Abstract

Optical two-dimensional Fourier transform (2DFT) spectroscopy has been developed over the last decade as a powerful tool for studying a variety of physical systems, ranging from atoms to molecules to solids. This review covers our use of 2DFT spectroscopy to study exciton dynamics in semiconductor nanostructures. In quantum wells, 2DFT spectroscopy confirms the importance of many-body contributions to the coherent optical response and reveals nonradiative double-quantum and Raman coherences. For natural quantum dots, 2DFT spectroscopy enables ensemble measurements of the homogeneous linewidth, including the temperature and density dependence. Relaxation from quantum well states into the quantum dots can also be studied using 2DFT spectroscopy.

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2011 (4)

A. D. Bristow, T. Zhang, M. E. Siemens, S. T. Cundiff, and R. P. Mirin, “Separating homogeneous and inhomogeneous line widths of heavy- and light-hole excitons in weakly disordered semiconductor quantum wells,” J. Phys. Chem. B 115, 5365–5371 (2011).
[CrossRef]

G. Moody, M. E. Siemens, A. D. Bristow, X. Dai, D. Karaiskaj, A. S. Bracker, D. Gammon, and S. T. Cundiff, “Exciton-exciton and exciton-phonon interactions in an interfacial GaAs quantum dot ensemble,” Phys. Rev. B 83, 115324 (2011).
[CrossRef]

G. Moody, M. E. Siemens, A. D. Bristow, X. Dai, A. S. Bracker, D. Gammon, and S. T. Cundiff, “Exciton relaxation and coupling dynamics in a GaAs/AlxGa1−xAs quantum well and quantum dot ensemble,” Phys. Rev. B 83, 245316 (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 (3)

I. Kuznetsova, N. Gogh, J. Foerstner, T. Meier, S. T. Cundiff, I. Varga, and P. Thomas, “Modeling excitonic line shapes in weakly disordered semiconductor nanostructures,” Phys. Rev. B 81 (2010).
[CrossRef]

M. E. Siemens, G. Moody, H. Li, A. D. Bristow, and S. T. Cundiff, “Resonance lineshapes in two-dimensional Fourier transform spectroscopy,” Opt. Express 18, 17699–17708 (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 (4)

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]

A. D. Bristow, D. Karaiskaj, X. Dai, T. Zhang, C. Carlsson, K. R. Hagen, R. Jimenez, and S. T. Cundiff, “A versatile ultrastable platform for optical multidimensional Fourier-transform spectroscopy,” Rev. Sci. Instrum. 80, 073108 (2009).
[CrossRef]

K. W. Stone, D. B. Turner, K. Gundogdu, S. T. Cundiff, and K. A. Nelson, “Exciton-exciton correlations revealed by two-quantum two-dimensional Fourier transform optical spectroscopy,” Acc. Chem. Res. 42, 1452–1461 (2009).
[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]

2008 (4)

L. Yang, T. Zhang, A. D. Bristow, S. T. Cundiff, and S. Mukamel, “Isolating excitonic Raman coherence in semiconductors using two-dimensional correlation spectroscopy,” J. Chem. Phys. 129, 234711 (2008).
[CrossRef]

S. T. Cundiff, “Coherent spectroscopy of semiconductors,” Opt. Express 16, 4639–4664 (2008).
[CrossRef]

A. D. Bristow, D. Karaiskaj, X. Dai, and S. T. Cundiff, “All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy,” Opt. Express 16, 18017–18027(2008).
[CrossRef]

M. Cho, “Coherent two-dimensional optical spectroscopy,” Chem. Rev. 108, 1331–1418 (2008).
[CrossRef]

2007 (5)

P. F. Tekavec, G. A. Lott, and A. H. Marcus, “Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation,” J. Chem. Phys. 127, 214307 (2007).
[CrossRef]

