Abstract

Multidimensional Coherent Optical Photocurrent Spectroscopy (MD-COPS) is implemented using unstabilized interferometers. Photocurrent from a semiconductor sample is generated using a sequence of four excitation pulses in a collinear geometry. Each pulse is frequency shifted by a unique radio frequency through acousto-optical modulation; the Four-Wave Mixing (FWM) signal is then selected in the frequency domain. The interference of an auxiliary continuous wave laser, which is sent through the same interferometers as the excitation pulses, is used to synthesize reference frequencies for lock-in detection of the photocurrent FWM signal. This scheme enables the partial compensation of mechanical fluctuations in the setup, achieving sufficient phase stability without the need for active stabilization. The method intrinsically provides both the real and imaginary parts of the FWM signal as a function of inter-pulse delays. This signal is subsequently Fourier transformed to create a multi-dimensional spectrum. Measurements made on the excitonic resonance in a double InGaAs quantum well embedded in a p-i-n diode demonstrate the technique.

© 2013 Optical Society of America

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2013 (5)

S. T. Cundiff and S. Mukamel, “Optical multidimensional coherent spectroscopy,” Phys. Today66, 44 (2013).

R. Singh, T. M. Autry, G. Nardin, G. Moody, H. Li, K. Pierz, M. Bieler, and S. T. Cundiff, “Anisotropic homogeneous linewidth of the heavy-hole exciton in (110)-oriented GaAs quantum wells,” Phys. Rev. B88, 045304 (2013).
[CrossRef]

H. Li, A. D. Bristow, M. E. Siemens, G. Moody, and S. T. Cundiff, “Unraveling quantum pathways using optical 3D fourier-transform spectroscopy,” Nat. Commun.4, 1390 (2013).
[CrossRef] [PubMed]

F. Albert, K. Sivalertporn, J. Kasprzak, M. Strauss, C. Schneider, S. Höfling, M. Kamp, A. Forchel, S. Reitzenstein, E. A. Muljarov, and W. Langbein, “Microcavity controlled coupling of excitonic qubits,” Nat. Commun.4, 1747 (2013).
[CrossRef] [PubMed]

P. Krogstrup, H. I. Jørgensen, M. Heiss, O. Demichel, J. V. Holm, M. Aagesen, J. Nygard, and A. Fontcuberta i Morral, “Single-nanowire solar cells beyond the Shockley-Queisser limit,” Nat. Photonics7, 306–310 (2013).
[CrossRef]

2012 (1)

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science338, 1317–1321 (2012).
[CrossRef] [PubMed]

2011 (5)

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science333, 1723–1726 (2011).
[CrossRef] [PubMed]

J. A. Davis, C. R. Hall, L. V. Dao, K. A. Nugent, H. M. Quiney, H. H. Tan, and C. Jagadish, “Three-dimensional electronic spectroscopy of excitons in asymmetric double quantum wells,” J. Chem. Phys135, 044510 (2011).
[CrossRef] [PubMed]

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. B83, 115324 (2011).
[CrossRef]

J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photonics5, 57–63 (2011).
[CrossRef]

W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Two-dimensional terahertz correlation spectra of electronic excitations in semiconductor quantum wells,” J. Phys. Chem. B115, 5448–5455 (2011).
[CrossRef]

2010 (4)

X. Dai, A. D. Bristow, D. Karaiskaj, and S. T. Cundiff, “Two-dimensional fourier-transform spectroscopy of potassium vapor,” Phys. Rev. A82, 052503 (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. Express18, 17699–17708 (2010).
[CrossRef] [PubMed]

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] [PubMed]

M. Zecherle, C. Ruppert, E. C. Clark, G. Abstreiter, J. J. Finley, and M. Betz, “Ultrafast few-fermion optoelectronics in a single self-assembled InGaAs/GaAs quantum dot,” Phys. Rev. B82, 125314 (2010).
[CrossRef]

2009 (4)

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater.8, 643–647 (2009).
[CrossRef] [PubMed]

