Abstract

We investigate the coherent optical response of individual localized exciton–biexciton (XXX) systems formed at interface fluctuations of a growth-interrupted GaAs/AlAs quantum well. We apply heterodyne spectral interferometry to perform two-dimensional four-wave mixing (FWM) spectroscopy. We retrieve the binding energy of bound and unbound XXs, as well as characterize the system in terms of biexciton–exciton dipole moment ratio and mutual FWM phase. Polarization selection rules of the FWM are determined. FWM hyperspectral imaging and autocorrelation analysis reveal the expected spatial colocalization of XXs with respect to their Xs. A value for the biexciton renormalization in a coherently coupled pair of Xs is retrieved. Our study gives insight into the coherent optical properties of an exciton–biexciton system with a confinement energy comparable to the biexciton binding energy.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  27. J. Kasprzak and W. Langbein, “Vectorial four-wave mixing field dynamics from individual excitonic transitions,” Phys. Rev. B 78, 041103R (2008).
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  28. J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Stat. Sol. B 246, 820–823 (2009).
    [CrossRef]
  29. E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
    [CrossRef]
  30. G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
    [CrossRef]
  31. X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
    [CrossRef]
  32. P. Borri and W. Langbein, in Semiconductor Quantum Bits, F. Henneberger and O. Benson, eds. (Pan Stanford, 2009), pp. 269–320.
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    [CrossRef]
  36. A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
    [CrossRef]
  37. K. B. Ferrio and D. G. Steel, “Raman quantum beats of interacting excitons,” Phys. Rev. Lett. 80, 786–789 (1998).
    [CrossRef]
  38. X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
    [CrossRef]
  39. K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
    [CrossRef]
  40. Y. Sugimoto, T. Saiki, and S. Nomura, “Visualization of weak confinement potentials by near-field optical imaging spectroscopy of exciton and biexciton in a single quantum dot,” Appl. Phys. Lett. 93, 083116 (2008).
    [CrossRef]

2011

D. B. Turner, P. Wen, D. H. Arias, and K. A. Nelson, “Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy,” Phys. Rev. B 84, 165321 (2011).
[CrossRef]

J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photon. 5, 57–63 (2011).
[CrossRef]

2010

W. Langbein, “Coherent optical spectroscopy of semiconductor nanostructures,” Riv. Nuovo Cimento 33, 255–312(2010).

D. B. Turner and K. A. Nelson, “Coherent measurements of high-order electronic correlations in quantum wells,” Nature 466, 1089–1092 (2010).
[CrossRef]

D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

2009

K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
[CrossRef]

J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Stat. Sol. B 246, 820–823 (2009).
[CrossRef]

2008

J. Kasprzak and W. Langbein, “Vectorial four-wave mixing field dynamics from individual excitonic transitions,” Phys. Rev. B 78, 041103R (2008).
[CrossRef]

Y. Sugimoto, T. Saiki, and S. Nomura, “Visualization of weak confinement potentials by near-field optical imaging spectroscopy of exciton and biexciton in a single quantum dot,” Appl. Phys. Lett. 93, 083116 (2008).
[CrossRef]

2007

W. Langbein and B. Patton, “Transient coherent nonlinear spectroscopy of single quantum dots,” J. Phys. Condens. Matter 19, 295203 (2007).
[CrossRef]

2006

X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
[CrossRef]

V. Savona, and W. Langbein, “Realistic heterointerface model for excitonic states in growth-interrupted GaAs quantum wells,” Phys. Rev. B 74, 075311 (2006).
[CrossRef]

Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
[CrossRef]

W. Langbein and B. Patton, “Heterodyne spectral interferometry for multidimensional nonlinear spectroscopy of individual quantum systems,” Opt. Lett. 31, 1151–1153 (2006).
[CrossRef]

2005

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

W. Langbein, and B. Patton, “Microscopic measurement of photon echo formation in groups of individual excitonic transitions,” Phys. Rev. Lett. 95, 017403 (2005).
[CrossRef]

B. Patton, U. Woggon, and W. Langbein, “Coherent control and polarization readout of individual excitonic states,” Phys. Rev. Lett. 95, 266401 (2005).
[CrossRef]

