Abstract

We study the spin polarization of Doppler-broadened atoms by broadband nanosecond (ns) pulses, and compare the polarization efficiency with that by the transform-limited picosecond (ps) pulses that have the same spectral bandwidth. Specific calculations are performed for the case of muonium with a set of density matrix equations and with rate equations using the uncoupled basis states. We find that the polarization efficiency with the broadband ns laser pulses is rather good, although it is not as good as that with the transform-limited ps pulses. Our results imply that, depending on the available laser system, we can use either broadband ns or transform-limited ps laser pulses to polarize almost any Doppler-broadened atoms.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Fick, G. Grawert, and I. M. Turkiewicz, “Nuclear physics with polarized heavy ions,” Phys. Rep. 214, 1–111 (1992).
    [CrossRef]
  2. J. P. Miller, E. de Rafael, and B. L. Roberts, “Muon (g-2): experiment and theory,” Rep. Prog. Phys. 70, 795–881 (2007).
    [CrossRef]
  3. http://j-parc.jp/MatLife/en/index.html .
  4. S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
    [CrossRef]
  5. P. Dalmas de Réotier and A. Yaouanc, “Muon spin rotation and relaxation in magnetic materials,” J. Phys. Condens. Matter 9, 9113–9166 (1997).
    [CrossRef]
  6. P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
    [CrossRef]
  7. P. Bakule and E. Morenzoni, “Generation and application of slow polarized muons,” Contemp. Phys. 45, 203–225(2004).
    [CrossRef]
  8. R. Mahon, T. J. McIlrath, and D. Koopman, “Nonlinear generation of Lyman-alpha radiation,” Appl. Phys. Lett. 33, 305–307 (1978).
    [CrossRef]
  9. D. Cotter, “Tunable narrow-band coherent VUV source for the Lyman-alpha region,” Opt. Commun. 31, 397–400 (1979).
    [CrossRef]
  10. R. Wallenstein, “Generation of narrowband tunable VUV radiation at the Lyman-α wavelength,” Opt. Commun. 33, 119–122 (1980).
    [CrossRef]
  11. G. Hilber, A. Lago, and R. Wallenstein, “Broadly tunable vacuum-ultraviolet/extreme-ultraviolet radiation generated by resonant third-order frequency conversion in krypton,” J. Opt. Soc. Am. B 4, 1753–1764 (1987).
    [CrossRef]
  12. J. P. Marangos, N. Shen, H. Ma, M. H. R. Hutchinson, and J. P. Connerade, “Broadly tunable vacuum-ultraviolet radiation source employing resonant enhanced sum-difference frequency mixing in krypton,” J. Opt. Soc. Am. B 7, 1254–1263 (1990).
    [CrossRef]
  13. K. S. E. Eikema, J. Walz, and T. W. Hänscḧ, “Continuous wave coherent Lyman-α radiation,” Phys. Rev. Lett. 83, 3828–3831 (1999).
    [CrossRef]
  14. M. Scheid, D. Kolbe, F. Markert, T. W. Hänsch, and J. Walz, “Continuous-wave Lyman-α generation with solid-state lasers,” Opt. Express 17, 11274–11280 (2009).
    [CrossRef]
  15. T. Nakajima, “A scheme to polarize nuclear-spin of atoms by a sequence of short laser pulses: application to the muonium,” Opt. Express 18, 27468–27480 (2010).
  16. J. T. Cusma and L. W. Anderson, “Polarization of an atomic sodium beam by laser optical pumping,” Phys. Rev. A 28, 1195–1197 (1983).
    [CrossRef]
  17. G. W. Schinn, X.-L. Han, and A. Gallagher, “Production and diagnosis of a highly spin-polarized Na beam,” J. Opt. Soc. Am. B 8, 169–173 (1991).
    [CrossRef]
  18. C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
    [CrossRef]
  19. G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
    [CrossRef]
  20. P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field-atom interaction,” J. Phys. B 12, L547–L551 (1979).
    [CrossRef]

2010 (1)

2009 (1)

2007 (2)

J. P. Miller, E. de Rafael, and B. L. Roberts, “Muon (g-2): experiment and theory,” Rep. Prog. Phys. 70, 795–881 (2007).
[CrossRef]

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

2004 (1)

P. Bakule and E. Morenzoni, “Generation and application of slow polarized muons,” Contemp. Phys. 45, 203–225(2004).
[CrossRef]

2003 (1)

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

1999 (1)

K. S. E. Eikema, J. Walz, and T. W. Hänscḧ, “Continuous wave coherent Lyman-α radiation,” Phys. Rev. Lett. 83, 3828–3831 (1999).
[CrossRef]

1997 (1)