S.-H. Shim and M. T. Zanni, “How to turn your pumpprobe instrument into a multidimensional spectrometer: 2D IR and vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys.11, 748–761 (2009).
[CrossRef] [PubMed]

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,” Science324, 1169–1173 (2009).
[CrossRef] [PubMed]

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] [PubMed]

2008 (3)

2007 (3)

E. M. Grumstrup, S.-H. Shim, M. A. Montgomery, N. H. Damrauer, and M. T. Zanni, “Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping technology,” Opt. Express15, 16681–16689 (2007).
[CrossRef] [PubMed]

C. Li, W. Wagner, M. Ciocca, and W. S. Warren, “Multiphoton femtosecond phase-coherent two-dimensional electronic spectroscopy,” J. Chem. Phys.126, 164307 (2007).
[CrossRef] [PubMed]

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] [PubMed]

2006 (2)

P. F. Tekavec, T. R. Dyke, and A. H. Marcus, “Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation,” J. Chem. Phys.125, 194303 (2006).
[CrossRef] [PubMed]

X. Li, T. 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] [PubMed]

2005 (2)

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature434, 625–628 (2005).
[CrossRef] [PubMed]

T. Zhang, C. Borca, X. Li, and S. Cundiff, “Optical two-dimensional fourier transform spectroscopy with active interferometric stabilization,” Opt. Express13, 7432–7441 (2005).
[CrossRef] [PubMed]

2004 (1)

T. Brixner, T. Mančal, I. V. Stiopkin, and G. R. Fleming, “Phase-stabilized two-dimensional electronic spectroscopy,” J. Chem. Phys.121, 4221–4236 (2004).
[CrossRef] [PubMed]

2003 (5)

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining absorptive line shapes in two-dimensional infrared vibrational correlation spectra,” Phys. Rev. Lett.90, 047401 (2003).
[CrossRef] [PubMed]

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Coherent 2D IR spectroscopy: molecular structure and dynamics in solution,” J. Phys. Chem. A107, 5258–5279 (2003).
[CrossRef]

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem.54, 425–463 (2003).
[CrossRef] [PubMed]

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys.75, 325–342 (2003).
[CrossRef]

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science300, 1553–1555 (2003).
[CrossRef] [PubMed]

2002 (1)

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature418, 612–614 (2002).
[CrossRef] [PubMed]

2001 (3)

J. Wang, M. S. Gudiksen, X. Duan, Y. Cui, and C. M. Lieber, “Highly polarized photoluminescence and photodetection from single indium phosphide nanowires,” Science293, 1455–1457 (2001).
[CrossRef] [PubMed]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
[CrossRef] [PubMed]

D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,” Phys. Rev. Lett.87, 227401 (2001).
[CrossRef] [PubMed]

2000 (1)

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, “Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes,” Proc. Natl. Acad. Sci. USA97, 8219–8224 (2000).
[CrossRef]

1999 (2)

S. M. Gallagher Faeder and D. M. Jonas, “Two-dimensional electronic correlation and relaxation spectra: theory and model calculations,” J. Phys. Chem. A103, 10489–10505 (1999).
[CrossRef]

D. Keusters, H.-S. Tan, and W. S. Warren, “Role of pulse phase and direction in two-dimensional optical spectroscopy,” J. Phys. Chem. A103, 10369–10380 (1999).
[CrossRef]

Aagesen, M.

P. Krogstrup, H. I. Jørgensen, M. Heiss, O. Demichel, J. V. Holm, M. Aagesen, J. Nygard, and A. Fontcuberta i Morral, “Single-nanowire solar cells beyond the Shockley-Queisser limit,” Nat. Photonics7, 306–310 (2013).
[CrossRef]

Abstreiter, G.

