Abstract

We derive an analytical form for resonance lineshapes in two-dimensional (2D) Fourier transform spectroscopy. Our starting point is the solution of the optical Bloch equations for a two-level system in the 2D time domain. Application of the projection-slice theorem of 2D Fourier transforms reveals the form of diagonal and cross-diagonal slices in the 2D frequency data for arbitrary inhomogeneity. The results are applied in quantitative measurements of homogeneous and inhomogeneous broadening of multiple resonances in experimental data.

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    [CrossRef] [PubMed]
  9. S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. 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(5), 057406 (2006).
    [CrossRef] [PubMed]
  27. A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.
  28. 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(12), 121303 (2007).
    [CrossRef]

2009

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
[CrossRef] [PubMed]

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

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(16), 1–4 (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(7), 073108 (2009).
[CrossRef] [PubMed]

2008

M. Cho, “Coherent two-dimensional optical spectroscopy,” Chem. Rev. 108(4), 1331–1418 (2008).
[CrossRef] [PubMed]

S. T. Cundiff, “Coherent spectroscopy of semiconductors,” Opt. Express 16(7), 4639–4664 (2008).
[CrossRef] [PubMed]

2007

I. Kuznetsova, T. Meier, S. T. Cundiff, and P. Thomas, “Determination of homogeneous and inhomogeneous broadening in semiconductor nanostructures by two-dimensional Fourier-transform optical spectroscopy,” Phys. Rev. B 76(15), 153301 (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(12), 121303 (2007).
[CrossRef]

2006

K. Lazonder, M. S. Pshenichnikov, and D. A. Wiersma, “Easy interpretation of optical two-dimensional correlation spectra,” Opt. Lett. 31(22), 3354–3356 (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(5), 057406 (2006).
[CrossRef] [PubMed]

2005

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

2003

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54(1), 425–463 (2003).
[CrossRef] [PubMed]

K. Kwac and M. Cho, “Molecular dynamics simulation study of N-methylacetamide in water. II. Two-dimensional infrared pump-probe spectra,” J. Chem. Phys. 119(4), 2256–2263 (2003).
[CrossRef]

2001

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, “Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy,” Phys. Rev. Lett. 86(10), 2154–2157 (2001).
[CrossRef] [PubMed]

J. Hybl, A. Ferro, and D. Jonas, “Two-dimensional Fourier transform electronic spectroscopy,” J. Chem. Phys. 115(14), 6606–6622 (2001).
[CrossRef]

D. S. Chemla and J. Shah, “Many-body and correlation effects in semiconductors,” Nature 411(6837), 549–557 (2001).
[CrossRef] [PubMed]

2000

S. M. Gallagher Faeder and D. M. Jonas, “Phase-resolved time-domain nonlinear optical signals,” Phys. Rev. A 62(3), 033820 (2000).
[CrossRef]

A. Tokmakoff, “Two-dimensional line shapes derived from coherent third-order nonlinear spectroscopy,” J. Phys. Chem. A 104(18), 4247–4255 (2000).
[CrossRef]

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. U.S.A. 97(15), 8219–8224 (2000).
[CrossRef] [PubMed]

1979

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(5), 1620–1626 (1979).
[CrossRef]

1978

K. Nagayama, P. Bachmann, K. Wuthrich, and R. R. Ernst, “The Use of Cross-Sections and of Projections in Two-dimensional NMR Spectroscopy,” J. Magn. Reson. 31, 133–148 (1978).

1973

E. Bartholdi and R. R. Ernst, “Fourier Spectroscopy and the Causality Principle,” J. Magn. Reson. 11, 9–19 (1973).

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. U.S.A. 97(15), 8219–8224 (2000).
[CrossRef] [PubMed]

Bachmann, P.

K. Nagayama, P. Bachmann, K. Wuthrich, and R. R. Ernst, “The Use of Cross-Sections and of Projections in Two-dimensional NMR Spectroscopy,” J. Magn. Reson. 31, 133–148 (1978).

Bartholdi, E.

E. Bartholdi and R. R. Ernst, “Fourier Spectroscopy and the Causality Principle,” J. Magn. Reson. 11, 9–19 (1973).

Blankenship, R. E.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Borca, C. N.

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(5), 057406 (2006).
[CrossRef] [PubMed]

Bristow, A. D.

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(7), 073108 (2009).
[CrossRef] [PubMed]

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(16), 1–4 (2009).
[CrossRef]

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
[CrossRef] [PubMed]

A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.

Brixner, T.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Carlsson, C.

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(7), 073108 (2009).
[CrossRef] [PubMed]

Carter, S. G.

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(12), 121303 (2007).
[CrossRef]

Chemla, D. S.

