Abstract

By combining phase-modulated nonlinear spectroscopy with second harmonic generation, the concept of phase-modulated harmonic light spectroscopy is introduced. Simultaneous spectroscopy with different harmonics of the light is demonstrated and linear and nonlinear excitation of the spectroscopic sample is investigated. Sum frequency generation and stray light effects during temporal pulse overlap have been evaluated in detail, accompanied by simulations. The presented work provides a promising concept to facilitate coherent nonlinear time-domain spectroscopy in the extreme ultraviolet wavelength regime and contributes valuable insights for future studies in this direction.

© 2017 Optical Society of America

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  44. Phasing of 1H data was done as in [30]. For higher harmonic data, the frequency dependent phase shift of detection electronics was corrected in addition. More details will be published elsewhere.
  45. Y. Zhang, D. Healion, J. D. Biggs, and S. Mukamel, “Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy,” J. Chem. Phys. 138, 144301 (2013).
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    [Crossref]
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    [Crossref] [PubMed]

2016 (4)

K. C. Prince, E. Allaria, C. Callegari, R. Cucini, G. D. Ninno, S. D. Mitri, B. Diviacco, E. Ferrari, P. Finetti, D. Gauthier, L. Giannessi, N. Mahne, G. Penco, O. Plekan, L. Raimondi, P. Rebernik, E. Roussel, C. Svetina, M. Trovò, M. Zangrando, M. Negro, P. Carpeggiani, M. Reduzzi, G. Sansone, A. N. Grum-Grzhimailo, E. V. Gryzlova, S. I. Strakhova, K. Bartschat, N. Douguet, J. Venzke, D. Iablonskyi, Y. Kumagai, T. Takanashi, K. Ueda, A. Fischer, M. Coreno, F. Stienkemeier, Y. Ovcharenko, T. Mazza, and M. Meyer, “Coherent control with a short-wavelength free-electron laser,” Nat. Photonics 10, 176–179 (2016).
[Crossref]

D. Gauthier, P. R. Ribič, G. De Ninno, E. Allaria, P. Cinquegrana, M. B. Danailov, A. Demidovich, E. Ferrari, and L. Giannessi, “Generation of phase-locked pulses from a seeded free-electron laser,” Phys. Rev. Lett. 116, 024801 (2016).
[Crossref] [PubMed]

K. J. Karki, L. Kringle, A. H. Marcus, and T. Pullerits, “Phase-synchronous detection of coherent and incoherent nonlinear signals,” J. Opt. 18, 015504 (2016).
[Crossref]

O. Schepp, A. Baumann, D. Rompotis, T. Gebert, A. Azima, M. Wieland, and M. Drescher, “Tracing few-femtosecond photodissociation dynamics on molecular oxygen with a single-color pump-probe scheme in the VUV,” Phys. Rev. A 94, 033411 (2016).
[Crossref]

2015 (5)

F. D. Fuller and J. P. Ogilvie, “Experimental implementations of two-dimensional Fourier transform electronic spectroscopy,” Annu. Rev. Phys. Chem. 66, 667–690 (2015).
[Crossref] [PubMed]

L. Bruder, M. Mudrich, and F. Stienkemeier, “Phase-modulated electronic wave packet interferometry reveals high resolution spectra of free Rb atoms and Rb*He molecules,” Phys. Chem. Chem. Phys. 17, 23877–23885 (2015).
[Crossref] [PubMed]

L. Bruder, M. Binz, and F. Stienkemeier, “Efficient isolation of multiphoton processes and detection of collective resonances in dilute samples,” Phys. Rev. A 92, 053412 (2015).
[Crossref]

D. Gauthier, P. R. Ribič, G. De Ninno, E. Allaria, P. Cinquegrana, M. B. Danailov, A. Demidovich, E. Ferrari, L. Giannessi, B. Mahieu, and G. Penco, “Spectrotemporal shaping of seeded free-electron laser pulses,” Phys. Rev. Lett. 115, 114801 (2015).
[Crossref] [PubMed]