2004

A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
[CrossRef]

X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
[CrossRef]

2003

K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
[CrossRef]

2002

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

W. Langbein and J. M. Hvam, “Biexcitonic bound and continuum states of homogeneously and inhomogeneously broadened exciton resonances,” Phys. Stat. Sol. A 190, 167–174 (2002).
[CrossRef]

2001

2000

S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
[CrossRef]

U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
[CrossRef]

W. Langbein and J. M. Hvam, “Dephasing in the quasi two-dimensional exciton-biexciton system,” Phys. Rev. B 61, 1692–1695 (2000).
[CrossRef]

K. Leosson, J. R. Jensen, W. Langbein, and J. M. Hvam, “Exciton localization and interface roughness in growth-interrupted GaAs/AlAs quantum wells,” Phys. Rev. B 61, 10322–10329 (2000).
[CrossRef]

1999

W. Langbein and J. M. Hvam, “Localization-enhanced biexciton binding in semiconductors,” Phys. Rev. B 59, 15405–15408 (1999).
[CrossRef]

1998

W. Langbein and J. M. Hvam, “Localized biexcitons in quasi-2D and quasi-3D systems,” Phys. Stat. Sol. B 206, 111–118 (1998).
[CrossRef]

K. B. Ferrio and D. G. Steel, “Raman quantum beats of interacting excitons,” Phys. Rev. Lett. 80, 786–789 (1998).
[CrossRef]

1997

W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
[CrossRef]

A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
[CrossRef]

1996

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

1995

1990

H. Akiyama, T. Kuga, M. Matsuoka, and M. Kuwata-Gonokami, “Radiative decay and phonon scattering of biexcitons in CuCl,” Phys. Rev. B 42, 5621–5625 (1990).
[CrossRef]

D. Gammon, B. V. Shanabrook, and D. S. Katzer, “Interfaces in GaAs/AlAs quantum well structures,” Appl. Phys. Lett. 57, 2710–2712 (1990).
[CrossRef]

1966

J. R. Haynes, “Experimental observation of the excitonic molecule,” Phys. Rev. Lett. 17, 860–862 (1966).
[CrossRef]

1958

M. A. Lampert, “Mobile and immobile effective-mass-particle complexes in nonmetallic solids,” Phys. Rev. Lett. 1, 450–453 (1958).
[CrossRef]

Akiyama, H.

H. Akiyama, T. Kuga, M. Matsuoka, and M. Kuwata-Gonokami, “Radiative decay and phonon scattering of biexcitons in CuCl,” Phys. Rev. B 42, 5621–5625 (1990).
[CrossRef]

Albrecht, T. F.

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Aoyagi, Y.

K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
[CrossRef]

Arias, D. H.

D. B. Turner, P. Wen, D. H. Arias, and K. A. Nelson, “Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy,” Phys. Rev. B 84, 165321 (2011).
[CrossRef]

Axt, V. M.

S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
[CrossRef]

Batteh, E. T.

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

Bolton, S. R.

S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
[CrossRef]

Bonitz, M.

A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
[CrossRef]

Borri, P.

P. Borri and W. Langbein, in Semiconductor Quantum Bits, F. Henneberger and O. Benson, eds. (Pan Stanford, 2009), pp. 269–320.

Bott, K.

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Bristow, A. D.

D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
[CrossRef]

Chemla, D. S.

S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
[CrossRef]

Chen, G.

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

Cheng, J.

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

Chériaux, G.

Cundiff, S. T.

D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
[CrossRef]

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Dai, X.

D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
[CrossRef]

Duan, L. M.

Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
[CrossRef]

Euteneuer, A.

A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
[CrossRef]

Feldmann, J.

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Ferrio, K. B.

K. B. Ferrio and D. G. Steel, “Raman quantum beats of interacting excitons,” Phys. Rev. Lett. 80, 786–789 (1998).
[CrossRef]

Filinov, A. V.

A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
[CrossRef]

Gammon, D.

X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
[CrossRef]

Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
[CrossRef]

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
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X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
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G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
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U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
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A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
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K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
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U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
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A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
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Hvam, J. M.