D. S. Chemla and J. Shah, “Many-body and correlation effects in semiconductors,” Nature 411(6837), 549–557 (2001).
[CrossRef] [PubMed]

Chen, Z.

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(12), 121303 (2007).
[CrossRef]

Cho, M.

M. Cho, “Coherent two-dimensional optical spectroscopy,” Chem. Rev. 108(4), 1331–1418 (2008).
[CrossRef] [PubMed]

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

K. Kwac and M. Cho, “Molecular dynamics simulation study of N-methylacetamide in water. II. Two-dimensional infrared pump-probe spectra,” J. Chem. Phys. 119(4), 2256–2263 (2003).
[CrossRef]

Cundiff, S. 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(7), 073108 (2009).
[CrossRef] [PubMed]

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
[CrossRef] [PubMed]

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

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(16), 1–4 (2009).
[CrossRef]

S. T. Cundiff, “Coherent spectroscopy of semiconductors,” Opt. Express 16(7), 4639–4664 (2008).
[CrossRef] [PubMed]

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(12), 121303 (2007).
[CrossRef]

I. Kuznetsova, T. Meier, S. T. Cundiff, and P. Thomas, “Determination of homogeneous and inhomogeneous broadening in semiconductor nanostructures by two-dimensional Fourier-transform optical spectroscopy,” Phys. Rev. B 76(15), 153301 (2007).
[CrossRef]

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(5), 057406 (2006).
[CrossRef] [PubMed]

A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.

Dai, X.

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
[CrossRef] [PubMed]

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(16), 1–4 (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(7), 073108 (2009).
[CrossRef] [PubMed]

Demirdöven, N.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, “Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy,” Phys. Rev. Lett. 86(10), 2154–2157 (2001).
[CrossRef] [PubMed]

Ernst, R. R.

K. Nagayama, P. Bachmann, K. Wuthrich, and R. R. Ernst, “The Use of Cross-Sections and of Projections in Two-dimensional NMR Spectroscopy,” J. Magn. Reson. 31, 133–148 (1978).

E. Bartholdi and R. R. Ernst, “Fourier Spectroscopy and the Causality Principle,” J. Magn. Reson. 11, 9–19 (1973).

Ferro, A.

J. Hybl, A. Ferro, and D. Jonas, “Two-dimensional Fourier transform electronic spectroscopy,” J. Chem. Phys. 115(14), 6606–6622 (2001).
[CrossRef]

Fleming, G. R.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Gallagher Faeder, S. M.

S. M. Gallagher Faeder and D. M. Jonas, “Phase-resolved time-domain nonlinear optical signals,” Phys. Rev. A 62(3), 033820 (2000).
[CrossRef]

Golonzka, O.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, “Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy,” Phys. Rev. Lett. 86(10), 2154–2157 (2001).
[CrossRef] [PubMed]

Hagen, K. R.

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(7), 073108 (2009).
[CrossRef] [PubMed]

Hochstrasser, R. M.

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. U.S.A. 97(15), 8219–8224 (2000).
[CrossRef] [PubMed]

Hybl, J.

J. Hybl, A. Ferro, and D. Jonas, “Two-dimensional Fourier transform electronic spectroscopy,” J. Chem. Phys. 115(14), 6606–6622 (2001).
[CrossRef]

Jimenez, R.

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(7), 073108 (2009).
[CrossRef] [PubMed]

Jonas, D.

J. Hybl, A. Ferro, and D. Jonas, “Two-dimensional Fourier transform electronic spectroscopy,” J. Chem. Phys. 115(14), 6606–6622 (2001).
[CrossRef]

Jonas, D. M.

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54(1), 425–463 (2003).
[CrossRef] [PubMed]

S. M. Gallagher Faeder and D. M. Jonas, “Phase-resolved time-domain nonlinear optical signals,” Phys. Rev. A 62(3), 033820 (2000).
[CrossRef]

Karaiskaj, D.

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(7), 073108 (2009).
[CrossRef] [PubMed]

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(16), 1–4 (2009).
[CrossRef]

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
[CrossRef] [PubMed]

Khalil, M.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, “Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy,” Phys. Rev. Lett. 86(10), 2154–2157 (2001).
[CrossRef] [PubMed]

Kuznetsova, I.

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

I. Kuznetsova, T. Meier, S. T. Cundiff, and P. Thomas, “Determination of homogeneous and inhomogeneous broadening in semiconductor nanostructures by two-dimensional Fourier-transform optical spectroscopy,” Phys. Rev. B 76(15), 153301 (2007).
[CrossRef]

Kwac, K.

K. Kwac and M. Cho, “Molecular dynamics simulation study of N-methylacetamide in water. II. Two-dimensional infrared pump-probe spectra,” J. Chem. Phys. 119(4), 2256–2263 (2003).
[CrossRef]

Lazonder, K.

Li, X.