F. Bencivenga, R. Cucini, F. Capotondi, A. Battistoni, R. Mincigrucci, E. Giangrisostomi, A. Gessini, M. Manfredda, I. P. Nikolov, E. Pedersoli, E. Principi, C. Svetina, P. Parisse, F. Casolari, M. B. Danailov, M. Kiskinova, and C. Masciovecchio, “Four-wave mixing experiments with extreme ultraviolet transient gratings,” Nature 520, 205–208 (2015).
[Crossref] [PubMed]

2014 (5)

C. Benko, T. K. Allison, A. Cingöz, L. Hua, F. Labaye, D. C. Yost, and J. Ye, “Extreme ultraviolet radiation with coherence time greater than 1 s,” Nat. Photonics 8, 530–536 (2014).
[Crossref]

T. Gebert, D. Rompotis, M. Wieland, F. Karimi, A. Azima, and M. Drescher, “Michelson-type all-reflective interferometric autocorrelation in the VUV regime,” New J. Phys. 16, 073047 (2014).
[Crossref]

K. J. Karki, J. R. Widom, J. Seibt, I. Moody, M. C. Lonergan, T. Pullerits, and A. H. Marcus, “Coherent two-dimensional photocurrent spectroscopy in a PbS quantum dot photocell,” Nat. Commun. 5, 5869 (2014).
[Crossref] [PubMed]

J. Réhault, M. Maiuri, A. Oriana, and G. Cerullo, “Two-dimensional electronic spectroscopy with birefringent wedges,” Rev. Sci. Instrum. 85, 123107 (2014).
[Crossref]

Y.-H. Lai, S.-Y. Lee, C.-F. Chang, Y.-H. Cheng, and C.-K. Sun, “Nonlinear photoacoustic microscopy via a loss modulation technique: from detection to imaging,” Opt. Express 22, 525–536 (2014).
[Crossref] [PubMed]

2013 (4)

G. Nardin, T. M. Autry, K. L. Silverman, and S. T. Cundiff, “Multidimensional coherent photocurrent spectroscopy of a semiconductor nanostructure,” Opt. Express 21, 28617–28627 (2013).
[Crossref]

Y. Zhang, D. Healion, J. D. Biggs, and S. Mukamel, “Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy,” J. Chem. Phys. 138, 144301 (2013).
[Crossref] [PubMed]

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]

S. Mukamel, D. Healion, Y. Zhang, and J. D. Biggs, “Multidimensional attosecond resonant X-ray spectroscopy of molecules: Lessons from the optical regime,” Annu. Rev. Phys. Chem. 64, 101–127 (2013).
[Crossref]

2012 (1)

X. Dai, M. Richter, H. Li, A. D. Bristow, C. Falvo, S. Mukamel, and S. T. Cundiff, “Two-dimensional double-quantum spectra reveal collective resonances in an atomic vapor,” Phys. Rev. Lett. 108, 193201 (2012).
[Crossref] [PubMed]

2011 (4)

G. S. Schlau-Cohen, A. Ishizaki, and G. R. Fleming, “Two-dimensional electronic spectroscopy and photosynthesis: Fundamentals and applications to photosynthetic light-harvesting,” Chem. Phys. 386, 1–22 (2011).
[Crossref]

D. B. Turner, K. W. Stone, K. Gundogdu, and K. A. Nelson, “Invited Article: The coherent optical laser beam recombination technique (COLBERT) spectrometer: Coherent multidimensional spectroscopy made easier,” Rev. Sci. Instrum. 82, 081301 (2011).
[Crossref] [PubMed]

G. A. Lott, A. Perdomo-Ortiz, J. K. Utterback, J. R. Widom, A. Aspuru-Guzik, and A. H. Marcus, “Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2d fluorescence spectroscopy,” PNAS 108, 16521–16526 (2011).
[Crossref] [PubMed]

P. Tzallas, E. Skantzakis, L. a. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
[Crossref]

2010 (2)

Y. H. Jiang, T. Pfeifer, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, K. U. Kühnel, M. Lezius, M. F. Kling, X. Liu, K. Ueda, S. Düsterer, R. Treusch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Temporal coherence effects in multiple ionization of N2 via XUV pump-probe autocorrelation,” Phys. Rev. A 82, 041403 (2010).
[Crossref]

