Abstract

Pump-probe quantum state tomography was applied to the transmission of a coherent state through an In(Ga)As based quantum dot optical amplifier during the interaction with an optical pump pulse. The Wigner function and the statistical moments of the field were extracted and used to determine the degree of population inversion and the signal-to-noise ratio in a sub-picosecond time window.

© 2014 Optical Society of America

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References

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  1. P. Bhattacharya, S. Ghosh, and A. D. Stiff-Roberts, “Quantum dot opto-electronic devices,” Annu. Rev. Mater. Res. 34, 1–40 (2004).
    [Crossref]
  2. T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18 (4), 564–575 (1982).
    [Crossref]
  3. M. Shtaif and G. Eisenstein, “Noise properties of nonlinear semiconductor optical amplifiers,” Opt. Lett. 21 (22), 1851–1853 (1996).
    [Crossref] [PubMed]
  4. M. Shtaif and G. Eisenstein, “Experimental study of the statistical properties of nonlinearly amplified signals in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9 (7), 904–906 (1997).
    [Crossref]
  5. M. J. Munroe, J. Cooper, and M. G. Raymer, “Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier,” IEEE J. Quantum Electron. 34 (3), 548–551 (1998).
    [Crossref]
  6. M. Yamada, “Analysis of intensity and frequency noises in semiconductor optical amplifier,” IEEE J. Quantum Electron. 48 (8), 980–990 (2012).
    [Crossref]
  7. A. Bilenca and G. Eisenstein, “On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: The impact of inhomogeneously broadened gain and fast carrier dynamics,” IEEE J. Quantum Electron. 40 (6), 690–702 (2004).
    [Crossref]
  8. S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
    [Crossref]
  9. M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
    [Crossref] [PubMed]
  10. O. Karni, A. Capua, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Rabi oscillations and self-induced transparency in InAs/InP quantum dot semiconductor amplifier operating at room temperature,” Opt. Express 21 (22), 26786–26796 (2013).
    [Crossref] [PubMed]
  11. M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84 (6), 063840 (2011).
    [Crossref]
  12. M. Blazek, S. Hartman, A. Molitor, and W. Elsäßer, “Unifying intensity noise and second-order coherence properties of amplified spontaneous emission sources,” Opt. Lett. 36 (17), 3455–3457 (2011).
    [Crossref] [PubMed]
  13. S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor-laser,” Phys. Rev. Lett. 58 (10), 1000–1003 (1987).
    [Crossref] [PubMed]
  14. D. F. McAlister and M. G. Raymer, “Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection,” Phys. Rev. A 55 (3), R1609–R1612 (1997).
    [Crossref]
  15. M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
    [Crossref] [PubMed]
  16. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
    [Crossref] [PubMed]
  17. A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. of Mod. Phys. 81 (1), 299–332 (2009).
    [Crossref]
  18. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26 (8), 1817–1839 (1982).
    [Crossref]
  19. J. R. Jeffers, N. Imoto, and R. Loudon, “Quantum optics of traveling-wave attenuators and amplifiers,” Phys. Rev. A 47 (4), 3346–3359 (1993).
    [Crossref] [PubMed]
  20. K. Inoue, “Quantum mechanical treatment of optical amplifiers based on population inversion,” IEEE J. Quantum Electron. 50 (7), 563–567 (2014).
    [Crossref]
  21. N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
    [Crossref]
  22. S. Machida and Y. Yamamoto, “Quantum-Limited Operation of balanced mixer homodyne and heterodyne receivers,” IEEE J. Quantum Electron. 22 (5), 617–624 (1986).
    [Crossref]
  23. E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
    [Crossref]

2014 (2)

K. Inoue, “Quantum mechanical treatment of optical amplifiers based on population inversion,” IEEE J. Quantum Electron. 50 (7), 563–567 (2014).
[Crossref]

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

2013 (3)