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(5), 057406 (2006).
[CrossRef] [PubMed]

Meier, T.

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

I. Kuznetsova, T. Meier, S. T. Cundiff, and P. Thomas, “Determination of homogeneous and inhomogeneous broadening in semiconductor nanostructures by two-dimensional Fourier-transform optical spectroscopy,” Phys. Rev. B 76(15), 153301 (2007).
[CrossRef]

Mirin, R. P.

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(16), 1–4 (2009).
[CrossRef]

A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.

Nagayama, K.

K. Nagayama, P. Bachmann, K. Wuthrich, and R. R. Ernst, “The Use of Cross-Sections and of Projections in Two-dimensional NMR Spectroscopy,” J. Magn. Reson. 31, 133–148 (1978).

Pshenichnikov, M. S.

Shah, J.

D. S. Chemla and J. Shah, “Many-body and correlation effects in semiconductors,” Nature 411(6837), 549–557 (2001).
[CrossRef] [PubMed]

Siemens, M. E.

A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.

Stenger, J.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Taira, Y.

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(5), 1620–1626 (1979).
[CrossRef]

Thomas, P.

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

I. Kuznetsova, T. Meier, S. T. Cundiff, and P. Thomas, “Determination of homogeneous and inhomogeneous broadening in semiconductor nanostructures by two-dimensional Fourier-transform optical spectroscopy,” Phys. Rev. B 76(15), 153301 (2007).
[CrossRef]

Tokmakoff, A.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, “Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy,” Phys. Rev. Lett. 86(10), 2154–2157 (2001).
[CrossRef] [PubMed]

A. Tokmakoff, “Two-dimensional line shapes derived from coherent third-order nonlinear spectroscopy,” J. Phys. Chem. A 104(18), 4247–4255 (2000).
[CrossRef]

Vaswani, H. M.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

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[CrossRef]

Zanni, M. T.

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. U.S.A. 97(15), 8219–8224 (2000).
[CrossRef] [PubMed]

Zhang, T.

I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (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(7), 073108 (2009).
[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(5), 057406 (2006).
[CrossRef] [PubMed]

A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.

Acc. Chem. Res.

S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, “Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells,” Acc. Chem. Res. 42(9), 1423–1432 (2009).
[CrossRef] [PubMed]

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K. Nagayama, P. Bachmann, K. Wuthrich, and R. R. Ernst, “The Use of Cross-Sections and of Projections in Two-dimensional NMR Spectroscopy,” J. Magn. Reson. 31, 133–148 (1978).

E. Bartholdi and R. R. Ernst, “Fourier Spectroscopy and the Causality Principle,” J. Magn. Reson. 11, 9–19 (1973).

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[CrossRef]

J. Phys. Soc. Jpn.

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(5), 1620–1626 (1979).
[CrossRef]

Nature

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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I. Kuznetsova, T. Meier, S. T. Cundiff, and P. Thomas, “Determination of homogeneous and inhomogeneous broadening in semiconductor nanostructures by two-dimensional Fourier-transform optical spectroscopy,” Phys. Rev. B 76(15), 153301 (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(12), 121303 (2007).
[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(16), 1–4 (2009).
[CrossRef]

Phys. Rev. Lett.

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(5), 057406 (2006).
[CrossRef] [PubMed]

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I. Kuznetsova, P. Thomas, T. Meier, T. Zhang, and S. T. Cundiff, “Determination of homogeneous and inhomogeneous broadenings of quantum-well excitons by 2DFTS: An experiment-theory comparison,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 6(2), 445–448 (2009).

Proc. Natl. Acad. Sci. U.S.A.

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. U.S.A. 97(15), 8219–8224 (2000).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

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(7), 073108 (2009).
[CrossRef] [PubMed]

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A. D. Bristow, T. Zhang, M. E. Siemens, R. P. Mirin, and S. T. Cundiff, “Dephasing in Weakly Disordered GaAs Quantum Wells,” to be submitted.

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Figures (7)

Fig. 1
Fig. 1

2D amplitude lineshapes for rephasing signals. a-c) 2D frequency plots for a fixed value of homogeneous broadening with increasing inhomogeneous broadening. The diagonal (red dashes) and cross-diagonal (blue dots) lines are shown. The vertical scale for ωτ is negative because of phase-matching requirements, and increases (gets more negative) going down. d-f) Slices of the corresponding 2D frequency plots along the diagonal (red) and cross-diagonal (blue) directions. The inset compares cross-diagonal slices in the limits of strong homogeneous (dashes) and inhomogeneous (dots) broadening.

Fig. 2
Fig. 2

Real part of the OBE signal in the 2D time domain in the cases of a) homogeneous broadening, b) moderate inhomogeneity, and c) strong inhomogeneous broadening. The signals exhibit sharp edges along t = 0 and τ = 0 due to causality.