F. Sorgenfrei, W. F. Schlotter, T. Beeck, M. Nagasono, S. Gieschen, H. Meyer, A. Föhlisch, M. Beye, and W. Wurth, “The extreme ultraviolet split and femtosecond delay unit at the plane grating monochromator beamline PG2 at FLASH,” Rev. Sci. Instrum. 81, 043107 (2010).
[Crossref] [PubMed]

2009 (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]

2008 (2)

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

H.-S. Tan, “Theory and phase-cycling scheme selection principles of collinear phase coherent multi-dimensional optical spectroscopy,” J. Chem. Phys. 129, 124501 (2008).
[Crossref] [PubMed]

2007 (3)

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]

J. C. Vaughan, T. Hornung, K. W. Stone, and K. A. Nelson, “Coherently controlled ultrafast four-wave mixing spectroscopy,” J. Phys. Chem. A 111, 4873–4883 (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)

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]

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]

2005 (2)

M. Kovačev, S. V. Fomichev, E. Priori, Y. Mairesse, H. Merdji, P. Monchicourt, P. Breger, J. Norin, A. Persson, A. L’Huillier, C.-G. Wahlström, B. Carré, and P. Salières, “Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics,” Phys. Rev. Lett. 95, 223903 (2005).
[Crossref]

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]

2004 (1)

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

2003 (2)

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

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

2002 (1)

1999 (2)

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
[Crossref]

P. Salières, L. Le Déroff, T. Auguste, P. Monot, P. d’Oliveira, D. Campo, J.-F. Hergott, H. Merdji, and B. Carré, “Frequency-domain interferometry in the XUV with high-order harmonics,” Phys. Rev. Lett. 83, 5483–5486 (1999).
[Crossref]

1997 (1)

R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
[Crossref]

1995 (1)

W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute—solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
[Crossref]

1991 (1)

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: Time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[Crossref]

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P. Tzallas, E. Skantzakis, L. a. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
[Crossref]

Ueda, K.

K. C. Prince, E. Allaria, C. Callegari, R. Cucini, G. D. Ninno, S. D. Mitri, B. Diviacco, E. Ferrari, P. Finetti, D. Gauthier, L. Giannessi, N. Mahne, G. Penco, O. Plekan, L. Raimondi, P. Rebernik, E. Roussel, C. Svetina, M. Trovò, M. Zangrando, M. Negro, P. Carpeggiani, M. Reduzzi, G. Sansone, A. N. Grum-Grzhimailo, E. V. Gryzlova, S. I. Strakhova, K. Bartschat, N. Douguet, J. Venzke, D. Iablonskyi, Y. Kumagai, T. Takanashi, K. Ueda, A. Fischer, M. Coreno, F. Stienkemeier, Y. Ovcharenko, T. Mazza, and M. Meyer, “Coherent control with a short-wavelength free-electron laser,” Nat. Photonics 10, 176–179 (2016).
[Crossref]

Y. H. Jiang, T. Pfeifer, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, K. U. Kühnel, M. Lezius, M. F. Kling, X. Liu, K. Ueda, S. Düsterer, R. Treusch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Temporal coherence effects in multiple ionization of N2 via XUV pump-probe autocorrelation,” Phys. Rev. A 82, 041403 (2010).
[Crossref]

Ullrich, J.

Y. H. Jiang, T. Pfeifer, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, K. U. Kühnel, M. Lezius, M. F. Kling, X. Liu, K. Ueda, S. Düsterer, R. Treusch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Temporal coherence effects in multiple ionization of N2 via XUV pump-probe autocorrelation,” Phys. Rev. A 82, 041403 (2010).
[Crossref]

Utterback, J. K.

G. A. Lott, A. Perdomo-Ortiz, J. K. Utterback, J. R. Widom, A. Aspuru-Guzik, and A. H. Marcus, “Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2d fluorescence spectroscopy,” PNAS 108, 16521–16526 (2011).
[Crossref] [PubMed]

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, 625–628 (2005).
[Crossref] [PubMed]

Vaughan, J. C.

J. C. Vaughan, T. Hornung, K. W. Stone, and K. A. Nelson, “Coherently controlled ultrafast four-wave mixing spectroscopy,” J. Phys. Chem. A 111, 4873–4883 (2007).
[Crossref] [PubMed]

Venzke, J.