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

O. Karni, A. Capua, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Rabi oscillations and self-induced transparency in InAs/InP quantum dot semiconductor amplifier operating at room temperature,” Opt. Express 21 (22), 26786–26796 (2013).
[Crossref] [PubMed]

2012 (1)

M. Yamada, “Analysis of intensity and frequency noises in semiconductor optical amplifier,” IEEE J. Quantum Electron. 48 (8), 980–990 (2012).
[Crossref]

2011 (2)

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84 (6), 063840 (2011).
[Crossref]

M. Blazek, S. Hartman, A. Molitor, and W. Elsäßer, “Unifying intensity noise and second-order coherence properties of amplified spontaneous emission sources,” Opt. Lett. 36 (17), 3455–3457 (2011).
[Crossref] [PubMed]

2010 (1)

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

2009 (1)

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. of Mod. Phys. 81 (1), 299–332 (2009).
[Crossref]

2004 (2)

A. Bilenca and G. Eisenstein, “On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: The impact of inhomogeneously broadened gain and fast carrier dynamics,” IEEE J. Quantum Electron. 40 (6), 690–702 (2004).
[Crossref]

P. Bhattacharya, S. Ghosh, and A. D. Stiff-Roberts, “Quantum dot opto-electronic devices,” Annu. Rev. Mater. Res. 34, 1–40 (2004).
[Crossref]

1998 (1)

M. J. Munroe, J. Cooper, and M. G. Raymer, “Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier,” IEEE J. Quantum Electron. 34 (3), 548–551 (1998).
[Crossref]

1997 (2)

M. Shtaif and G. Eisenstein, “Experimental study of the statistical properties of nonlinearly amplified signals in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9 (7), 904–906 (1997).
[Crossref]

D. F. McAlister and M. G. Raymer, “Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection,” Phys. Rev. A 55 (3), R1609–R1612 (1997).
[Crossref]

1996 (1)

1995 (1)

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
[Crossref] [PubMed]

1993 (2)

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
[Crossref] [PubMed]

J. R. Jeffers, N. Imoto, and R. Loudon, “Quantum optics of traveling-wave attenuators and amplifiers,” Phys. Rev. A 47 (4), 3346–3359 (1993).
[Crossref] [PubMed]

1987 (1)

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor-laser,” Phys. Rev. Lett. 58 (10), 1000–1003 (1987).
[Crossref] [PubMed]

1986 (1)

S. Machida and Y. Yamamoto, “Quantum-Limited Operation of balanced mixer homodyne and heterodyne receivers,” IEEE J. Quantum Electron. 22 (5), 617–624 (1986).
[Crossref]

1982 (2)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26 (8), 1817–1839 (1982).
[Crossref]

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18 (4), 564–575 (1982).
[Crossref]

Anderson, M. E.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
[Crossref] [PubMed]

Beck, M.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
[Crossref] [PubMed]

Bhattacharya, P.

P. Bhattacharya, S. Ghosh, and A. D. Stiff-Roberts, “Quantum dot opto-electronic devices,” Annu. Rev. Mater. Res. 34, 1–40 (2004).
[Crossref]

Bilenca, A.

A. Bilenca and G. Eisenstein, “On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: The impact of inhomogeneously broadened gain and fast carrier dynamics,” IEEE J. Quantum Electron. 40 (6), 690–702 (2004).
[Crossref]

Bimberg, D.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Blazek, M.

M. Blazek, S. Hartman, A. Molitor, and W. Elsäßer, “Unifying intensity noise and second-order coherence properties of amplified spontaneous emission sources,” Opt. Lett. 36 (17), 3455–3457 (2011).
[Crossref] [PubMed]

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84 (6), 063840 (2011).
[Crossref]

Boggavarapu, D.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
[Crossref] [PubMed]

Capua, A.

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26 (8), 1817–1839 (1982).
[Crossref]

Cooper, J.