S. G. Carter, Z. Chen, and S. T. Cundiff, “Echo peak-shift spectroscopy of non-Markovian exciton dynamics in quantum wells,” Phys. Rev. B 76, 121303 (2007).
[CrossRef]

T. Zhang, I. Kuznetsova, T. Meier, X. Li, R. Mirin, P. Thomas, and S. Cundiff, “Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors,” Proc. Natl. Acad. Sci. USA 104, 14227–14232 (2007).
[CrossRef]

L. J. Yang, I. V. Schweigert, S. T. Cundiff, and S. Mukamel, “Two-dimensional optical spectroscopy of excitons in semiconductor quantum wells: Liouville-space pathway analysis,” Phys. Rev. B 75, 125302 (2007).
[CrossRef]

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, X. Li, R. P. Mirin, and S. T. Cundiff, “Signatures of many-particle correlations in two-dimensional Fourier-transform spectra of semiconductor nanostructures,” Solid State Commun. 142, 154–158(2007).
[CrossRef]

2006 (1)

X. Q. Li, T. H. Zhang, C. N. Borca, and S. T. Cundiff, “Many-body interactions in semiconductors probed by optical two-dimensional Fourier transform spectroscopy,” Phys. Rev. Lett. 96, 057406 (2006).
[CrossRef]

2005 (2)

C. N. Borca, T. H. Zhang, X. Q. Li, and S. T. Cundiff, “Optical two-dimensional Fourier transform spectroscopy of semiconductors,” Chem. Phys. Lett. 416, 311–315 (2005).
[CrossRef]

T. H. Zhang, C. N. Borca, X. Q. Li, and S. T. Cundiff, “Optical two-dimensional Fourier transform spectroscopy with active interferometric stabilization,” Opt. Express 13, 7432–7441 (2005).
[CrossRef]

2004 (2)

T. Brixner, T. Mancal, I. Stiopkin, and G. Fleming, “Phase-stabilized two-dimensional electronic spectroscopy,” J. Chem. Phys. 121, 4221–4236 (2004).
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M. Cowan, J. Ogilvie, and R. Miller, “Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes,” Chem. Phys. Lett. 386, 184–189 (2004).
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2003 (4)

D. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54, 425–463 (2003).
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P. Tian, D. Keusters, Y. Suzaki, and W. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
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M. Khalil, N. Demirdoven, and A. Tokmakoff, “Obtaining absorptive line shapes in two-dimensional infrared vibrational correlation spectra,” Phys. Rev. Lett. 90, 047401 (2003).
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S. A. Hawkins, E. J. Gansen, M. J. Stevens, A. L. Smirl, I. Rumyantsev, R. Takayama, N. H. Kwong, R. Binder, and D. G. Steel, “Differential measurements of Raman coherence and two-exciton correlations in quantum wells,” Phys. Rev. B 68, 035313 (2003).
[CrossRef]

2002 (2)

J. Guest, T. Stievater, X. Li, J. Cheng, D. Steel, D. Gammon, D. Katzer, D. Park, C. Ell, A. Thranhardt, G. Khitrova, and H. Gibbs, “Measurement of optical absorption by a single quantum dot exciton,” Phys. Rev. B 65, 241310 (2002).
[CrossRef]

J. M. Shacklette and S. T. Cundiff, “Role of excitation-induced shift in the coherent optical response of semiconductors,” Phys. Rev. B 66, 045309 (2002).
[CrossRef]

2001 (2)

J. Hybl, A. Ferro, and D. Jonas, “Two-dimensional Fourier transform electronic spectroscopy,” J. Chem. Phys. 115, 6606–6622 (2001).
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D. S. Chemla and J. Shah, “Many-body and correlation effects in semiconductors,” Nature 411, 549–557 (2001).
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2000 (3)

S. Mukamel, “Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations,” Annu. Rev. Phys. Chem. 51, 691–729 (2000).
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S. Weiser, T. Meier, J. Mobius, A. Euteneuer, E. J. Mayer, W. Stolz, M. Hofmann, W. W. Ruhle, P. Thomas, and S. W. Koch, “Disorder-induced dephasing in semiconductors,” Phys. Rev. B 61, 13088–13098 (2000).
[CrossRef]

