## Multidimensional coherent photocurrent spectroscopy of a semiconductor nanostructure |

Optics Express, Vol. 21, Issue 23, pp. 28617-28627 (2013)

http://dx.doi.org/10.1364/OE.21.028617

Acrobat PDF (1005 KB)

### 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

## 1. Introduction

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

4. 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. USA **97**, 8219–8224 (2000). [CrossRef]

6. M. Khalil, N. Demirdöven, and A. Tokmakoff, “Coherent 2D IR spectroscopy: molecular structure and dynamics in solution,” J. Phys. Chem. A **107**, 5258–5279 (2003). [CrossRef]

7. 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]

8. 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]

10. 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. B **88**, 045304 (2013). [CrossRef]

11. X. Dai, A. D. Bristow, D. Karaiskaj, and S. T. Cundiff, “Two-dimensional fourier-transform spectroscopy of potassium vapor,” Phys. Rev. A **82**, 052503 (2010). [CrossRef]

12. 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]

10. 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. B **88**, 045304 (2013). [CrossRef]

13. 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] [PubMed]

14. 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] [PubMed]

15. 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]

8. 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]

16. 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. Phys **135**, 044510 (2011). [CrossRef] [PubMed]

18. 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]

20. 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]

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

20. 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]

## 2. Experiment

6. M. Khalil, N. Demirdöven, and A. Tokmakoff, “Coherent 2D IR spectroscopy: molecular structure and dynamics in solution,” J. Phys. Chem. A **107**, 5258–5279 (2003). [CrossRef]

21. 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]

22. 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]

8. 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]

23. 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]

14. 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] [PubMed]

15. 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]

22. 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]

24. S. M. Gallagher 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]

27. E. H. G. Backus, S. Garrett-Roe, and P. Hamm, “Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy,” Opt. Lett. **33**, 2665–2667 (2008). [CrossRef] [PubMed]

28. 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. Express **15**, 16681–16689 (2007). [CrossRef] [PubMed]

23. 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]

29. J. A. Myers, K. L. Lewis, P. F. Tekavec, and J. P. Ogilvie, “Two-color two-dimensional fourier transform electronic spectroscopy with a pulse-shaper,” Opt. Express **16**, 17420–17428 (2008). [CrossRef] [PubMed]

30. 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]

31. 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,” Science **333**, 1723–1726 (2011). [CrossRef] [PubMed]

31. 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,” Science **333**, 1723–1726 (2011). [CrossRef] [PubMed]

34. 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]

35. 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]

9. 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. B **115**, 5448–5455 (2011). [CrossRef]

22. 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]

29. J. A. Myers, K. L. Lewis, P. F. Tekavec, and J. P. Ogilvie, “Two-color two-dimensional fourier transform electronic spectroscopy with a pulse-shaper,” Opt. Express **16**, 17420–17428 (2008). [CrossRef] [PubMed]

30. 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]

*et al*, where the fourth order population generated in an atomic vapor was detected in the form of a fluorescence signal [35

35. 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]

*τ*,

*T*and

*t*. (Fig. 1(a)). The four-pulse sequence is generated by sending the beam of a mode-locked Ti:Sapph oscillator (Coherent MIRA −76 MHz repetition rate [36]) into a set of two Mach-Zehnder interferometers nested within a larger Mach-Zehnder interferometer (Fig. 1(b)). Three translation stages are used to control inter-pulse delays

*τ*,

*T*and

*t*. Each interferometer arm contains an Acoustic Optical Modulator (AOM) (Isomet 1205c-1) driven by a phase-locked direct digital synthesizer (Analog Devices AD9959). In each arm the 0

*diffraction order of the AOM is spatially blocked and the 1*

^{th}*order beam is used. Each AOM is driven with a unique radio frequency*

^{st}*ω*, with

_{i}*i*= {

*A*,

*B*,

*C*,

*D*}. By scattering on the acoustic grating, the optical carrier frequency

*ω*

_{0}of the pulse gets shifted by an amount that equals the frequency of the acoustic wave. Each excitation pulse is thus “tagged” by oscillating at a uniquely shifted optical frequency