K. C. Prince, E. Allaria, C. Callegari, R. Cucini, G. D. Ninno, S. D. Mitri, B. Diviacco, E. Ferrari, P. Finetti, D. Gauthier, L. Giannessi, N. Mahne, G. Penco, O. Plekan, L. Raimondi, P. Rebernik, E. Roussel, C. Svetina, M. Trovò, M. Zangrando, M. Negro, P. Carpeggiani, M. Reduzzi, G. Sansone, A. N. Grum-Grzhimailo, E. V. Gryzlova, S. I. Strakhova, K. Bartschat, N. Douguet, J. Venzke, D. Iablonskyi, Y. Kumagai, T. Takanashi, K. Ueda, A. Fischer, M. Coreno, F. Stienkemeier, Y. Ovcharenko, T. Mazza, and M. Meyer, “Coherent control with a short-wavelength free-electron laser,” Nat. Photonics 10, 176–179 (2016).
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Wagner, W.

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

M. Kovačev, S. V. Fomichev, E. Priori, Y. Mairesse, H. Merdji, P. Monchicourt, P. Breger, J. Norin, A. Persson, A. L’Huillier, C.-G. Wahlström, B. Carré, and P. Salières, “Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics,” Phys. Rev. Lett. 95, 223903 (2005).
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R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
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Warren, W. S.

C. Li, W. Wagner, M. Ciocca, and W. S. Warren, “Multiphoton femtosecond phase-coherent two-dimensional electronic spectroscopy,” J. Chem. Phys. 126, 164307 (2007).
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P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
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P. Tian and W. S. Warren, “Ultrafast measurement of two-photon absorption by loss modulation,” Opt. Lett. 27, 1634–1636 (2002).
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Widom, J. R.

K. J. Karki, J. R. Widom, J. Seibt, I. Moody, M. C. Lonergan, T. Pullerits, and A. H. Marcus, “Coherent two-dimensional photocurrent spectroscopy in a PbS quantum dot photocell,” Nat. Commun. 5, 5869 (2014).
[Crossref] [PubMed]

G. A. Lott, A. Perdomo-Ortiz, J. K. Utterback, J. R. Widom, A. Aspuru-Guzik, and A. H. Marcus, “Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2d fluorescence spectroscopy,” PNAS 108, 16521–16526 (2011).
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Wieland, M.

O. Schepp, A. Baumann, D. Rompotis, T. Gebert, A. Azima, M. Wieland, and M. Drescher, “Tracing few-femtosecond photodissociation dynamics on molecular oxygen with a single-color pump-probe scheme in the VUV,” Phys. Rev. A 94, 033411 (2016).
[Crossref]

T. Gebert, D. Rompotis, M. Wieland, F. Karimi, A. Azima, and M. Drescher, “Michelson-type all-reflective interferometric autocorrelation in the VUV regime,” New J. Phys. 16, 073047 (2014).
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W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute—solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
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F. Sorgenfrei, W. F. Schlotter, T. Beeck, M. Nagasono, S. Gieschen, H. Meyer, A. Föhlisch, M. Beye, and W. Wurth, “The extreme ultraviolet split and femtosecond delay unit at the plane grating monochromator beamline PG2 at FLASH,” Rev. Sci. Instrum. 81, 043107 (2010).
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Ye, J.

C. Benko, T. K. Allison, A. Cingöz, L. Hua, F. Labaye, D. C. Yost, and J. Ye, “Extreme ultraviolet radiation with coherence time greater than 1 s,” Nat. Photonics 8, 530–536 (2014).
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Yost, D. C.

C. Benko, T. K. Allison, A. Cingöz, L. Hua, F. Labaye, D. C. Yost, and J. Ye, “Extreme ultraviolet radiation with coherence time greater than 1 s,” Nat. Photonics 8, 530–536 (2014).
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K. C. Prince, E. Allaria, C. Callegari, R. Cucini, G. D. Ninno, S. D. Mitri, B. Diviacco, E. Ferrari, P. Finetti, D. Gauthier, L. Giannessi, N. Mahne, G. Penco, O. Plekan, L. Raimondi, P. Rebernik, E. Roussel, C. Svetina, M. Trovò, M. Zangrando, M. Negro, P. Carpeggiani, M. Reduzzi, G. Sansone, A. N. Grum-Grzhimailo, E. V. Gryzlova, S. I. Strakhova, K. Bartschat, N. Douguet, J. Venzke, D. Iablonskyi, Y. Kumagai, T. Takanashi, K. Ueda, A. Fischer, M. Coreno, F. Stienkemeier, Y. Ovcharenko, T. Mazza, and M. Meyer, “Coherent control with a short-wavelength free-electron laser,” Nat. Photonics 10, 176–179 (2016).
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Zerne, R.