L. Andreani, G. Panzarini, and J.-M. Gérard, “Vacuum—field rabi splitting for quantum boxes in pillar microcavities?,” Phys. Stat. Sol. A 178, 145–148 (2000).
[CrossRef]

1999 (3)

T. Takagahara, “Theory of exciton dephasing in semiconductor quantum dots,” Phys. Rev. B 60, 2638–2652 (1999).
[CrossRef]

M. Phillips and H. Wang, “Coherent oscillation in four-wave mixing of interacting excitons,” Solid State Commun. 111, 317–321 (1999).
[CrossRef]

A. L. Smirl, M. J. Stevens, X. Chen, and O. Buccafusca, “Heavy-hole and light-hole oscillations in the coherent emission from quantum wells: evidence for exciton-exciton correlations,” Phys. Rev. B 60, 8267–8275 (1999).
[CrossRef]

1998 (2)

P. Kner, W. Schäfer, R. Lövenich, and D. S. Chemla, “Coherence of four-particle correlations in semiconductors,” Phys. Rev. Lett. 81, 5386–5389 (1998).
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K. B. Ferrio and D. G. Steel, “Raman quantum beats of interacting excitons,” Phys. Rev. Lett. 80, 786–789 (1998).
[CrossRef]

1997 (2)

M. U. Wehner, M. H. Ulm, and M. Wegener, “Scanning interferometer stabilized by use of Pancharatnam’s phase,” Opt. Lett. 22, 1455–1457 (1997).
[CrossRef]

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

1996 (5)

D. Gammon, E. Snow, B. Shanabrook, D. Katzer, and D. Park, “Homogeneous linewidths in the optical spectrum of a single gallium arsenide quantum dot,” Science 273, 87–90 (1996).
[CrossRef]

D. Birkedal, V. G. Lyssenko, J. M. Hvam, and K. E. Sayed, “Continuum contribution to excitonic four-wave mixing due to interaction-induced nonlinearities,” Phys. Rev. B 54, R14250–R14253 (1996).
[CrossRef]

S. T. Cundiff, M. Koch, W. H. Knox, J. Shah, and W. Stolz, “Optical coherence in semiconductors: strong emission mediated by nondegenerate interactions,” Phys. Rev. Lett. 77, 1107–1110 (1996).
[CrossRef]

M. U. Wehner, D. Steinbach, and M. Wegener, “Ultrafast coherent transients due to exciton-continuum scattering in bulk GaAs,” Phys. Rev. B 54, R5211–R5214 (1996).
[CrossRef]

K. B. Ferrio and D. G. Steel, “Observation of the ultrafast two-photon coherent biexciton oscillation in a GaAs/AlxGa1−xAs multiple quantum well,” Phys. Rev. B 54, R5231–R5234(1996).
[CrossRef]

1995 (1)

1994 (10)

H. Wang, J. Shah, T. Damen, and L. Pfeiffer, “Polarization-dependent coherent nonlinear optical response in GaAs quantum wells: dominant effects of two-photon coherence between ground and biexciton states,” Solid State Commun. 91, 869–874 (1994).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient 4-wave-mixing line-shapes—effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551–R1554 (1994).
[CrossRef]

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, D. Bennhardt, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, “Evidence of biexcitonic contributions to 4-wave-mixing in GaAs quantum-wells,” Phys. Rev. B 50, 14730–14733 (1994).
[CrossRef]

V. M. Axt and A. Stahl, “The role of the biexciton in a dynamic density-matrix theory of the semiconductor band-edge,” Z. Phys. B 93, 205–211 (1994).
[CrossRef]

V. M. Axt and A. Stahl, “A dynamics-controlled truncation scheme for the hierarchy of density-matrices in semiconductor optics,” Z. Phys. B 93, 195–204 (1994).
[CrossRef]