W. Langbein and J. M. Hvam, “Biexcitonic bound and continuum states of homogeneously and inhomogeneously broadened exciton resonances,” Phys. Stat. Sol. A 190, 167–174 (2002).
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K. Leosson, J. R. Jensen, W. Langbein, and J. M. Hvam, “Exciton localization and interface roughness in growth-interrupted GaAs/AlAs quantum wells,” Phys. Rev. B 61, 10322–10329 (2000).
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W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
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W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
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D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
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A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
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J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photon. 5, 57–63 (2011).
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J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Stat. Sol. B 246, 820–823 (2009).
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J. Kasprzak and W. Langbein, “Vectorial four-wave mixing field dynamics from individual excitonic transitions,” Phys. Rev. B 78, 041103R (2008).
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E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

D. Gammon, B. V. Shanabrook, and D. S. Katzer, “Interfaces in GaAs/AlAs quantum well structures,” Appl. Phys. Lett. 57, 2710–2712 (1990).
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U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
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T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
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Koch, S. W.

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
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H. Akiyama, T. Kuga, M. Matsuoka, and M. Kuwata-Gonokami, “Radiative decay and phonon scattering of biexcitons in CuCl,” Phys. Rev. B 42, 5621–5625 (1990).
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J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photon. 5, 57–63 (2011).
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J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Stat. Sol. B 246, 820–823 (2009).
[CrossRef]

J. Kasprzak and W. Langbein, “Vectorial four-wave mixing field dynamics from individual excitonic transitions,” Phys. Rev. B 78, 041103R (2008).
[CrossRef]

W. Langbein and B. Patton, “Transient coherent nonlinear spectroscopy of single quantum dots,” J. Phys. Condens. Matter 19, 295203 (2007).
[CrossRef]

V. Savona, and W. Langbein, “Realistic heterointerface model for excitonic states in growth-interrupted GaAs quantum wells,” Phys. Rev. B 74, 075311 (2006).
[CrossRef]

W. Langbein and B. Patton, “Heterodyne spectral interferometry for multidimensional nonlinear spectroscopy of individual quantum systems,” Opt. Lett. 31, 1151–1153 (2006).
[CrossRef]

W. Langbein, and B. Patton, “Microscopic measurement of photon echo formation in groups of individual excitonic transitions,” Phys. Rev. Lett. 95, 017403 (2005).
[CrossRef]

B. Patton, U. Woggon, and W. Langbein, “Coherent control and polarization readout of individual excitonic states,” Phys. Rev. Lett. 95, 266401 (2005).
[CrossRef]

W. Langbein and J. M. Hvam, “Biexcitonic bound and continuum states of homogeneously and inhomogeneously broadened exciton resonances,” Phys. Stat. Sol. A 190, 167–174 (2002).
[CrossRef]

W. Langbein, T. Meier, S. Koch, and J. Hvam, “Spectral signatures of χ(5) processes in four-wave mixing of homogeneously broadened excitons,” J. Opt. Soc. Am. B 18, 1318–1325 (2001).
[CrossRef]

U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
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K. Leosson, J. R. Jensen, W. Langbein, and J. M. Hvam, “Exciton localization and interface roughness in growth-interrupted GaAs/AlAs quantum wells,” Phys. Rev. B 61, 10322–10329 (2000).
[CrossRef]

W. Langbein and J. M. Hvam, “Dephasing in the quasi two-dimensional exciton-biexciton system,” Phys. Rev. B 61, 1692–1695 (2000).
[CrossRef]

W. Langbein and J. M. Hvam, “Localization-enhanced biexciton binding in semiconductors,” Phys. Rev. B 59, 15405–15408 (1999).
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[CrossRef]

W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
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K. Leosson, J. R. Jensen, W. Langbein, and J. M. Hvam, “Exciton localization and interface roughness in growth-interrupted GaAs/AlAs quantum wells,” Phys. Rev. B 61, 10322–10329 (2000).
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Li, X.