M. J. Munroe, J. Cooper, and M. G. Raymer, “Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier,” IEEE J. Quantum Electron. 34 (3), 548–551 (1998).
[Crossref]

Eisenstein, G.

O. Karni, A. Capua, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Rabi oscillations and self-induced transparency in InAs/InP quantum dot semiconductor amplifier operating at room temperature,” Opt. Express 21 (22), 26786–26796 (2013).
[Crossref] [PubMed]

A. Bilenca and G. Eisenstein, “On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: The impact of inhomogeneously broadened gain and fast carrier dynamics,” IEEE J. Quantum Electron. 40 (6), 690–702 (2004).
[Crossref]

M. Shtaif and G. Eisenstein, “Experimental study of the statistical properties of nonlinearly amplified signals in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9 (7), 904–906 (1997).
[Crossref]

M. Shtaif and G. Eisenstein, “Noise properties of nonlinear semiconductor optical amplifiers,” Opt. Lett. 21 (22), 1851–1853 (1996).
[Crossref] [PubMed]

Elsäßer, W.

M. Blazek, S. Hartman, A. Molitor, and W. Elsäßer, “Unifying intensity noise and second-order coherence properties of amplified spontaneous emission sources,” Opt. Lett. 36 (17), 3455–3457 (2011).
[Crossref] [PubMed]

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84 (6), 063840 (2011).
[Crossref]

Faridani, A.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
[Crossref] [PubMed]

Ghosh, S.

P. Bhattacharya, S. Ghosh, and A. D. Stiff-Roberts, “Quantum dot opto-electronic devices,” Annu. Rev. Mater. Res. 34, 1–40 (2004).
[Crossref]

Gomis-Bresco, J.

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

Grosse, N. B.

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

Hartman, S.

Hartmann, G.

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

Imoto, N.

J. R. Jeffers, N. Imoto, and R. Loudon, “Quantum optics of traveling-wave attenuators and amplifiers,” Phys. Rev. A 47 (4), 3346–3359 (1993).
[Crossref] [PubMed]

Inoue, K.

K. Inoue, “Quantum mechanical treatment of optical amplifiers based on population inversion,” IEEE J. Quantum Electron. 50 (7), 563–567 (2014).
[Crossref]

Itaya, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor-laser,” Phys. Rev. Lett. 58 (10), 1000–1003 (1987).
[Crossref] [PubMed]

Ivanov, V.

Jeffers, J. R.

J. R. Jeffers, N. Imoto, and R. Loudon, “Quantum optics of traveling-wave attenuators and amplifiers,” Phys. Rev. A 47 (4), 3346–3359 (1993).
[Crossref] [PubMed]

Kaptan, Y.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Kaptan, Y. I.

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

Karni, O.

Knorr, A.

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

Kolarczik, M.

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Korn, J.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

Lingnau, B.

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Loudon, R.

J. R. Jeffers, N. Imoto, and R. Loudon, “Quantum optics of traveling-wave attenuators and amplifiers,” Phys. Rev. A 47 (4), 3346–3359 (1993).
[Crossref] [PubMed]

Lüdge, K.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

Lvovsky, A. I.

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. of Mod. Phys. 81 (1), 299–332 (2009).
[Crossref]

Machida, S.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor-laser,” Phys. Rev. Lett. 58 (10), 1000–1003 (1987).
[Crossref] [PubMed]

S. Machida and Y. Yamamoto, “Quantum-Limited Operation of balanced mixer homodyne and heterodyne receivers,” IEEE J. Quantum Electron. 22 (5), 617–624 (1986).
[Crossref]

Malic, E.

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

McAlister, D. F.

D. F. McAlister and M. G. Raymer, “Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection,” Phys. Rev. A 55 (3), R1609–R1612 (1997).
[Crossref]

Molitor, A.

Mukai, T.

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18 (4), 564–575 (1982).
[Crossref]

Munroe, M.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
[Crossref] [PubMed]

Munroe, M. J.