M. Zecherle, C. Ruppert, E. C. Clark, G. Abstreiter, J. J. Finley, and M. Betz, “Ultrafast few-fermion optoelectronics in a single self-assembled InGaAs/GaAs quantum dot,” Phys. Rev. B82, 125314 (2010).
[CrossRef]

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature418, 612–614 (2002).
[CrossRef] [PubMed]

Aeschlimann, M.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science333, 1723–1726 (2011).
[CrossRef] [PubMed]

Albert, F.

F. Albert, K. Sivalertporn, J. Kasprzak, M. Strauss, C. Schneider, S. Höfling, M. Kamp, A. Forchel, S. Reitzenstein, E. A. Muljarov, and W. Langbein, “Microcavity controlled coupling of excitonic qubits,” Nat. Commun.4, 1747 (2013).
[CrossRef] [PubMed]

Aloni, S.

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science338, 1317–1321 (2012).
[CrossRef] [PubMed]

Asplund, M. C.

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, “Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes,” Proc. Natl. Acad. Sci. USA97, 8219–8224 (2000).
[CrossRef]

Autry, T. M.

R. Singh, T. M. Autry, G. Nardin, G. Moody, H. Li, K. Pierz, M. Bieler, and S. T. Cundiff, “Anisotropic homogeneous linewidth of the heavy-hole exciton in (110)-oriented GaAs quantum wells,” Phys. Rev. B88, 045304 (2013).
[CrossRef]

G. Nardin, G. Moody, R. Singh, T. M. Autry, H. Li, F. Morier-Genoud, and S. T. Cundiff, “Coherent excitonic coupling in an asymmetric double InGaAs quantum well,” arXiv e-print 1308.1689 (2013).

Backus, E. H. G.

Bao, W.

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science338, 1317–1321 (2012).
[CrossRef] [PubMed]

Beham, E.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature418, 612–614 (2002).
[CrossRef] [PubMed]

Betz, M.

M. Zecherle, C. Ruppert, E. C. Clark, G. Abstreiter, J. J. Finley, and M. Betz, “Ultrafast few-fermion optoelectronics in a single self-assembled InGaAs/GaAs quantum dot,” Phys. Rev. B82, 125314 (2010).
[CrossRef]

Bichler, M.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature418, 612–614 (2002).
[CrossRef] [PubMed]

Bieler, M.

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W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science338, 1317–1321 (2012).
[CrossRef] [PubMed]

Woerner, M.

W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Two-dimensional terahertz correlation spectra of electronic excitations in semiconductor quantum wells,” J. Phys. Chem. B115, 5448–5455 (2011).
[CrossRef]

Woggon, U.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
[CrossRef] [PubMed]

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R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of nuclear magnetic resonance in one and two dimensions (Oxford Uni. Press, London/New York, 1987).

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S. Woutersen and P. Hamm, “Nonlinear two-dimensional vibrational spectroscopy of peptides,” J. Phys.: Condens. Matter14, R1035 (2002).
[CrossRef]

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W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science338, 1317–1321 (2012).
[CrossRef] [PubMed]

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] [PubMed]

Ye, J.

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys.75, 325–342 (2003).
[CrossRef]

Zanni, M. T.

S.-H. Shim and M. T. Zanni, “How to turn your pumpprobe instrument into a multidimensional spectrometer: 2D IR and vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys.11, 748–761 (2009).
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E. M. Grumstrup, S.-H. Shim, M. A. Montgomery, N. H. Damrauer, and M. T. Zanni, “Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping technology,” Opt. Express15, 16681–16689 (2007).
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M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, “Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes,” Proc. Natl. Acad. Sci. USA97, 8219–8224 (2000).
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Zhang, T.

