Abstract

Optical two-dimensional Fourier transform spectroscopy is implemented near 800 nm with active stabilization. Excitation pulse delay is stabilized during data acquisition and stepped with interferometric accuracy. The reference used for heterodyne detecting the complete transient four-wave mixing signal is also phase-stabilized. The phase evolution of the four-wave mixing signal during the initial evolution period and the final detection period is then measured and correlated. Two-dimensional spectra with absorption and emission frequency axes are obtained by Fourier transforms with respect to the corresponding time variables. Measurement performed on a GaAs multiple quantum well sample shows light-hole and heavy-hole exciton transitions as the diagonal peaks and coupling between these two resonances as off-diagonal peaks.

© 2005 Optical Society of America

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References

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  1. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford Science Publications, 1987).
  2. D. M. Jonas, "Two-dimensional femtosecond spectroscopy," Annu. Rev. Phys. Chem. 54, 425-463 (2003).
    [CrossRef] [PubMed]
  3. R. A. Palmer, C. J. Manning, J. L. Chao, I. Noda, A. E. Dowrey, and C. Marcott, "Application of Step-Scan Interferometry to 2-Dimensional Fourier-Transform Infrared (2d Ft-Ir) - Correlation Spectroscopy," Appl Spectrosc 45, 12-17 (1991).
    [CrossRef]
  4. I. Noda, "Two-Dimensional Infrared-Spectroscopy," J. Am. Chem. Soc. 111, 8116-8118 (1989).
    [CrossRef]
  5. Y. Tanimura and S. Mukamel, "2-Dimensional Femtosecond Vibrational Spectroscopy of Liquids," J. Chem. Phys. 99, 9496-9511 (1993).
    [CrossRef]
  6. A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, "Two-dimensional Raman spectroscopy of vibrational interactions in liquids," Phys. Rev. Lett. 79, 2702-2705 (1997).
    [CrossRef]
  7. D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
    [CrossRef]
  8. O. Golonzka, N. Demirdoven, M. Khalil, and A. Tokmakoff, "Separation of cascaded and direct fifth-order Raman signals using phase-sensitive intrinsic heterodyne detection," J. Chem. Phys. 113, 9893-9896 (2000).
    [CrossRef]
  9. O. Golonzka, M. Khalil, N. Demirdoven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
    [CrossRef] [PubMed]
  10. N. Demirdoven, M. Khalil, and A. Tokmakoff, "Correlated vibrational dynamics revealed by two-dimensional infrared spectroscopy," Phys. Rev. Lett. 89, 237401 (2002).
    [CrossRef] [PubMed]
  11. M. Khalil, N. Demirdoven, and A. Tokmakoff, "Obtaining absorptive line shapes in two-dimensional infrared vibrational correlation spectra," Phys. Rev. Lett. 90, 047401 (2003).
    [CrossRef] [PubMed]
  12. J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, "Two-dimensional electronic spectroscopy," Chem. Phys. Lett. 297, 307-313 (1998).
    [CrossRef]
  13. J. D. Hybl, A. A. Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
    [CrossRef]
  14. 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, 625-628 (2005).
    [CrossRef] [PubMed]
  15. T. Brixner, I. V. Stiopkin, and G. R. Fleming, "Tunable two-dimensional femtosecond spectroscopy," Opt. Lett. 29, 884-886 (2004).
    [CrossRef] [PubMed]
  16. F. Rossi and T. Kuhn, "Theory of ultrafast phenomena in photoexcited semiconductors," Rev Mod Phys 74, 895-950 (2002).
    [CrossRef]
  17. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer Verlag, Berlin, 1999).
  18. P. F. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, "Femtosecond phase-coherent two-dimensional spectroscopy," Science 300, 1553-1555 (2003).
    [CrossRef] [PubMed]
  19. N. Belabas and M. Joffre, "Visible-infrared two-dimensional Fourier-transform spectroscopy," Opt. Lett. 27, 2043-2045 (2002).
    [CrossRef]
  20. V. Volkov, R. Schanz, and P. Hamm, "Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy," Opt. Lett. 30, 2010-2012 (2005).
    [CrossRef] [PubMed]
  21. M. Khalil, N. Demirdoven, and A. Tokmakoff, "Coherent 2D IR spectroscopy: Molecular structure and dynamics in solution," J Phys Chem A 107, 5258-5279 (2003).
    [CrossRef]
  22. D. Keusters, H. S. Tan, and W. S. Warren, "Role of pulse phase and direction in two-dimensional optical spectroscopy," J Phys Chem A 103, 10369-10380 (1999).
    [CrossRef]
  23. L. Lepetit, G. Cheriaux, and M. Joffre, "Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995).
    [CrossRef]
  24. C. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, "Spectral resolution and sampling issues in Fourier-transform spectral interferometry," J. Opt. Soc. Am. B 17, 1795-1802 (2000).
    [CrossRef]
  25. S. M. G. Faeder and D. M. Jonas, "Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations," J Phys Chem A 103, 10489-10505 (1999).
    [CrossRef]
  26. C. N. Borca, T. Zhang, X. Li, and S. T. Cundiff, "Optical Two Dimensional Fourier Tranform Spectroscopy of Semiconductors," submitted for publication (2005).
  27. X. Li, T. Zhang, C. N. Borca, and S. T. Cundiff, "Many-Body Interactions in Semiconductors Probed by Optical Two-Dimensional Fourier Tranform Spectroscopy," submitted for publication (2005).
  28. 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).
    [CrossRef] [PubMed]

Annu. Rev. Phys. Chem.