M. J. Munroe, J. Cooper, and M. G. Raymer, “Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier,” IEEE J. Quantum Electron. 34 (3), 548–551 (1998).
[Crossref]

Owschimikow, N.

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Raymer, M. G.

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. of Mod. Phys. 81 (1), 299–332 (2009).
[Crossref]

M. J. Munroe, J. Cooper, and M. G. Raymer, “Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier,” IEEE J. Quantum Electron. 34 (3), 548–551 (1998).
[Crossref]

D. F. McAlister and M. G. Raymer, “Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection,” Phys. Rev. A 55 (3), R1609–R1612 (1997).
[Crossref]

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
[Crossref] [PubMed]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
[Crossref] [PubMed]

Reithmaier, J. P.

Richter, M.

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

Schöll, E.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

Shtaif, M.

M. Shtaif and G. Eisenstein, “Experimental study of the statistical properties of nonlinearly amplified signals in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9 (7), 904–906 (1997).
[Crossref]

M. Shtaif and G. Eisenstein, “Noise properties of nonlinear semiconductor optical amplifiers,” Opt. Lett. 21 (22), 1851–1853 (1996).
[Crossref] [PubMed]

Sichkovskyi, V.

Smithey, D. T.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
[Crossref] [PubMed]

Stiff-Roberts, A. D.

P. Bhattacharya, S. Ghosh, and A. D. Stiff-Roberts, “Quantum dot opto-electronic devices,” Annu. Rev. Mater. Res. 34, 1–40 (2004).
[Crossref]

Wilkinson, S.

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

Woggon, U.

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

Yamada, M.

M. Yamada, “Analysis of intensity and frequency noises in semiconductor optical amplifier,” IEEE J. Quantum Electron. 48 (8), 980–990 (2012).
[Crossref]

Yamamoto, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor-laser,” Phys. Rev. Lett. 58 (10), 1000–1003 (1987).
[Crossref] [PubMed]

S. Machida and Y. Yamamoto, “Quantum-Limited Operation of balanced mixer homodyne and heterodyne receivers,” IEEE J. Quantum Electron. 22 (5), 617–624 (1986).
[Crossref]

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18 (4), 564–575 (1982).
[Crossref]

Annu. Rev. Mater. Res. (1)

P. Bhattacharya, S. Ghosh, and A. D. Stiff-Roberts, “Quantum dot opto-electronic devices,” Annu. Rev. Mater. Res. 34, 1–40 (2004).
[Crossref]

Appl. Phys. Lett. (1)

N. Owschimikow, M. Kolarczik, Y. I. Kaptan, N. B. Grosse, and U. Woggon, “Crossed excitons in a semiconductor nanostructure of mixed dimensionality,” Appl. Phys. Lett. 105 (10), 101108 (2014).
[Crossref]

IEEE J. Quantum Electron. (6)

S. Machida and Y. Yamamoto, “Quantum-Limited Operation of balanced mixer homodyne and heterodyne receivers,” IEEE J. Quantum Electron. 22 (5), 617–624 (1986).
[Crossref]

T. Mukai and Y. Yamamoto, “Noise in an AlGaAs semiconductor laser amplifier,” IEEE J. Quantum Electron. 18 (4), 564–575 (1982).
[Crossref]

M. J. Munroe, J. Cooper, and M. G. Raymer, “Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier,” IEEE J. Quantum Electron. 34 (3), 548–551 (1998).
[Crossref]

M. Yamada, “Analysis of intensity and frequency noises in semiconductor optical amplifier,” IEEE J. Quantum Electron. 48 (8), 980–990 (2012).
[Crossref]

A. Bilenca and G. Eisenstein, “On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: The impact of inhomogeneously broadened gain and fast carrier dynamics,” IEEE J. Quantum Electron. 40 (6), 690–702 (2004).
[Crossref]