M. Lindberg, Y. Z. Hu, R. Binder, and S. W. Koch, “χ(3) formalism in optically-excited semiconductors and its applications in 4-wave-mixing spectroscopy,” Phys. Rev. B 50, 18060–18072 (1994).
[CrossRef]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor 4-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382–14386 (1994).
[CrossRef]

S. T. Cundiff, “Effects of correlation between inhomogeneously broadened transitions on quantum beats in transient 4-wave-mixing,” Phys. Rev. A 49, 3114–3118 (1994).
[CrossRef]

M. Koch, J. Feldmann, G. von Plessen, S. T. Cundiff, E. O. Göbel, P. Thomas, and K. Köhler, “Koch et al. reply,” Phys. Rev. Lett. 73, 210 (1994).
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X. Zhu, M. S. Hybertsen, and P. B. Littlewood, “Quantum beats in photon echo from four-waving mixing,” Phys. Rev. Lett. 73, 209 (1994).
[CrossRef]

1993 (7)

W. Schäfer, F. Jahnke, and S. Schmitt-Rink, “Many-particle effects on transient 4-wave-mixing signals in semiconductors,” Phys. Rev. B 47, 1217–1220 (1993).
[CrossRef]

H. L. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear-optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261–1264 (1993).
[CrossRef]

V. G. Lyssenko, J. Erland, I. Balslev, K. H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear 4-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical-response in GaAs quantum-wells,” Phys. Rev. B 48, 17418–17426(1993).
[CrossRef]

R. Eccleston, J. Kuhl, D. Bennhardt, and P. Thomas, “Intensity dependent four-wave-mixing polarization rules in quantum wells,” Solid State Commun. 86, 93–97 (1993).
[CrossRef]

H. H. Yaffe, Y. Prior, J. P. Harbison, and L. T. Florez, “Polarization dependence and selection rules of transient four-wave mixing in GaAs quantum-well excitons,” J. Opt. Soc. Am. B 10, 578–583 (1993).
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D. Bennhardt, P. Thomas, R. Eccleston, E. J. Mayer, and J. Kuhl, “Polarization dependence of four-wave-mixing signals in quantum wells,” Phys. Rev. B 47, 13485–13490 (1993).
[CrossRef]

1992 (8)

D. J. Lovering, R. T. Phillips, G. J. Denton, and G. W. Smith, “Resonant generation of biexcitons in a GaAs quantum-well,” Phys. Rev. Lett. 68, 1880–1883 (1992).
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D. S. Kim, J. Shah, J. E. Cunningham, T. C. Damen, W. Schäfer, M. Hartmann, and S. Schmitt-Rink, “Giant excitonic resonance in time-resolved 4-wave-mixing in quantum-wells,” Phys. Rev. Lett. 68, 1006–1009 (1992).
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S. T. Cundiff and D. G. Steel, “Coherent transient spectroscopy of excitons in GaAs-AlGaAs quantum-wells,” IEEE J. Quantum Electron. 28, 2423–2433 (1992).
[CrossRef]

S. T. Cundiff, H. Wang, and D. G. Steel, “Polarization-dependent picosecond excitonic nonlinearities and the complexities of disorder,” Phys. Rev. B 46, 7248–7251 (1992).
[CrossRef]

M. Koch, J. Feldmann, G. von Plessen, E. O. Göbel, P. Thomas, and K. Kohler, “Quantum beats versus polarization interference—an experimental distinction,” Phys. Rev. Lett. 69, 3631–3634 (1992).
[CrossRef]

M. Lindberg, R. Binder, and S. W. Koch, “Theory of the semiconductor photon-echo,” Phys. Rev. A 45, 1865–1875 (1992).
[CrossRef]

D. S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, “Unusually slow temporal evolution of femtosecond 4-wave-mixing signals in intrinsic GaAs quantum-wells—direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725–2728 (1992).
[CrossRef]