*ω′*=

_{i}*ω*

_{0}+

*ω*. Although much smaller than the laser pulse bandwidth, the frequency shift

_{i}*ω*does impact the laser beam when its effect is considered on a train of pulses (whose interference produces a frequency comb [37

_{i}37. S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. **75**, 325–342 (2003). [CrossRef]

*τ*,

*T*and

*t*can be stepped to record 2D or 3D data, which can be Fourier transformed with respect to each delay to produce multi-dimensional spectra. The most typical 2D spectrum in conventional MDCS is obtained by stepping delays

*τ*and

*t*while keeping

*T*at a constant value. To produce the appropriate lock-in reference for the FWM signal, we detect the beat notes

*ω*and

_{AB}*ω*on two separate photodetectors (REF1 and REF2 in Fig. 1(b)). These beat frequencies are mixed digitally using a digital signal processor (DSP) (SigmaStudios ADAU1761Z [36]). The mixing algorithm (in-quadrature mixing) is as follows: the beat notes cos(

_{CD}*ω*

_{AB}t^{*}) and cos(

*ω*

_{CD}t^{*}) (with

*t*

^{*}being the real time) are input into the DSP, where they independently undergo a Hilbert transform [41]. For a general function, the Hilbert transform shifts the phase of positive frequency components by

*ω*

_{AB}t^{*}) is:

*ω*

_{AB}t^{*}) and in-phase sin(

*ω*

_{AB}t^{*}) components of the beat note (and the same thing is done for cos(

*ω*

_{CD}t^{*})). These components are then appropriately multiplied with each other, and we make use of the identity

*k⃗*= −

_{FWM}*k⃗*+

_{A}*k⃗*+

_{B}*k⃗*and

_{C}*k⃗*=

_{FWM}*k⃗*−

_{A}*k⃗*+

_{B}*k⃗*of non-collinear MDCS, corresponding to the so-called rephasing (or

_{C}*S*) and non-rephasing (or

_{I}*S*) pulse sequences, respectively. In the box geometry,

_{II}*S*and

_{I}*S*need to be recorded separately since they correspond to a different pulse sequence, while with frequency domain selection

_{II}*S*and

_{I}*S*can be recorded simultaneously on two separate lock-in amplifiers. It is also possible to detect two-quantum (or

_{II}*S*) signals that oscillate at the radio frequency

_{III}*ω*

_{SIII}=

*ω*+

_{A}*ω*−

_{B}*ω*−

_{C}*ω*. The reference frequency that allows demodulation of such a signal cannot be generated from reference detectors REF1 and REF2. It can be extracted from detector REF3 at the output of the nested Mach-Zehnder interferometer (see Fig. 1), after appropriate frequency mixing and filtering by the DSP.

_{D}## 3. Analogy with phase-cycling

31. 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,” Science **333**, 1723–1726 (2011). [CrossRef] [PubMed]

34. 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]

*f*[37

_{CE}37. S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. **75**, 325–342 (2003). [CrossRef]

*f*the laser repetition rate). The nested interferometers create four copies of the original pulse train. However, due to the acousto-optical modulation, each of the four pulse trains is frequency-shifted by a unique radio frequency

_{rep}*ω*(without altering the repetition rate

_{i}*f*). Thus, each beam acquires an

_{rep}*additional*, unique carrier-envelope offset frequency, resulting in a pulse-to-pulse carrier-envelope phase shift that is different for each pulse train. In this way, the phase difference between the pulses of trains A and B is cycled pulse-to-pulse. Explicitly, the electric field of the

*n*pulse in train

^{th}*i*as a function real time

*t*

^{*}can be written as where

*a*(

*t*

^{*}) is the pulse envelope and

*ω′*=

_{i}*ω*

_{0}+

*ω*= 2

_{i}*π*(

*N*×

*f*+

_{rep}*f*) +

_{CE}*ω*, where

_{i}*ω*

_{0}is the original carrier frequency and

*N*is an integer. Since

*ω*and

_{i}*f*are much smaller than the pulse bandwidth, the frequency shift results in a pulse-to-pulse carrier-envelope phase shift for beam

