exponential decay. (b) Same as (a) but including inhomogeneous dephasing from a Gaussian distribution of g-factors. (c) Same as (b), but with a bimodal Gaussian g-factor distribution.

Fig. 2
Fig. 2

Schematic of FTSR setup. Pump and probe diode lasers are driven by signals modulated at low frequencies f1 = 20 kHz and f2 = 520 Hz combined via bias tees with high frequency modulation (Ω~GHz) from a divided RF signal generator. The circularly polarized pump and linearly polarized probe are focused to overlapping spots within the sample in a transverse magnetic field B. The angle between pump and probe beams at the sample ~6°, and is exaggerated in the figure for clarity. The rotation of the probe polarization is then measured by a balanced photodiode bridge.

Fig. 3
Fig. 3

(a) Hanle measurement: Faraday rotation Θ0 vs. magnetic field B with continuous-wave pump and probe. (b) FTSR measurement: Θ0 vs. B with pump and probe in phase and modulated at Ω = 5.65 GHz. Peaks arise from resonances between frequency components of the pump and probe at integer multiples of Ω, and coherent spin dynamics in the sample. Fit is to Eqs. (6) and (9).

Fig. 4
Fig. 4

FTSR data at three modulation frequencies Ω (curves are offset vertically). Resonance peaks shift linearly with increasing Ω, as indicated by dashed lines. Fit is to all three curves simultaneously, using Eqs. (6) and (9). Inset shows FTSR data at Ω = 0.69 GHz (black) to Ω = 5.72 GHz (white) in 0.63 GHz steps. Inset curves are offset, and the peak at B = 0 is normalized to Θ0 = 1.

Tables (1)

Tables Icon

Table 1 Best-fit parameters from the fits shown in Fig. 3(b) and Fig. 4.

Equations (9)

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s( t ) = 0 g( t t )s ( t )d t =γRe n=0 [ α n e inΩt 0 s( t ) e inΩ t d t ] .
s( t ) =γRe n=0 α n s ˜ ( nΩ ) e inΩt .
Θ( t )= 1 4 θγ n,m=0 s ˜ z ( nΩ ) α n β m e i( n+m )Ωt + s ˜ * z ( nΩ ) α * n β * m e i( n+m )Ωt + s ˜ z ( nΩ ) α n β * m e i( nm )Ωt + s ˜ * z ( nΩ ) α * n β m e i( nm )Ωt .
Θ 0 = 1 2 θγ[ 2 s ˜ z ( 0 ) α 0 β 0 + n=1 Re( s ˜ ( nΩ ) α n β * n ) ]
Θ 0 = 1 2 θγ{ 2 s ˜ z ( 0 )+Re s ˜ z ( Ω ) 2 s ˜ z ( 0 )+Im s ˜ z ( Ω ) ϕ=0 ϕ=π/2.
Θ 0 ( B,Ω )2 s ˜ z ( B,0 )+{ n=1 c n Re s ˜ z ( B,nΩ ) ϕ=0 n=1 c n Im s ˜ z ( B,nΩ ) ϕ=π/2
s z ( B,t )=Aexp( t/τ ) P( g g 0 ) cos( g μ B Bt/ )dg =Aexp( t/τ )cos( g 0 μ B Bt/ )Re P ˜ ( μ B Bt/ )
s z ( B,t )=A [ exp( t/ τ 1 )cos( g 1 μ B Bt/ )Re P ˜ 1 ( μ B Bt/ ) + ηexp( t/ τ 2 )cos( g 2 μ B Bt/ )Re P ˜ 2 ( μ B Bt/ ) ]
s z ( B,t )=A [ exp( Δ g 1 μ B Bt/ )exp( t/ τ 1 )cos( g 1 μ B Bt/ ) + ηexp( Δ g 2 μ B Bt/ )exp( t/ τ 2 )cos( g 2 μ B Bt/ ) ].

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