K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
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X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
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Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
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X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
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G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
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A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
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K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
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H. Akiyama, T. Kuga, M. Matsuoka, and M. Kuwata-Gonokami, “Radiative decay and phonon scattering of biexcitons in CuCl,” Phys. Rev. B 42, 5621–5625 (1990).
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A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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W. Langbein, T. Meier, S. Koch, and J. Hvam, “Spectral signatures of χ(5) processes in four-wave mixing of homogeneously broadened excitons,” J. Opt. Soc. Am. B 18, 1318–1325 (2001).
[CrossRef]

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
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K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
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D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
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A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
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Nair, S.

K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
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D. B. Turner, P. Wen, D. H. Arias, and K. A. Nelson, “Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy,” Phys. Rev. B 84, 165321 (2011).
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D. B. Turner and K. A. Nelson, “Coherent measurements of high-order electronic correlations in quantum wells,” Nature 466, 1089–1092 (2010).
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S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
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Nomura, S.

Y. Sugimoto, T. Saiki, and S. Nomura, “Visualization of weak confinement potentials by near-field optical imaging spectroscopy of exciton and biexciton in a single quantum dot,” Appl. Phys. Lett. 93, 083116 (2008).
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K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
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Park, D.

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

Patton, B.

J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photon. 5, 57–63 (2011).
[CrossRef]

W. Langbein and B. Patton, “Transient coherent nonlinear spectroscopy of single quantum dots,” J. Phys. Condens. Matter 19, 295203 (2007).
[CrossRef]

W. Langbein and B. Patton, “Heterodyne spectral interferometry for multidimensional nonlinear spectroscopy of individual quantum systems,” Opt. Lett. 31, 1151–1153 (2006).
[CrossRef]

W. Langbein, and B. Patton, “Microscopic measurement of photon echo formation in groups of individual excitonic transitions,” Phys. Rev. Lett. 95, 017403 (2005).
[CrossRef]

B. Patton, U. Woggon, and W. Langbein, “Coherent control and polarization readout of individual excitonic states,” Phys. Rev. Lett. 95, 266401 (2005).
[CrossRef]

Peeters, F. M.

A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
[CrossRef]

Rettig, R.

A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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Riva, C.

A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
[CrossRef]

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A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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Saiki, T.

Y. Sugimoto, T. Saiki, and S. Nomura, “Visualization of weak confinement potentials by near-field optical imaging spectroscopy of exciton and biexciton in a single quantum dot,” Appl. Phys. Lett. 93, 083116 (2008).
[CrossRef]

K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
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J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photon. 5, 57–63 (2011).
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V. Savona, and W. Langbein, “Realistic heterointerface model for excitonic states in growth-interrupted GaAs quantum wells,” Phys. Rev. B 74, 075311 (2006).
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T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Sham, L. J.

X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
[CrossRef]

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D. Gammon, B. V. Shanabrook, and D. S. Katzer, “Interfaces in GaAs/AlAs quantum well structures,” Appl. Phys. Lett. 57, 2710–2712 (1990).
[CrossRef]

Steel, D. G.

Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
[CrossRef]

X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
[CrossRef]

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
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G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
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Stolz, W.

A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
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T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Stone, K. W.

K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
[CrossRef]

Sugimoto, Y.

Y. Sugimoto, T. Saiki, and S. Nomura, “Visualization of weak confinement potentials by near-field optical imaging spectroscopy of exciton and biexciton in a single quantum dot,” Appl. Phys. Lett. 93, 083116 (2008).
[CrossRef]

Takagahara, T.

K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
[CrossRef]

Thomas, P.

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

Turner, D. B.

D. B. Turner, P. Wen, D. H. Arias, and K. A. Nelson, “Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy,” Phys. Rev. B 84, 165321 (2011).
[CrossRef]

D. B. Turner and K. A. Nelson, “Coherent measurements of high-order electronic correlations in quantum wells,” Nature 466, 1089–1092 (2010).
[CrossRef]

K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
[CrossRef]

Umlauff, M.

W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
[CrossRef]

Wen, P.

D. B. Turner, P. Wen, D. H. Arias, and K. A. Nelson, “Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy,” Phys. Rev. B 84, 165321 (2011).
[CrossRef]

Woggon, U.