P. Dalmas de Réotier and A. Yaouanc, “Muon spin rotation and relaxation in magnetic materials,” J. Phys. Condens. Matter 9, 9113–9166 (1997).
[CrossRef]

1992 (1)

D. Fick, G. Grawert, and I. M. Turkiewicz, “Nuclear physics with polarized heavy ions,” Phys. Rep. 214, 1–111 (1992).
[CrossRef]

1991 (1)

1990 (1)

1987 (2)

G. Hilber, A. Lago, and R. Wallenstein, “Broadly tunable vacuum-ultraviolet/extreme-ultraviolet radiation generated by resonant third-order frequency conversion in krypton,” J. Opt. Soc. Am. B 4, 1753–1764 (1987).
[CrossRef]

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

1983 (1)

J. T. Cusma and L. W. Anderson, “Polarization of an atomic sodium beam by laser optical pumping,” Phys. Rev. A 28, 1195–1197 (1983).
[CrossRef]

1980 (1)

R. Wallenstein, “Generation of narrowband tunable VUV radiation at the Lyman-α wavelength,” Opt. Commun. 33, 119–122 (1980).
[CrossRef]

1979 (2)

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field-atom interaction,” J. Phys. B 12, L547–L551 (1979).
[CrossRef]

D. Cotter, “Tunable narrow-band coherent VUV source for the Lyman-alpha region,” Opt. Commun. 31, 397–400 (1979).
[CrossRef]

1978 (1)

R. Mahon, T. J. McIlrath, and D. Koopman, “Nonlinear generation of Lyman-alpha radiation,” Appl. Phys. Lett. 33, 305–307 (1978).
[CrossRef]

1975 (1)

S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
[CrossRef]

Anderson, L. W.

J. T. Cusma and L. W. Anderson, “Polarization of an atomic sodium beam by laser optical pumping,” Phys. Rev. A 28, 1195–1197 (1983).
[CrossRef]

Avila, G.

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

Bakule, P.

P. Bakule and E. Morenzoni, “Generation and application of slow polarized muons,” Contemp. Phys. 45, 203–225(2004).
[CrossRef]

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

Behr, J. A.

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Candelier, V.

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

Cerez, P.

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

Cocolios, T. E.

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Connerade, J. P.

Cotter, D.

D. Cotter, “Tunable narrow-band coherent VUV source for the Lyman-alpha region,” Opt. Commun. 31, 397–400 (1979).
[CrossRef]

Cusma, J. T.

J. T. Cusma and L. W. Anderson, “Polarization of an atomic sodium beam by laser optical pumping,” Phys. Rev. A 28, 1195–1197 (1983).
[CrossRef]

de Clercq, E.

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

de Rafael, E.

J. P. Miller, E. de Rafael, and B. L. Roberts, “Muon (g-2): experiment and theory,” Rep. Prog. Phys. 70, 795–881 (2007).
[CrossRef]

de Réotier, P. Dalmas

P. Dalmas de Réotier and A. Yaouanc, “Muon spin rotation and relaxation in magnetic materials,” J. Phys. Condens. Matter 9, 9113–9166 (1997).
[CrossRef]

Eikema, K. S. E.

K. S. E. Eikema, J. Walz, and T. W. Hänscḧ, “Continuous wave coherent Lyman-α radiation,” Phys. Rev. Lett. 83, 3828–3831 (1999).
[CrossRef]

Fick, D.

D. Fick, G. Grawert, and I. M. Turkiewicz, “Nuclear physics with polarized heavy ions,” Phys. Rep. 214, 1–111 (1992).
[CrossRef]

Gallagher, A.

Giordano, V.

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

Grawert, G.

D. Fick, G. Grawert, and I. M. Turkiewicz, “Nuclear physics with polarized heavy ions,” Phys. Rep. 214, 1–111 (1992).
[CrossRef]

Han, X.-L.

Hänsch, T. W.

M. Scheid, D. Kolbe, F. Markert, T. W. Hänsch, and J. Walz, “Continuous-wave Lyman-α generation with solid-state lasers,” Opt. Express 17, 11274–11280 (2009).
[CrossRef]

K. S. E. Eikema, J. Walz, and T. W. Hänscḧ, “Continuous wave coherent Lyman-α radiation,” Phys. Rev. Lett. 83, 3828–3831 (1999).
[CrossRef]

Hashimoto, O.

S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
[CrossRef]

Hilber, G.

Hutchinson, M. H. R.

Jayamanna, K.

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Kolbe, D.

Koopman, D.

R. Mahon, T. J. McIlrath, and D. Koopman, “Nonlinear generation of Lyman-alpha radiation,” Appl. Phys. Lett. 33, 305–307 (1978).
[CrossRef]

Lago, A.