S. Weiss, M. A. Mycek, J. Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay—do semiconductors and atoms emit coherent-light in different ways,” Phys. Rev. Lett. 69, 2685–2688 (1992).
[CrossRef]

1991 (3)

M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon-echoes and free polarization decay in GaAs/AlGaAs multiple quantum-wells,” Phys. Rev. Lett. 66, 934–937 (1991).
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M. D. Webb, S. T. Cundiff, and D. G. Steel, “Stimulated-picosecond-photon-echo studies of localized exciton relaxation and dephasing in GaAs/AlxGa1−xAs multiple quantum-wells,” Phys. Rev. B 43, 12658–12661 (1991).
[CrossRef]

B. F. Feuerbacher, J. Kuhl, and K. Ploog, “Biexcitonic contribution to the degenerate-4-wave-mixing signal from a GaAs/AlxGa1−xAs quantum-well,” Phys. Rev. B 43, 2439–2441(1991).
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1990 (6)

G. Noll, U. Siegner, S. G. Shevel, and E. O. Göbel, “Picosecond stimulated photon-echo due to intrinsic excitations in semiconductor mixed-crystals,” Phys. Rev. Lett. 64, 792–795 (1990).
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K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Göbel, T. C. Damen, S. Schmitt-Rink, and W. Schäfer, “Effects of coherent polarization interactions on time-resolved degenerate 4-wave-mixing,” Phys. Rev. Lett. 65, 1340–1343 (1990).
[CrossRef]

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Schäfer, “Line-shape of time-resolved 4-wave-mixing,” Phys. Rev. A 42, 5675–5683 (1990).
[CrossRef]

B. Feuerbacher, J. Kuhl, R. Eccleston, and K. Ploog, “Quantum beats between the light and heavy hole excitons in a quantum well,” Solid State Commun. 74, 1279–1283 (1990).
[CrossRef]

K. Leo, T. C. Damen, J. Shah, E. O. Göbel, and K. Kohler, “Quantum beats of light hole and heavy hole excitons in quantum wells,” Appl. Phys. Lett. 57, 19–21 (1990).
[CrossRef]

E. O. Göbel, K. Leo, T. C. Damen, J. Shah, S. Schmitt-Rink, W. Schäfer, J. F. Muller, and K. Köhler, “Quantum beats of excitons in quantum-wells,” Phys. Rev. Lett. 64, 1801–1804 (1990).
[CrossRef]

1988 (1)

P. C. Becker, H. L. Fragnito, C. H. B. Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon-echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
[CrossRef]

1986 (3)

L. Schultheis, J. Kuhl, A. Honold, and C. W. Tu, “Picosecond phase coherence and orientational relaxation of excitons in GaAs,” Phys. Rev. Lett. 57, 1797–1800 (1986).
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L. Schultheis, A. Honold, J. Kuhl, K. Köhler, and C. W. Tu, “Optical dephasing of homogeneously broadened two-dimensional exciton-transitions in GaAs quantum-wells,” Phys. Rev. B 34, 9027–9030 (1986).
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L. Schultheis, J. Kuhl, A. Honold, and C. W. Tu, “Ultrafast phase relaxation of excitons via exciton-exciton and exciton-electron collisions,” Phys. Rev. Lett. 57, 1635–1638 (1986).
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1985 (3)

L. Schultheis, M. D. Sturge, and J. Hegarty, “Photon-echoes from two-dimensional excitons in GaAs-AlGaAs quantum wells,” Appl. Phys. Lett. 47, 995–997 (1985).
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T. Takagahara, “Localization and homogeneous dephasing relaxation of quasi-2-dimensional excitons in quantum-well heterostructures,” Phys. Rev. B 32, 7013–7015 (1985).
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T. Takagahara, “Localization and energy-transfer of quasi-2-dimensional excitons in GaAs-AlAs quantum-well heterostructures,” Phys. Rev. B 31, 6552–6573 (1985).
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1983 (1)