B. Patton, U. Woggon, and W. Langbein, “Coherent control and polarization readout of individual excitonic states,” Phys. Rev. Lett. 95, 266401 (2005).
[CrossRef]

U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
[CrossRef]

Wu, Y.

X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
[CrossRef]

Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
[CrossRef]

X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
[CrossRef]

Xu, X.

X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
[CrossRef]

Yang, L.

D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

Appl. Phys. Lett.

D. Gammon, B. V. Shanabrook, and D. S. Katzer, “Interfaces in GaAs/AlAs quantum well structures,” Appl. Phys. Lett. 57, 2710–2712 (1990).
[CrossRef]

Y. Sugimoto, T. Saiki, and S. Nomura, “Visualization of weak confinement potentials by near-field optical imaging spectroscopy of exciton and biexciton in a single quantum dot,” Appl. Phys. Lett. 93, 083116 (2008).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Condens. Matter

W. Langbein and B. Patton, “Transient coherent nonlinear spectroscopy of single quantum dots,” J. Phys. Condens. Matter 19, 295203 (2007).
[CrossRef]

Nat. Photon.

J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photon. 5, 57–63 (2011).
[CrossRef]

Nature

D. B. Turner and K. A. Nelson, “Coherent measurements of high-order electronic correlations in quantum wells,” Nature 466, 1089–1092 (2010).
[CrossRef]

Opt. Lett.

Phys. Rev. B

K. Leosson, J. R. Jensen, W. Langbein, and J. M. Hvam, “Exciton localization and interface roughness in growth-interrupted GaAs/AlAs quantum wells,” Phys. Rev. B 61, 10322–10329 (2000).
[CrossRef]

V. Savona, and W. Langbein, “Realistic heterointerface model for excitonic states in growth-interrupted GaAs quantum wells,” Phys. Rev. B 74, 075311 (2006).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, “Polarization dependence of semiconductor exciton and biexciton contributions to phase-resolved optical two-dimensional Fourier-transform spectra,” Phys. Rev. B 79, 161305 (2009).
[CrossRef]

D. B. Turner, P. Wen, D. H. Arias, and K. A. Nelson, “Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy,” Phys. Rev. B 84, 165321 (2011).
[CrossRef]

H. Akiyama, T. Kuga, M. Matsuoka, and M. Kuwata-Gonokami, “Radiative decay and phonon scattering of biexcitons in CuCl,” Phys. Rev. B 42, 5621–5625 (1990).
[CrossRef]

U. Woggon, K. Hild, F. Gindele, W. Langbein, M. Hetterich, M. Grün, and C. Klingshirn, “Huge binding energy of localized biexcitons in CdS/ZnS quantum structures,” Phys. Rev. B 61, 12632–12635 (2000).
[CrossRef]

T. F. Albrecht, K. Bott, T. Meier, A. Schulze, M. Koch, S. T. Cundiff, J. Feldmann, W. Stolz, P. Thomas, S. W. Koch, and E. O. Göbel, “Disorder mediated biexcitonic beats in semiconductor quantum wells,” Phys. Rev. B 54, 4436–4439 (1996).
[CrossRef]

A. Euteneuer, J. Möbius, R. Rettig, E. J. Mayer, M. Hofmann, W. Stolz, E. O. Göbel, and W. W. Rühle, “Biexcitonic binding energies in the transition regime from three- to two-dimensional semiconductors,” Phys. Rev. B 56, R10028–R10031 (1997).
[CrossRef]

W. Langbein and J. M. Hvam, “Localization-enhanced biexciton binding in semiconductors,” Phys. Rev. B 59, 15405–15408 (1999).
[CrossRef]

W. Langbein and J. M. Hvam, “Dephasing in the quasi two-dimensional exciton-biexciton system,” Phys. Rev. B 61, 1692–1695 (2000).
[CrossRef]

J. Kasprzak and W. Langbein, “Vectorial four-wave mixing field dynamics from individual excitonic transitions,” Phys. Rev. B 78, 041103R (2008).
[CrossRef]