Fig. 3
Fig. 3

a) 2D time and b) frequency coordinates for photon echo signals. c) 2D time projection onto the diagonal corresponding to a slice along ωt’ . d) 2D time projection onto the cross-diagonal corresponding to a slice along ωτ’ . A signal with moderate inhomogeneity, simulated from Eq. (1), is shown in the background for reference. The gray triangles indicate areas of zero signal as enforced by the Θ functions in Eq. (1).

Fig. 4
Fig. 4

Coherent signal amplitude in the 2D time domain for a) pure homogeneous b) moderately inhomogeneous, and c) strongly inhomogeneous broadening. Frames d, e, and f show projections onto the t’ (blue) and τ’ (red) axes in the corresponding cases.

Fig. 5
Fig. 5

Imaginary part of the 2D signal. Parts a, b, and c) show a calculated signal in the 2D frequency domain obtained by the 2D Fourier transform of the corresponding panels in Fig. 4. Panels d, e, and f) depict the imaginary part of the lineshapes derived in the text for the homogeneous, moderately inhomogeneous, and strongly inhomogeneous cases.

Fig. 6
Fig. 6

As in Fig. 5, but real part of 2D frequency (a, b, and c) and slice (d, e, and f) data.

Fig. 7
Fig. 7

Fitting analytical lineshapes to experimental data from excitons in GaAs quantum wells. a) Experimental and b) simulated 2D frequency spectra. c) Diagonal (red) and cross-diagonal (blue) experimental data (dots) and analytical fits (lines) using Eq. (13) and Eq. (11) for the HH excitonic resonance. d) Data and fits for the LH. Homogeneous and inhomogeneous parameters measured from the fits in c) and d) were used in the simulation shown in b).

Tables (1)

Tables Icon

Table 1 Imaginary, real, and amplitude lineshapes and widths in homogeneous and inhomogeneous limits

Equations (13)

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s ( t , τ ) = s 0 , 0 e ( γ ( t + τ ) + i ω 0 ( t τ ) + σ 2 ( t τ ) 2 / 2 ) Θ ( t ) Θ ( τ ) .
s ( t ' , τ ' ) = s 0 , 0 e ( γ t ' + i ω 0 τ ' + σ 2 τ ' 2 / 2 ) Θ ( t ' τ ' ) Θ ( t ' + τ ' ) .
s ω 0 ( t ' , τ ' ) = s ( t ' , τ ' ) e i ω 0 τ ' s 0 , 0 = e ( γ t ' + σ 2 τ ' 2 / 2 ) Θ ( t ' τ ' ) Θ ( t ' + τ ' ) .
s Pr o j , ω 0 ( t ' ) = s ω 0 ( t ' , τ ' ) d τ ' = e γ t ' t ' t ' e σ 2 τ ' 2 / 2 d τ ' .
s Pr o j , ω 0 ( τ ' ) = s ω 0 ( t ' , τ ' ) d t ' = e σ 2 τ ' 2 / 2 | τ ' | e γ t ' d t ' .
s Pr o j I n ( t ' ) = Θ ( t ' ) e γ t ' S S l i c e I n ( ω t ' ) = 1 2 π ( γ i ω t ' ) ,
s Pr o j I n ( τ ' ) = e σ 2 τ ' 2 / 2 0 e γ t ' d t ' = e σ 2 τ ' 2 / 2 S S l i c e I n ( ω τ ' ) = 1 σ e ω τ ' 2 / 2 σ 2 .
s Pr o j H o ( t ' ) = Θ ( t ' ) 2 t ' e γ t ' S S l i c e H o ( ω t ' ) = 1 2 π ( γ i ω t ' ) 2 .
s Pr o j H o ( τ ' ) = 1 γ e γ | τ ' | S S l i c e I n ( ω τ ' ) = 2 π 1 γ 2 + ω τ ' 2 ,
s Pr o j , ω 0 ( t ' ) = Θ ( t ' ) e γ t t ' t ' e σ 2 τ 2 / 2 d τ = 2 π σ Θ ( t ) e γ t Erf ( σ t / 2 ) ,
S Pr o j , ω 0 ( ω t ' ) = e ( γ i ω t ) 2 2 σ 2 Erfc ( γ i ω t 2 σ ) σ ( γ i ω t ) ,
s Pr o j , ω 0 ( τ ' ) = e σ 2 τ 2 / 2 | τ | e γ t d t = 1 γ e σ 2 τ 2 / 2 e γ | τ | .
S Pr o j , ω 0 ( ω τ ) = 2 π σ 2 e ω τ 2 / 2 σ 2 1 γ 2 + ω 2 τ ' = 2 π γ Voigt ( γ , σ , ω τ ) .

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