R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
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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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S. Mukamel, D. Healion, Y. Zhang, and J. D. Biggs, “Multidimensional attosecond resonant X-ray spectroscopy of molecules: Lessons from the optical regime,” Annu. Rev. Phys. Chem. 64, 101–127 (2013).
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Y. Zhang, D. Healion, J. D. Biggs, and S. Mukamel, “Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy,” J. Chem. Phys. 138, 144301 (2013).
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F. D. Fuller and J. P. Ogilvie, “Experimental implementations of two-dimensional Fourier transform electronic spectroscopy,” Annu. Rev. Phys. Chem. 66, 667–690 (2015).
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W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute—solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
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M. Cho, “Coherent two-dimensional optical spectroscopy,” Chem. Rev. 108, 1331–1418 (2008).
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N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: Time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
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C. Li, W. Wagner, M. Ciocca, and W. S. Warren, “Multiphoton femtosecond phase-coherent two-dimensional electronic spectroscopy,” J. Chem. Phys. 126, 164307 (2007).
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H.-S. Tan, “Theory and phase-cycling scheme selection principles of collinear phase coherent multi-dimensional optical spectroscopy,” J. Chem. Phys. 129, 124501 (2008).
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Y. Zhang, D. Healion, J. D. Biggs, and S. Mukamel, “Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy,” J. Chem. Phys. 138, 144301 (2013).
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J. Opt. (1)

K. J. Karki, L. Kringle, A. H. Marcus, and T. Pullerits, “Phase-synchronous detection of coherent and incoherent nonlinear signals,” J. Opt. 18, 015504 (2016).
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J. Phys. Chem. A (1)

J. C. Vaughan, T. Hornung, K. W. Stone, and K. A. Nelson, “Coherently controlled ultrafast four-wave mixing spectroscopy,” J. Phys. Chem. A 111, 4873–4883 (2007).
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Nat Commun (1)

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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Nat. Commun. (1)

K. J. Karki, J. R. Widom, J. Seibt, I. Moody, M. C. Lonergan, T. Pullerits, and A. H. Marcus, “Coherent two-dimensional photocurrent spectroscopy in a PbS quantum dot photocell,” Nat. Commun. 5, 5869 (2014).
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Nat. Photonics (2)

K. C. Prince, E. Allaria, C. Callegari, R. Cucini, G. D. Ninno, S. D. Mitri, B. Diviacco, E. Ferrari, P. Finetti, D. Gauthier, L. Giannessi, N. Mahne, G. Penco, O. Plekan, L. Raimondi, P. Rebernik, E. Roussel, C. Svetina, M. Trovò, M. Zangrando, M. Negro, P. Carpeggiani, M. Reduzzi, G. Sansone, A. N. Grum-Grzhimailo, E. V. Gryzlova, S. I. Strakhova, K. Bartschat, N. Douguet, J. Venzke, D. Iablonskyi, Y. Kumagai, T. Takanashi, K. Ueda, A. Fischer, M. Coreno, F. Stienkemeier, Y. Ovcharenko, T. Mazza, and M. Meyer, “Coherent control with a short-wavelength free-electron laser,” Nat. Photonics 10, 176–179 (2016).
[Crossref]

C. Benko, T. K. Allison, A. Cingöz, L. Hua, F. Labaye, D. C. Yost, and J. Ye, “Extreme ultraviolet radiation with coherence time greater than 1 s,” Nat. Photonics 8, 530–536 (2014).
[Crossref]

Nat. Phys. (1)

P. Tzallas, E. Skantzakis, L. a. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
[Crossref]

Nature (2)