E. T. Batteh, J. Cheng, G. Chen, D. G. Steel, D. Gammon, D. S. Katzer, and D. Park, “Coherent nonlinear optical spectroscopy of fluctuation quantum dots: evidence for coupling between quantum dots,” Phys. Rev. B 71, 155327 (2005).
[CrossRef]

X. Li, Y. Wu, X. Xu, D. G. Steel, and D. Gammon, “Transient nonlinear optical spectroscopy studies involving biexciton coherence in single quantum dots,” Phys. Rev. B 73, 153304 (2006).
[CrossRef]

W. Langbein, J. M. Hvam, M. Umlauff, H. Kalt, B. Jobst, and D. Hommel, “Binding-energy distribution and dephasing of localized biexcitons,” Phys. Rev. B 55, R7383–R7386(1997).
[CrossRef]

A. V. Filinov, C. Riva, F. M. Peeters, Y. E. Lozovik, and M. Bonitz, “Influence of well-width fluctuations on the binding energy of excitons, charged excitons and biexcitons in GaAs-based quantum wells,” Phys. Rev. B 70, 035323 (2004).
[CrossRef]

X. Li, Y. Wu, D. G. Steel, D. Gammon, and L. J. Sham, “Raman coherence beats from the entangled state involving polarized excitons in single quantum dots,” Phys. Rev. B 70, 195330 (2004).
[CrossRef]

Phys. Rev. Lett.

K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, and T. Takagahara, “Near-field optical mapping of exciton wave functions in a GaAs quantum dot,” Phys. Rev. Lett. 91, 177401 (2003).
[CrossRef]

K. B. Ferrio and D. G. Steel, “Raman quantum beats of interacting excitons,” Phys. Rev. Lett. 80, 786–789 (1998).
[CrossRef]

G. Chen, T. H. Stievater, E. T. Batteh, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, and L. J. Sham, “Biexciton quantum coherence in a single quantum dot,” Phys. Rev. Lett. 88, 117901 (2002).
[CrossRef]

W. Langbein, and B. Patton, “Microscopic measurement of photon echo formation in groups of individual excitonic transitions,” Phys. Rev. Lett. 95, 017403 (2005).
[CrossRef]

B. Patton, U. Woggon, and W. Langbein, “Coherent control and polarization readout of individual excitonic states,” Phys. Rev. Lett. 95, 266401 (2005).
[CrossRef]

Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, “Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot,” Phys. Rev. Lett. 96, 087402 (2006).
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M. A. Lampert, “Mobile and immobile effective-mass-particle complexes in nonmetallic solids,” Phys. Rev. Lett. 1, 450–453 (1958).
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J. R. Haynes, “Experimental observation of the excitonic molecule,” Phys. Rev. Lett. 17, 860–862 (1966).
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D. Karaiskaj, A. D. Bristow, L. Yang, X. Dai, R. P. Mirin, S. Mukamel, and S. T. Cundiff, “Two-quantum many-body coherences in two-dimensional Fourier-transform spectra of exciton resonances in semiconductor quantum wells,” Phys. Rev. Lett. 104, 117401 (2010).
[CrossRef]

S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000).
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Phys. Stat. Sol. A

W. Langbein and J. M. Hvam, “Biexcitonic bound and continuum states of homogeneously and inhomogeneously broadened exciton resonances,” Phys. Stat. Sol. A 190, 167–174 (2002).
[CrossRef]

Phys. Stat. Sol. B

W. Langbein and J. M. Hvam, “Localized biexcitons in quasi-2D and quasi-3D systems,” Phys. Stat. Sol. B 206, 111–118 (1998).
[CrossRef]

J. Kasprzak and W. Langbein, “Four-wave mixing from individual excitons: Intensity dependence and imaging,” Phys. Stat. Sol. B 246, 820–823 (2009).
[CrossRef]

Riv. Nuovo Cimento

W. Langbein, “Coherent optical spectroscopy of semiconductor nanostructures,” Riv. Nuovo Cimento 33, 255–312(2010).

Science

K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324, 1169–1173 (2009).
[CrossRef]

Other

P. Borri and W. Langbein, in Semiconductor Quantum Bits, F. Henneberger and O. Benson, eds. (Pan Stanford, 2009), pp. 269–320.