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).
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X. Li, T. 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).
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T. Zhang, C. Borca, X. Li, and S. Cundiff, “Optical two-dimensional fourier transform spectroscopy with active interferometric stabilization,” Opt. Express13, 7432–7441 (2005).
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A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature418, 612–614 (2002).
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Annu. Rev. Phys. Chem. (1)

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J. Chem. Phys (1)

J. A. Davis, C. R. Hall, L. V. Dao, K. A. Nugent, H. M. Quiney, H. H. Tan, and C. Jagadish, “Three-dimensional electronic spectroscopy of excitons in asymmetric double quantum wells,” J. Chem. Phys135, 044510 (2011).
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W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Two-dimensional terahertz correlation spectra of electronic excitations in semiconductor quantum wells,” J. Phys. Chem. B115, 5448–5455 (2011).
[CrossRef]

Nat. Commun. (2)

H. Li, A. D. Bristow, M. E. Siemens, G. Moody, and S. T. Cundiff, “Unraveling quantum pathways using optical 3D fourier-transform spectroscopy,” Nat. Commun.4, 1390 (2013).
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F. Albert, K. Sivalertporn, J. Kasprzak, M. Strauss, C. Schneider, S. Höfling, M. Kamp, A. Forchel, S. Reitzenstein, E. A. Muljarov, and W. Langbein, “Microcavity controlled coupling of excitonic qubits,” Nat. Commun.4, 1747 (2013).
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Nat. Mater. (1)

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater.8, 643–647 (2009).
[CrossRef] [PubMed]

Nat. Photonics (2)

P. Krogstrup, H. I. Jørgensen, M. Heiss, O. Demichel, J. V. Holm, M. Aagesen, J. Nygard, and A. Fontcuberta i Morral, “Single-nanowire solar cells beyond the Shockley-Queisser limit,” Nat. Photonics7, 306–310 (2013).
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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. Photonics5, 57–63 (2011).
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Nature (2)

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature434, 625–628 (2005).
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A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature418, 612–614 (2002).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

S.-H. Shim and M. T. Zanni, “How to turn your pumpprobe instrument into a multidimensional spectrometer: 2D IR and vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys.11, 748–761 (2009).
[CrossRef] [PubMed]

Phys. Rev. A (1)

X. Dai, A. D. Bristow, D. Karaiskaj, and S. T. Cundiff, “Two-dimensional fourier-transform spectroscopy of potassium vapor,” Phys. Rev. A82, 052503 (2010).
[CrossRef]

Phys. Rev. B (3)

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. B83, 115324 (2011).
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R. Singh, T. M. Autry, G. Nardin, G. Moody, H. Li, K. Pierz, M. Bieler, and S. T. Cundiff, “Anisotropic homogeneous linewidth of the heavy-hole exciton in (110)-oriented GaAs quantum wells,” Phys. Rev. B88, 045304 (2013).
[CrossRef]

M. Zecherle, C. Ruppert, E. C. Clark, G. Abstreiter, J. J. Finley, and M. Betz, “Ultrafast few-fermion optoelectronics in a single self-assembled InGaAs/GaAs quantum dot,” Phys. Rev. B82, 125314 (2010).
[CrossRef]

Phys. Rev. Lett. (5)

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
[CrossRef] [PubMed]

D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,” Phys. Rev. Lett.87, 227401 (2001).
[CrossRef] [PubMed]

X. Li, T. 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] [PubMed]

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] [PubMed]

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining absorptive line shapes in two-dimensional infrared vibrational correlation spectra,” Phys. Rev. Lett.90, 047401 (2003).
[CrossRef] [PubMed]

Phys. Today (1)

S. T. Cundiff and S. Mukamel, “Optical multidimensional coherent spectroscopy,” Phys. Today66, 44 (2013).

Proc. Natl. Acad. Sci. USA (1)

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, “Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes,” Proc. Natl. Acad. Sci. USA97, 8219–8224 (2000).
[CrossRef]

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys.75, 325–342 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

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] [PubMed]

Science (5)

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science333, 1723–1726 (2011).
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P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science300, 1553–1555 (2003).
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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,” Science324, 1169–1173 (2009).
[CrossRef] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science338, 1317–1321 (2012).
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[CrossRef] [PubMed]

Other (7)

F. W. King, Hilbert Transforms, vol. 1 & 2 of Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, 2009).

J. G. Graeme, Photodiode Amplifiers: OP AMP Solutions (McGraw Hill Professional, 1996).

See also application note from http://cds.linear.com/docs/en/datasheet/6244fb.pdf .