Lambropoulos, P.

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field-atom interaction,” J. Phys. B 12, L547–L551 (1979).
[CrossRef]

Levy, C. D. P.

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Ma, H.

Mahon, R.

R. Mahon, T. J. McIlrath, and D. Koopman, “Nonlinear generation of Lyman-alpha radiation,” Appl. Phys. Lett. 33, 305–307 (1978).
[CrossRef]

Makimura, S.

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

Marangos, J. P.

Markert, F.

Matsuda, Y.

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

McIlrath, T. J.

R. Mahon, T. J. McIlrath, and D. Koopman, “Nonlinear generation of Lyman-alpha radiation,” Appl. Phys. Lett. 33, 305–307 (1978).
[CrossRef]

Miller, J. P.

J. P. Miller, E. de Rafael, and B. L. Roberts, “Muon (g-2): experiment and theory,” Rep. Prog. Phys. 70, 795–881 (2007).
[CrossRef]

Minamisono, K.

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Miyake, Y.

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

Morenzoni, E.

P. Bakule and E. Morenzoni, “Generation and application of slow polarized muons,” Contemp. Phys. 45, 203–225(2004).
[CrossRef]

Nagamine, K.

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
[CrossRef]

Nagamiya, S.

S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
[CrossRef]

Nakajima, T.

Person, M. R.

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Roberts, B. L.

J. P. Miller, E. de Rafael, and B. L. Roberts, “Muon (g-2): experiment and theory,” Rep. Prog. Phys. 70, 795–881 (2007).
[CrossRef]

Scheid, M.

Schinn, G. W.

Shen, N.

Shimomura, K.

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

Straser, P.

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

Theobald, G.

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

Turkiewicz, I. M.

D. Fick, G. Grawert, and I. M. Turkiewicz, “Nuclear physics with polarized heavy ions,” Phys. Rep. 214, 1–111 (1992).
[CrossRef]

Wallenstein, R.

Walz, J.

M. Scheid, D. Kolbe, F. Markert, T. W. Hänsch, and J. Walz, “Continuous-wave Lyman-α generation with solid-state lasers,” Opt. Express 17, 11274–11280 (2009).
[CrossRef]

K. S. E. Eikema, J. Walz, and T. W. Hänscḧ, “Continuous wave coherent Lyman-α radiation,” Phys. Rev. Lett. 83, 3828–3831 (1999).
[CrossRef]

Yamazaki, T.

S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
[CrossRef]

Yaouanc, A.

P. Dalmas de Réotier and A. Yaouanc, “Muon spin rotation and relaxation in magnetic materials,” J. Phys. Condens. Matter 9, 9113–9166 (1997).
[CrossRef]

Zoller, P.

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field-atom interaction,” J. Phys. B 12, L547–L551 (1979).
[CrossRef]

Appl. Phys. Lett. (1)

R. Mahon, T. J. McIlrath, and D. Koopman, “Nonlinear generation of Lyman-alpha radiation,” Appl. Phys. Lett. 33, 305–307 (1978).
[CrossRef]

Contemp. Phys. (1)

P. Bakule and E. Morenzoni, “Generation and application of slow polarized muons,” Contemp. Phys. 45, 203–225(2004).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

P. Zoller and P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field-atom interaction,” J. Phys. B 12, L547–L551 (1979).
[CrossRef]

J. Phys. Condens. Matter (1)

P. Dalmas de Réotier and A. Yaouanc, “Muon spin rotation and relaxation in magnetic materials,” J. Phys. Condens. Matter 9, 9113–9166 (1997).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

C. D. P. Levy, T. E. Cocolios, J. A. Behr, K. Jayamanna, K. Minamisono, and M. R. Person, “Feasibility study of in-beam polarization of fluorine,” Nucl. Instrum. Methods Phys. Res. A 580, 1571–1577 (2007).
[CrossRef]

Opt. Commun. (2)

D. Cotter, “Tunable narrow-band coherent VUV source for the Lyman-alpha region,” Opt. Commun. 31, 397–400 (1979).
[CrossRef]

R. Wallenstein, “Generation of narrowband tunable VUV radiation at the Lyman-α wavelength,” Opt. Commun. 33, 119–122 (1980).
[CrossRef]

Opt. Express (2)

Phys. Rep. (1)

D. Fick, G. Grawert, and I. M. Turkiewicz, “Nuclear physics with polarized heavy ions,” Phys. Rep. 214, 1–111 (1992).
[CrossRef]

Phys. Rev. A (2)