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Figures (5)

Fig. 1.
Fig. 1.

(a), (b) Two-dimensional FWM |R1,2(ω3,ω1)|2 showing individual Xs along with their corresponding (a) bound (XX) and (b) unbound (XX*) biexcitons. FWM phase shifts of π between X and XX are observed (yellow traces). In (a), logarithmic color scale over five and three orders of magnitude for ω3>1.691eV and ω3<1.691eV (see vertical, dashed line), respectively. Magnification by a factor of 100 for ω3<1.691eV was applied to visualize XXs. In (b), logarithmic color scale over three orders of magnitude. c) Statistics of XXs’ binding energy (black dots) and dipole moment ratio μXX/μX (green circles), d) statistics of XX*s’ binding energy (black triangles). Its negative value should be understood as a repulsion energy of a two-particle state.

Fig. 2.
Fig. 2.

Polarization dependence and selection rules in the FWM of an individual 0XXX system weakly localized on a monolayer fluctuation of a 5 nm GaAs/AlGaAs QW. (a) (σ+,σ+,) polarization configuration, τ=+1ps. For negative delays no FWM is observed within the noise. The spectral amplitude of the excitation fields is given by the green dashed curve. (b) (,,) polarization configuration producing FWM on both 0X and XXX transitions, for τ=+1ps and τ=1ps. (c) (,,) configuration. For τ=+1ps, FWM is observed at the XXX transition. The amplitude range in (a), (b) is three times bigger than in (c).

Fig. 3.
Fig. 3.

(a) FWM intensity |R1,2(ω3)|2 (black) and phase arg[R1,2(ω3)] (green) of an individual 0XXX system. FWM imaging at τ=0.1ps (b) at the 0X transition energy, |R1,2(x,y,1695.2meV)|, and (c) at the XXX transition energy, |R1,2(x,y,1690.17meV)|. The white cross indicates the X position at (x,y)=(2.5,1.5)μm. (d) FWM intensity |R1,2(ω3)|2 (black) and phase arg[R1,2(ω3)] (green) showing an XXX doublet arising from the same X. (e) Same as (b) at 0X transition energy ω3=1694.3meV; (f), (g) same as (c) at XXX transition energies ω3=(1689.29,1689.45)meV. The white cross indicates the X position at (x,y)=(1.9,1.1)μm. Linear color scale from 0 to (0.3, 0.9, 10, 1, 1) arbitrary units in (b), (c), (e), (f), (g), respectively.

Fig. 4.
Fig. 4.

FWM hyperspectral background-corrected autocorrelation, ΔC¯(Δω3). Analysis performed on (a) a 5 nm and (b) a 7 nm GaAs/AlGaAs disordered QW. Blue shaded regions indicate measured XX binding energies of (4.9±0.2)meV (a) and (3.5±0.9)meV (b).

Fig. 5.
Fig. 5.

Retrieval of biexcitonic renormalization δ providing coherent coupling between individual Xs in a 5 nm QW. (a) |R1,2(ω3,ω1)|2 revealing coherently coupled Xs at ω3=1688.37meV and ω3=1691.16meV. Logarithmic color scale over 4.5 orders of magnitude. (b) FWM field R1,2(ω3,ω1) in real and imaginary parts at ω1=1691.16meV (along the yellow arrow). The X resonance at ω3=1691.16meV is fitted by a single complex Lorentzian (red traces). (c) Same as (b), but at ω1=1688.37meV (along the orange arrow). The off-diagonal signal is modeled (red traces) with a double complex Lorentzian of the 0X and XXX transitions (see text), yielding δ=(314i)μeV.

Equations (4)

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

μXXμX=2PXAXXγXXPXXAXγX,
C(Δx,Δy,Δω3)=|R1,2(x+Δx,y+Δy,ω3+Δω3)||R1,2(x,y,ω3)|x,y,ω3|R1,2(x,y,ω3)|x,y,ω32.
LX(ω)=AXexp(iφ)iγX+(ωωX),
Loff(ω)=AXexp(iφ)iγX+(ωωX)AXXexp(iφ)iγXX+(ωωXX),

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