D. A. Kleinman, “Binding energy of biexcitons and bound excitons in quantum wells,” Phys. Rev. B 28, 871–879 (1983).
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1982 (1)

J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Resonant degenerate 4-wave mixing in GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132–134 (1982).
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1979 (1)

T. Yajima and Y. Taira, “Spatial optical parametric coupling of picosecond light-pulses and transverse relaxation effect in resonant media,” J. Phys. Soc. Jpn. 47, 1620–1626 (1979).
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1966 (1)

I. Abella, N. Kurnit, and S. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
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1964 (1)

N. Kurnit, S. Hartmann, and I. Abella, “Observation of photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
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1957 (1)

R. J. Elliott, “Intensity of optical absorption by excitons,” Phys. Rev. 108, 1384–1389 (1957).
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1950 (1)

E. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
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Abella, I.

I. Abella, N. Kurnit, and S. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
[CrossRef]

N. Kurnit, S. Hartmann, and I. Abella, “Observation of photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
[CrossRef]

Andreani, L.

L. Andreani, G. Panzarini, and J.-M. Gérard, “Vacuum—field rabi splitting for quantum boxes in pillar microcavities?,” Phys. Stat. Sol. A 178, 145–148 (2000).
[CrossRef]

Axt, V. M.

V. M. Axt and A. Stahl, “A dynamics-controlled truncation scheme for the hierarchy of density-matrices in semiconductor optics,” Z. Phys. B 93, 195–204 (1994).
[CrossRef]

V. M. Axt and A. Stahl, “The role of the biexciton in a dynamic density-matrix theory of the semiconductor band-edge,” Z. Phys. B 93, 205–211 (1994).
[CrossRef]

Balslev, I.

V. G. Lyssenko, J. Erland, I. Balslev, K. H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear 4-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Becker, P. C.

P. C. Becker, H. L. Fragnito, C. H. B. Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon-echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
[CrossRef]

Bennhardt, D.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, D. Bennhardt, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, “Evidence of biexcitonic contributions to 4-wave-mixing in GaAs quantum-wells,” Phys. Rev. B 50, 14730–14733 (1994).
[CrossRef]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical-response in GaAs quantum-wells,” Phys. Rev. B 48, 17418–17426(1993).
[CrossRef]

D. Bennhardt, P. Thomas, R. Eccleston, E. J. Mayer, and J. Kuhl, “Polarization dependence of four-wave-mixing signals in quantum wells,” Phys. Rev. B 47, 13485–13490 (1993).
[CrossRef]

R. Eccleston, J. Kuhl, D. Bennhardt, and P. Thomas, “Intensity dependent four-wave-mixing polarization rules in quantum wells,” Solid State Commun. 86, 93–97 (1993).
[CrossRef]

Berman, P. R.

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient 4-wave-mixing line-shapes—effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551–R1554 (1994).
[CrossRef]

Bigot, J. Y.

S. Weiss, M. A. Mycek, J. Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay—do semiconductors and atoms emit coherent-light in different ways,” Phys. Rev. Lett. 69, 2685–2688 (1992).
[CrossRef]

Bimberg, D.

D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, 1999).

Binder, R.

S. A. Hawkins, E. J. Gansen, M. J. Stevens, A. L. Smirl, I. Rumyantsev, R. Takayama, N. H. Kwong, R. Binder, and D. G. Steel, “Differential measurements of Raman coherence and two-exciton correlations in quantum wells,” Phys. Rev. B 68, 035313 (2003).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient 4-wave-mixing line-shapes—effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551–R1554 (1994).
[CrossRef]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor 4-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382–14386 (1994).
[CrossRef]

M. Lindberg, Y. Z. Hu, R. Binder, and S. W. Koch, “χ(3) formalism in optically-excited semiconductors and its applications in 4-wave-mixing spectroscopy,” Phys. Rev. B 50, 18060–18072 (1994).
[CrossRef]

H. L. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear-optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261–1264 (1993).
[CrossRef]

M. Lindberg, R. Binder, and S. W. Koch, “Theory of the semiconductor photon-echo,” Phys. Rev. A 45, 1865–1875 (1992).
[CrossRef]

Birkedal, D.