K. Inoue, “Quantum mechanical treatment of optical amplifiers based on population inversion,” IEEE J. Quantum Electron. 50 (7), 563–567 (2014).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Wilkinson, B. Lingnau, J. Korn, E. Schöll, and K. Lüdge, “Influence of noise on the signal properties of quantum-dot semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 19 (4), 1900106 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Shtaif and G. Eisenstein, “Experimental study of the statistical properties of nonlinearly amplified signals in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9 (7), 904–906 (1997).
[Crossref]

Nat. Commun. (1)

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Schöll, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

New J. Phys. (1)

E. Malic, M. Richter, G. Hartmann, J. Gomis-Bresco, U. Woggon, and A. Knorr, “Analytical description of gain depletion and recovery in quantum dot optical amplifiers,” New J. Phys. 12, 063012 (2010).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (4)

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84 (6), 063840 (2011).
[Crossref]

J. R. Jeffers, N. Imoto, and R. Loudon, “Quantum optics of traveling-wave attenuators and amplifiers,” Phys. Rev. A 47 (4), 3346–3359 (1993).
[Crossref] [PubMed]

D. F. McAlister and M. G. Raymer, “Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection,” Phys. Rev. A 55 (3), R1609–R1612 (1997).
[Crossref]

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52 (2), R924–R927 (1995).
[Crossref] [PubMed]

Phys. Rev. D (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26 (8), 1817–1839 (1982).
[Crossref]

Phys. Rev. Lett. (2)

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70 (9), 1244–1247 (1993).
[Crossref] [PubMed]

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor-laser,” Phys. Rev. Lett. 58 (10), 1000–1003 (1987).
[Crossref] [PubMed]

Rev. of Mod. Phys. (1)

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. of Mod. Phys. 81 (1), 299–332 (2009).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 (a) Experimental setup. (b) Spectra of ASE from the QD SOA for various injection currents (given in mA). (c) Example of marginal probablity distribution data. This distribution has been used to reconstruct the Wigner function of the state shown in Fig. 2(e).
Fig. 2
Fig. 2 Wigner functions W obtained via quantum state tomography. Color-coded probability density distribution with black contour drawn at max ( W ) / e. (a) Detector/instrument noise. (b) Vacuum state for calibration. (c) Thermal state from ASE with SOA driven at 50 mA. (d) Input probe state measured via a bypass path. (e) Amplified probe state that exits the SOA (without pump). (f) Amplified probe state (QD GS) under the influence of the QD ES pump with the delay varied.
Fig. 3
Fig. 3 Amplitude quadrature in the Wigner function as a function of pump delay (black circles), including reference measurements without pump (red crosses). Quadrature amplitude (a) and variance (b) of the emitted probe state. (c) Variance of ASE alone. (d) Calculated intensity gain. (e) Population inversion derived from amplitude and variance. The blue lines are a fitted impulse response (τ=0.35 ps) (dashed) and its convolution with the experimental resolution (τ=0.27 ps) (solid).

Equations (5)

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W ( X + , X ) = 1 π d X X + + X | ρ ^ | X + X e 2 i X X ,
P θ ( X ^ θ ) = d X ^ θ + π 2 W ( X ^ θ cos θ X ^ θ + π 2 sin θ , X ^ θ sin θ + X ^ θ + π 2 cos θ ) .
μ ( X ^ out ± ) = G μ ( X ^ in ± ) ,
σ 2 ( X ^ out ± ) = G σ 2 ( X ^ in ± ) + ( G 1 ) ( 2 N 2 / ( N 2 N 1 ) 1 ) .
R = μ 2 ( X ^ out + ) [ σ 2 ( X ^ out + ) 1 ] μ 2 ( X ^ in + ) [ σ 2 ( X ^ out + ) 1 ] 2 [ μ 2 ( X ^ out + ) σ 2 ( X ^ in + ) μ 2 ( X ^ in + ) σ 2 ( X ^ out + ) ] .

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