_{CE}*i*that is

*n*= 0, as in Fig. 3, then we can write the phase difference between the

*n*pulses of train

^{th}*i*and

*j*as Δ

*ϕ*= (

_{i,j}*ω*−

_{i}*ω*)(

_{j}*nT*). In our situation, we obtain

_{rep}*ω*and

_{AB}*ω*, respectively. The principle can be visualized in Fig. 3, for the simple situation where the delays

_{CD}*τ*,

*T*, and

*t*are equal to 0. This dynamic, pulse-to-pulse phase-cycling results in an evolution of the phase of the FWM signals

*S*and

_{I}*S*as

_{II}*ϕ*

_{SI}= Δ

*ϕ*− Δ

_{C,D}*ϕ*and

_{A,B}*ϕ*

_{SII}= Δ

*ϕ*+ Δ

_{C,D}*ϕ*. This phase cycling leads to the oscillation of the FWM signal amplitudes at the precise frequencies that are selected by the lock-in detection scheme detailed in the previous section. Let us note that this picture of the dynamic phase-cycling does not need a stable

_{A,B}*f*to be valid: fluctuations of

_{CE}*f*are duplicated in all four pulse trains, and cancel as we measure the phase difference between two pulse trains.

_{CE}## 4. Results

_{0.2}Ga

_{0.8}As/GaAs QW, embedded within the intrinsic region of a p-i-n diode. The double QW consists in a 4.8 nm thick QW and a 8 nm thick QW, separated by a barrier of 4 nm thickness. An Au-Ni-Ge bottom contact was deposited on the n-doped substrate. A top contact (5nm Ti and 200nm Au) was deposited on part of the sample surface. The sample was kept at a temperature of 15.5K in a cold finger liquid Helium cryostat. In order to deal with the sample capacitance, a “bootstrap” trans-impedance circuit [42, 43

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

*ω*= 80.109 MHz,

_{A}*ω*= 80.104 MHz,

_{B}*ω*= 80.019 MHz,

_{C}*ω*= 80 MHz. The beat notes recorded by reference detectors REF1 and REF2 as a result of the cw laser interference are then

_{D}*ω*= 5 kHz and

_{AB}*ω*= 19 kHz, respectively. As a result of in-quadrature mixing by the DSP, the reference frequencies provided to the lock-in amplifiers for the

_{CD}*S*and

_{I}*S*FWM signal are

_{II}*ω*

_{SI}= 14kHz and

*ω*

_{SII}= 24kHz.

**80**, 073108 (2009). [CrossRef] [PubMed]

*V*= 0.5 V, for which we obtain the strongest FWM signal, was applied through the bootstrap circuit (see Fig. 4). The laser spectrum was the same as shown in Fig. 2(b), exciting the lowest energy excitonic resonance of the double QW structure. The total excitation power (four pulses) was 250

_{b}*μW*. The pulse sequence was focused on the sample using a microscope lens (Nikon EPI ELWD CF Plan 20x, NA = 0.4 [36]), providing an excitation spot of ∼5

*μ*m diameter. While delays

*τ*and

*t*were stepped, delay

*T*was kept at 200 fs. A fast Fourier transform with respect to delays

*τ*and

*t*provides 2D spectra as a function of

*h̄ω*and

_{τ}*h̄ω*. Non-rephasing (

_{t}*S*- Fig. 5(a)–(b)) and rephasing ((

_{II}*S*- Fig. 5(c)–(d)) spectra were obtained simultaneously from two separate lock-in amplifiers.

_{I}*S*and

_{II}*S*spectra (Fig. 5(a) and (c)) show a peak on the diagonal corresponding to the lowest energy exciton of the double QW. In the

_{I}*S*spectrum the peak is slightly elongated along the diagonal, a sign of slight inhomogeneous broadening of the excitonic resonance. Thanks to the intrinsic phase resolution of the technique, real and imaginary parts of the data are directly obtained as well. To determine the absolute phase offset of the signal, we set the phase of the time domain data to be zero at zero

_{I}*τ*and

*t*delays [35

35. 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]

*arg*{

*Z*(

*τ*= 0,

*T*= 200

*fs*,

*t*= 0)} = 0. We show in Fig. 5(b) and (d) the real parts of the

*S*and

_{I}*S*spectra, respectively, exhibiting a typical absorptive line shape.