D. Birkedal, V. G. Lyssenko, J. M. Hvam, and K. E. Sayed, “Continuum contribution to excitonic four-wave mixing due to interaction-induced nonlinearities,” Phys. Rev. B 54, R14250–R14253 (1996).
[CrossRef]

Bodenhausen, G.

R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions(Oxford Science, Oxford, 1987).

Borca, C. N.

X. Q. Li, T. H. Zhang, C. N. Borca, and S. T. Cundiff, “Many-body interactions in semiconductors probed by optical two-dimensional Fourier transform spectroscopy,” Phys. Rev. Lett. 96, 057406 (2006).
[CrossRef]

C. N. Borca, T. H. Zhang, X. Q. Li, and S. T. Cundiff, “Optical two-dimensional Fourier transform spectroscopy of semiconductors,” Chem. Phys. Lett. 416, 311–315 (2005).
[CrossRef]

T. H. Zhang, C. N. Borca, X. Q. Li, and S. T. Cundiff, “Optical two-dimensional Fourier transform spectroscopy with active interferometric stabilization,” Opt. Express 13, 7432–7441 (2005).
[CrossRef]

Bott, K.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, D. Bennhardt, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, “Evidence of biexcitonic contributions to 4-wave-mixing in GaAs quantum-wells,” Phys. Rev. B 50, 14730–14733 (1994).
[CrossRef]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical-response in GaAs quantum-wells,” Phys. Rev. B 48, 17418–17426(1993).
[CrossRef]

Bracker, A. S.

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K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical-response in GaAs quantum-wells,” Phys. Rev. B 48, 17418–17426(1993).
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S. A. Hawkins, E. J. Gansen, M. J. Stevens, A. L. Smirl, I. Rumyantsev, R. Takayama, N. H. Kwong, R. Binder, and D. G. Steel, “Differential measurements of Raman coherence and two-exciton correlations in quantum wells,” Phys. Rev. B 68, 035313 (2003).
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H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient 4-wave-mixing line-shapes—effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551–R1554 (1994).
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Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor 4-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382–14386 (1994).
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H. L. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear-optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261–1264 (1993).
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S. T. Cundiff and D. G. Steel, “Coherent transient spectroscopy of excitons in GaAs-AlGaAs quantum-wells,” IEEE J. Quantum Electron. 28, 2423–2433 (1992).
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S. T. Cundiff, H. Wang, and D. G. Steel, “Polarization-dependent picosecond excitonic nonlinearities and the complexities of disorder,” Phys. Rev. B 46, 7248–7251 (1992).
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M. D. Webb, S. T. Cundiff, and D. G. Steel, “Stimulated-picosecond-photon-echo studies of localized exciton relaxation and dephasing in GaAs/AlxGa1−xAs multiple quantum-wells,” Phys. Rev. B 43, 12658–12661 (1991).
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M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon-echoes and free polarization decay in GaAs/AlGaAs multiple quantum-wells,” Phys. Rev. Lett. 66, 934–937 (1991).
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K. W. Stone, D. B. Turner, K. Gundogdu, S. T. Cundiff, and K. A. Nelson, “Exciton-exciton correlations revealed by two-quantum two-dimensional Fourier transform optical spectroscopy,” Acc. Chem. Res. 42, 1452–1461 (2009).
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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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M. D. Webb, S. T. Cundiff, and D. G. Steel, “Stimulated-picosecond-photon-echo studies of localized exciton relaxation and dephasing in GaAs/AlxGa1−xAs multiple quantum-wells,” Phys. Rev. B 43, 12658–12661 (1991).
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Figures (11)

Fig. 1.
Fig. 1.