G. Avila, V. Giordano, V. Candelier, E. de Clercq, G. Theobald, and P. Cerez, “State selection in a cesium beam by laser-diode optical pumping,” Phys. Rev. A 36, 3719–3728 (1987).
[CrossRef]

J. T. Cusma and L. W. Anderson, “Polarization of an atomic sodium beam by laser optical pumping,” Phys. Rev. A 28, 1195–1197 (1983).
[CrossRef]

Phys. Rev. Lett. (2)

S. Nagamiya, K. Nagamine, O. Hashimoto, and T. Yamazaki, “Negative-muon spin rotation at the oxygen site in paramagnetic MnO+,” Phys. Rev. Lett. 35, 308–311 (1975).
[CrossRef]

K. S. E. Eikema, J. Walz, and T. W. Hänscḧ, “Continuous wave coherent Lyman-α radiation,” Phys. Rev. Lett. 83, 3828–3831 (1999).
[CrossRef]

Rep. Prog. Phys. (1)

J. P. Miller, E. de Rafael, and B. L. Roberts, “Muon (g-2): experiment and theory,” Rep. Prog. Phys. 70, 795–881 (2007).
[CrossRef]

Spectrochim. Acta Part B (1)

P. Bakule, Y. Matsuda, Y. Miyake, P. Straser, K. Shimomura, S. Makimura, and K. Nagamine, “Slow muon experiment by laser resonant ionization method at RIKEN-RAL muon facility,” Spectrochim. Acta Part B 58, 1019–1030 (2003).
[CrossRef]

Other (1)

http://j-parc.jp/MatLife/en/index.html .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Level scheme considered in this paper where the muonium is initially 50% spin polarized. (b) Relevant states in terms of the uncoupled basis description. The curved arrow between |8 and |9 indicates hyperfine coupling, and the up/down arrows by the ket vectors represent the nuclear-spin orientations. Note that the numbering of the states is not sequential, to be consistent with the numbering of states in our previous work [15], where a set of density matrix equations have been derived.

Fig. 2.
Fig. 2.

Excited state population as a function of laser detuning by the 2 ns pulse with a 230 GHz bandwidth and transform-limited 2 ps laser pulse. Doppler broadening is not included in the calculations.

Fig. 3.
Fig. 3.

(a) Spin polarization as a function of laser detuning by the single 2 ns laser pulse at the intensities of 104 (lower curve), 105 (middle curve), and 106W/cm2 (upper curve). (b) Spin polarization as a function of intensity by the one (lower curve), two (middle curve), and four (upper curve) 2 ns laser pulses. The laser bandwidth is 230 GHz for all curves. In both panels (a) and (b), the thick and thin curves represent the results with and without 230 GHz Doppler broadening, and the dashed curves are the results obtained by solving the rate equations.

Fig. 4.
Fig. 4.

(a) Spin polarization as a function of laser detuning by the single 2 ps laser pulse at the intensities of 107 (middle curve), 5×107 (upper curve), and 108W/cm2 (lower curve). (b) Spin polarization as a function of intensity by the one (lower curve), two (middle curve), and four (upper curve) 2 ps laser pulses. The 2 ps pulses are transform limited for all curves. In panels (a) and (b), the thick and thin curves represent the results with and without 230 GHz Doppler broadening.

Fig. 5.
Fig. 5.

Comparison of spin-polarization efficiency by the 2 ns and 2 ps pulses. The results by the single, two, and four pulses with a duration of 2 ps (2 ns) with the time interval of 5 ns are shown by the solid (dashed) lower, middle, and upper curves, respectively.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

σ˙00=γsp(13σ77+16σ88+12σ99)k=7,8,9γΩ0k2Δk02+(γ/2)2(σ00σkk),
σ.66=γsp(13σ77+16σ88+12σ99)k=7,8,9γΩ6k2Δk62+(γ/2)2(σ66σkk),
σ.77=γspσ77+k=0,6γΩk72Δ7k2+(γ/2)2(σkkσ77),
σ.88=γspσ88+k=0,6γΩk82Δ8k2+(γ/2)2(σkkσ88)+2Ω89(H)2γsp(σ99σ88),
σ.99=γspσ99+k=0,6γΩk92Δ9k2+(γ/2)2(σkkσ99)2Ω89(H)2γsp(σ99σ88),
σ.1010=γsp(13σ77+23σ88+σ1111)γΩ11102Δ11102+(γ/2)2(σ1010σ1111),
σ.1111=γspσ1111+γΩ11102Δ11102+(γ/2)2(σ1010σ1111),
P=PupPdownPup+Pdown,
Pup=12σ00(t=)+12σ66(t=)+σ1010(t=),
Pdown=12σ00(t=)+12σ66(t=).

Metrics