_{II}## 5. Conclusion

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12. 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]

16. 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. Phys **135**, 044510 (2011). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | S. T. Cundiff and S. Mukamel, “Optical multidimensional coherent spectroscopy,” Phys. Today |

2. | R. Ernst, G. Bodenhausen, and A. Wokaun, |

3. | D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. |

4. | 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. USA |

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

6. | M. Khalil, N. Demirdöven, and A. Tokmakoff, “Coherent 2D IR spectroscopy: molecular structure and dynamics in solution,” J. Phys. Chem. A |

7. | 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 |

8. | 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. |

9. | 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. B |

10. | 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. B |

11. | X. Dai, A. D. Bristow, D. Karaiskaj, and S. T. Cundiff, “Two-dimensional fourier-transform spectroscopy of potassium vapor,” Phys. Rev. A |

12. | 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. |

13. | M. E. Siemens, G. Moody, H. Li, A. D. Bristow, and S. T. Cundiff, “Resonance lineshapes in two-dimensional fourier transform spectroscopy,” Opt. Express |

14. | 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 |

15. | 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. |

16. | 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. Phys |

17. | 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). |

18. | 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 |

19. | J. Kasprzak, B. Patton, V. Savona, and W. Langbein, “Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging,” Nat. Photonics |

20. | 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. |

21. | T. Brixner, T. Mančal, I. V. Stiopkin, and G. R. Fleming, “Phase-stabilized two-dimensional electronic spectroscopy,” J. Chem. Phys. |

22. | 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. |

23. | M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining absorptive line shapes in two-dimensional infrared vibrational correlation spectra,” Phys. Rev. Lett. |

24. | S. M. Gallagher Faeder and D. M. Jonas, “Two-dimensional electronic correlation and relaxation spectra: theory and model calculations,” J. Phys. Chem. A |

25. | T. Zhang, C. Borca, X. Li, and S. Cundiff, “Optical two-dimensional fourier transform spectroscopy with active interferometric stabilization,” Opt. Express |

26. | 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 |

27. | E. H. G. Backus, S. Garrett-Roe, and P. Hamm, “Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy,” Opt. Lett. |

28. | 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. Express |

29. | J. A. Myers, K. L. Lewis, P. F. Tekavec, and J. P. Ogilvie, “Two-color two-dimensional fourier transform electronic spectroscopy with a pulse-shaper,” Opt. Express |

30. | 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. |

31. | 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,” Science |

32. | D. Keusters, H.-S. Tan, and W. S. Warren, “Role of pulse phase and direction in two-dimensional optical spectroscopy,” J. Phys. Chem. A |

33. | P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science |

34. | C. Li, W. Wagner, M. Ciocca, and W. S. Warren, “Multiphoton femtosecond phase-coherent two-dimensional electronic spectroscopy,” J. Chem. Phys. |

35. | 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. |

36. | Mention of commercial products is for information only ; it does not imply NIST recommendation or endorsment, nor does it imply that the products mentioned are necessarily the best available for the purpose. |

37. | S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. |

38. | 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. |

39. | 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. |

40. | D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,” Phys. Rev. Lett. |

41. | F. W. King, |

42. | J. G. Graeme, |

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

44. | 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,” Nature |

45. | 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. B |

46. | 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,” Science |

47. | J. Wang, M. S. Gudiksen, X. Duan, Y. Cui, and C. M. Lieber, “Highly polarized photoluminescence and photodetection from single indium phosphide nanowires,” Science |

48. | 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. |

49. | 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. Photonics |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(300.6250) Spectroscopy : Spectroscopy, condensed matter

(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: September 17, 2013

Revised Manuscript: November 1, 2013

Manuscript Accepted: November 2, 2013

Published: November 13, 2013

**Citation**

Gaël Nardin, Travis M. Autry, Kevin L. Silverman, and S. T. Cundiff, "Multidimensional coherent photocurrent spectroscopy of a semiconductor nanostructure," Opt. Express **21**, 28617-28627 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28617

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### References

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- 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]
- 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]

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