(a) Band structure of bulk GaAs near the fundamental gap between valence and CBs, (b) magnetic substates of bulk GaAs, (c) band structure of a GaAs QW, (d) magnetic substates of a GaAs QW, and (e) low-temperature linear absorption spectrum of of a GaAs QW showing HH and LH excitonic resonances.

Fig. 2.
Fig. 2.

(a) Two-pulse and (b) three-pulse box geometries used for TFWM.

Fig. 3.
Fig. 3.

Schematic apparatus for generating a pulse pair with fixed and controllable delay. The femtosecond laser beam (red, solid) is combined with the cw He–Ne beam (orange, dashed) by a dichroic beam splitter (DBS). The combined beams are split by a beam splitter and with each arm traversing an optical delay line. The output of two delay lines then go through a DBS that reflects the He–Ne beam back through the interferometer. The He–Ne beams recombine in the beams splitter to produce an interference signal that is used by a servo-loop to actively control the relative lengths of the two arms.

Fig. 4.
Fig. 4.

Simulated 2D lineshapes for (a) homogeneous, (c) intermediate, and (e) inhomogeneously broadened cases. Diagonal (solid line) and cross-diagonal (dashed line) slices for (b) homogeneous, (d) intermediate, and (f) inhomogeneously broadened cases. In (d), the inset shows a comparison of the cross-diagonal slices for homogeneous (solid line) and inhomogeneous (dashed line) broadening, but with identical homogeneous widths. (Adapted from [86].)

Fig. 5.
Fig. 5.

(a) Experimental SI(ωτ,T,ωt) for cocircularly polarized excitation of a GaAs multiple quantum well. Theoretical results (b) in the Pauli–Blocking approximation, (c) in the Hartree–Fock approximation, and (d) for dynamics-controlled truncation. Panels above (a) and (b) are respectively experimental and theoretical absorption (black) and laser (red) spectra. (Adapted from [10].)

Fig. 6.
Fig. 6.

Rephasing spectrum SI(ωτ,T,ωt) of a GaAs quantum well excited with (a) colinearly polarized and (b) cross-linear excitation pulses. (Adapted from [11].)

Fig. 7.
Fig. 7.

Raman spectrum SI(τ,ωT,ωt) of a GaAs quantum well. (Adapted from [83].)

Fig. 8.
Fig. 8.

Real two-quantum spectrum SIII(τ,ωT,ωt) for cross-circular excitation of two-exciton states in a GaAs quantum well. (Adapted from [13].)

Fig. 9.
Fig. 9.

(a) Rephasing spectrum SI(ωτ,T,ωt) of a GaAs quantum well for cocircular excitation. The dashed lines indicate the diagonal and antidiagonal slices for HH and LH excitons. Diagonal (red circles) and cross-diagonal (blue squares) data slices along with their respective fits (lines) for the (b) HH and (c) LH exciton resonances. (Adapted from [12].)

Fig. 10.
Fig. 10.

Rephasing spectrum SI(ωτ,T,ωt) of a GaAs natural quantum dot sample showing the localized quantum dot states and the quantum wells states for lattice temperatures of (a) 6 and (b) 50 K. Extracted linewidths within the inhomogeneous distribution as function of (c) temperature and (d) excitation power. In (d), the dashed line shows the dephasing rate extrapolated to zero excitation density (Adapted from [14].)

Fig. 11.
Fig. 11.

Amplitude of SI(ωτ,T,ωt) for increasing T showing peaks due to the QW exciton (QW), QW biexciton (QWBX), QD exciton ensemble (QDs), QWQD relaxation (RP), and QDQW excitation (EP). The temperature is fixed at 35 K. Each spectrum is normalized to the QW peak, and the amplitudes relative to the T=5ps spectrum are shown as the maximum of the gray scale bar. (Adapted from [15].)

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