G. Nardin, G. Moody, R. Singh, T. M. Autry, H. Li, F. Morier-Genoud, and S. T. Cundiff, “Coherent excitonic coupling in an asymmetric double InGaAs quantum well,” arXiv e-print 1308.1689 (2013).

S. Woutersen and P. Hamm, “Nonlinear two-dimensional vibrational spectroscopy of peptides,” J. Phys.: Condens. Matter14, R1035 (2002).
[CrossRef]

R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of nuclear magnetic resonance in one and two dimensions (Oxford Uni. Press, London/New York, 1987).

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Figures (5)

Fig. 1
Fig. 1

(a) Pulse sequence used in the experiment. The four pulses form a collinear sequence. In a simple picture, the black line shows the first order polarization, second order population, and third order polarization generated by pulses A, B, and C, respectively. (b) Scheme of the experimental setup (described in text). Note: the cw laser is actually vertically offset, but shown horizontally offset in the figure for clarity.

Fig. 2
Fig. 2

(a) Result of a pulse-pulse correlation between pulses A and B, recorded on a broadband detector. X and Y are the in-phase and in-quadrature outputs of the lock-in amplifier, corresponding to the real and imaginary parts of the two-wave mixing signal Z = X + iY. R = X 2 + Y 2 is the field amplitude. X and Y oscillate with τ at the reduced frequency ν* ∼ 3.5 THz (see text). (b) Fast Fourier transform (FFT) of the complex signal. As the detector is broadband, |FFT(Z)| (red curve) provides the power spectrum of the laser. The relative spectral phase is given by arg(FFT(Z)) (blue dots). A normalized spectrum of the excitation laser, recorded with an Ocean Optics USB 4000 spectrometer [36], is plotted for comparison (green circles).

Fig. 3
Fig. 3

Illustration of how the phase modulation by AOM’s can be seen as a dynamic, pulse-to-pulse phase cycling between the four pulse trains. The four pulse trains (A,B,C,D) are represented as a function of real time t*. For simplicity, delays τ, T and t are set to 0. Each beam is modulated by a separate AOM, and thus shifted by a unique radio frequency. This leads to an effective carrier-envelope offset frequency that is different for every beam. Δϕi is the pulse-to-pulse carrier-envelope phase shift for the pulse train i. Phase differences ΔϕA,B and ΔϕC,D are shown (modulo 2π) for pulse n = 2.

Fig. 4
Fig. 4

Scheme of the electronic circuitry used to detect photocurrent from the sample and to generate lock-in references for rephasing (SI) and non-rephasing (SII) signals. MO: microscope objective. REF: reference photodetector. DSP: digital signal processor.

Fig. 5
Fig. 5

(a) Absolute value, and (b) real part of the 2D spectrum recorded on the double InGaAs QW sample, using a non-rephasing pulse sequence (SII). The spectra are plotted as a function of h̄ωτ and h̄ωt. (c) Absolute value, and (d) real part of the 2D spectrum recorded using a rephasing pulse sequence (SI). The data to produce (a), (b), (c) and (d) were collected simultaneously.

Equations (8)

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

H [ cos ( ω A B t * ) ] = sin ( ω A B t * ) .
cos ( ω A B t * ± ω C D t * ) = cos ( ω A B t * ) cos ( ω C D t * ) sin ( ω A B t * ) sin ( ω C D t * ) .
ω S I = ω C D ω A B = ω A + ω B + ω C ω D
ω S I I = ω C D + ω A B = ω A ω B + ω C ω D
E ( n , t * ) i = a ( t * n T rep ) cos ( ω i t * ) ,
Δ ϕ i = ( ω i + 2 π f C E ) T rep .
Δ ϕ A , B = ω A B ( n T rep )
Δ ϕ C , D = ω C D ( n T rep ) .

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