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

Appl. Spectrosc.

Chem. Phys. Lett.

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, "Two-dimensional electronic spectroscopy," Chem. Phys. Lett. 297, 307-313 (1998).
[CrossRef]

J Phys Chem A

M. Khalil, N. Demirdoven, and A. Tokmakoff, "Coherent 2D IR spectroscopy: Molecular structure and dynamics in solution," J Phys Chem A 107, 5258-5279 (2003).
[CrossRef]

D. Keusters, H. S. Tan, and W. S. Warren, "Role of pulse phase and direction in two-dimensional optical spectroscopy," J Phys Chem A 103, 10369-10380 (1999).
[CrossRef]

S. M. G. Faeder and D. M. Jonas, "Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations," J Phys Chem A 103, 10489-10505 (1999).
[CrossRef]

J. Am. Chem. Soc.

I. Noda, "Two-Dimensional Infrared-Spectroscopy," J. Am. Chem. Soc. 111, 8116-8118 (1989).
[CrossRef]

J. Chem. Phys.

Y. Tanimura and S. Mukamel, "2-Dimensional Femtosecond Vibrational Spectroscopy of Liquids," J. Chem. Phys. 99, 9496-9511 (1993).
[CrossRef]

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

D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

O. Golonzka, N. Demirdoven, M. Khalil, and A. Tokmakoff, "Separation of cascaded and direct fifth-order Raman signals using phase-sensitive intrinsic heterodyne detection," J. Chem. Phys. 113, 9893-9896 (2000).
[CrossRef]

J. Opt. Soc. Am. B

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, 625-628 (2005).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

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

N. Demirdoven, M. Khalil, and A. Tokmakoff, "Correlated vibrational dynamics revealed by two-dimensional infrared spectroscopy," Phys. Rev. Lett. 89, 237401 (2002).
[CrossRef] [PubMed]

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

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, "Two-dimensional Raman spectroscopy of vibrational interactions in liquids," Phys. Rev. Lett. 79, 2702-2705 (1997).
[CrossRef]

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).
[CrossRef] [PubMed]

Rev. Mod. Phys.

F. Rossi and T. Kuhn, "Theory of ultrafast phenomena in photoexcited semiconductors," Rev Mod Phys 74, 895-950 (2002).
[CrossRef]

Science

P. F. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, "Femtosecond phase-coherent two-dimensional spectroscopy," Science 300, 1553-1555 (2003).
[CrossRef] [PubMed]

Other

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer Verlag, Berlin, 1999).

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

C. N. Borca, T. Zhang, X. Li, and S. T. Cundiff, "Optical Two Dimensional Fourier Tranform Spectroscopy of Semiconductors," submitted for publication (2005).

X. Li, T. Zhang, C. N. Borca, and S. T. Cundiff, "Many-Body Interactions in Semiconductors Probed by Optical Two-Dimensional Fourier Tranform Spectroscopy," submitted for publication (2005).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Excitation scheme and (b) experimental setup for 2D Fourier transform spectroscopy. The delay between first two excitation pulses is stabilized and scanned by a stabilization interferometer (enclosed in the right box). The reference phase is locked by another stabilization interferometer (enclosed in the left box). CMP: chirped mirror pair; D: photodiode; BS: beam splitter; DBS: dichroic beam splitter; PZT: piezoelectric actuator.

Fig. 2.
Fig. 2.

(a) Error signal from the excitation phase stabilization interferometer while delay τ is unlocked and locked; (b) Error signal from the reference stabilization interferometer while the reference phase is unlocked and locked. Each locked error signal is shown in smaller scale in inset.

Fig. 3.
Fig. 3.

(a) The error signal from the He-Ne interferometer during locking and stepping (the circled dots are where delay τ is locked). (b) The flowchart of locking and stepping delay τ by monitoring the error signal. N is the total number of measurements.

Fig. 4.
Fig. 4.

(a) A typical spectral interferogram between the signal and reference, where the reference arrives 7.66 ps earlier; (b) The magnitude (solid line) and phase (dotted line) of the signal retrieved by Fourier transform spectral interferometry.

Fig. 5.
Fig. 5.

The fluctuations of signal phase change as a function of delay τ at the frequency of 372.12 THz. The nominal value of 0.79π has been subtracted, leaving the a mean value of 0.02π and a standard deviation of 0.06π.

Fig. 6.
Fig. 6.

A typical pump-probe measurement (dotted) and the least-squared match of phase corrected FWM spectrum (solid). The maximal mismatch is below 10%.

Fig. 7.
Fig. 7.

The 2D spectra of a GaAs multi-quantum well sample. Both the non-rephasing (upper row) and rephasing (lower row) data are shown in amplitude (A, D), real part (B, E) and imaginary part (C, F). Contour spacing is 5%. Note that absorption frequencies (vertical axis) in rephasing measurements are negative. Solid while lines are drawn to help identify the diagonal peaks corresponding to heavy hole (HH) and light hole (LH) excitons. The background level in the 2D spectrum is typically about 5% of the maximum peak strength.

Equations (1)

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E s ( τ , T , t ) = μ ij 2 μ kl 2 D ( τ , T , t ) e i ( ω kl t ± ω ij τ )

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