F. Bencivenga, R. Cucini, F. Capotondi, A. Battistoni, R. Mincigrucci, E. Giangrisostomi, A. Gessini, M. Manfredda, I. P. Nikolov, E. Pedersoli, E. Principi, C. Svetina, P. Parisse, F. Casolari, M. B. Danailov, M. Kiskinova, and C. Masciovecchio, “Four-wave mixing experiments with extreme ultraviolet transient gratings,” Nature 520, 205–208 (2015).
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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).
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New J. Phys. (1)

T. Gebert, D. Rompotis, M. Wieland, F. Karimi, A. Azima, and M. Drescher, “Michelson-type all-reflective interferometric autocorrelation in the VUV regime,” New J. Phys. 16, 073047 (2014).
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Opt. Express (2)

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

L. Bruder, M. Mudrich, and F. Stienkemeier, “Phase-modulated electronic wave packet interferometry reveals high resolution spectra of free Rb atoms and Rb*He molecules,” Phys. Chem. Chem. Phys. 17, 23877–23885 (2015).
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Phys. Rev. A (3)

L. Bruder, M. Binz, and F. Stienkemeier, “Efficient isolation of multiphoton processes and detection of collective resonances in dilute samples,” Phys. Rev. A 92, 053412 (2015).
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Y. H. Jiang, T. Pfeifer, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, K. U. Kühnel, M. Lezius, M. F. Kling, X. Liu, K. Ueda, S. Düsterer, R. Treusch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Temporal coherence effects in multiple ionization of N2 via XUV pump-probe autocorrelation,” Phys. Rev. A 82, 041403 (2010).
[Crossref]

O. Schepp, A. Baumann, D. Rompotis, T. Gebert, A. Azima, M. Wieland, and M. Drescher, “Tracing few-femtosecond photodissociation dynamics on molecular oxygen with a single-color pump-probe scheme in the VUV,” Phys. Rev. A 94, 033411 (2016).
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Phys. Rev. Lett. (7)

X. Dai, M. Richter, H. Li, A. D. Bristow, C. Falvo, S. Mukamel, and S. T. Cundiff, “Two-dimensional double-quantum spectra reveal collective resonances in an atomic vapor,” Phys. Rev. Lett. 108, 193201 (2012).
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D. Gauthier, P. R. Ribič, G. De Ninno, E. Allaria, P. Cinquegrana, M. B. Danailov, A. Demidovich, E. Ferrari, L. Giannessi, B. Mahieu, and G. Penco, “Spectrotemporal shaping of seeded free-electron laser pulses,” Phys. Rev. Lett. 115, 114801 (2015).
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R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
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P. Salières, L. Le Déroff, T. Auguste, P. Monot, P. d’Oliveira, D. Campo, J.-F. Hergott, H. Merdji, and B. Carré, “Frequency-domain interferometry in the XUV with high-order harmonics,” Phys. Rev. Lett. 83, 5483–5486 (1999).
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M. Kovačev, S. V. Fomichev, E. Priori, Y. Mairesse, H. Merdji, P. Monchicourt, P. Breger, J. Norin, A. Persson, A. L’Huillier, C.-G. Wahlström, B. Carré, and P. Salières, “Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics,” Phys. Rev. Lett. 95, 223903 (2005).
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D. Gauthier, P. R. Ribič, G. De Ninno, E. Allaria, P. Cinquegrana, M. B. Danailov, A. Demidovich, E. Ferrari, and L. Giannessi, “Generation of phase-locked pulses from a seeded free-electron laser,” Phys. Rev. Lett. 116, 024801 (2016).
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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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PNAS (1)

G. A. Lott, A. Perdomo-Ortiz, J. K. Utterback, J. R. Widom, A. Aspuru-Guzik, and A. H. Marcus, “Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2d fluorescence spectroscopy,” PNAS 108, 16521–16526 (2011).
[Crossref] [PubMed]

Rev. Sci. Instrum. (4)

F. Sorgenfrei, W. F. Schlotter, T. Beeck, M. Nagasono, S. Gieschen, H. Meyer, A. Föhlisch, M. Beye, and W. Wurth, “The extreme ultraviolet split and femtosecond delay unit at the plane grating monochromator beamline PG2 at FLASH,” Rev. Sci. Instrum. 81, 043107 (2010).
[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).
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Science (1)

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300, 1553–1555 (2003).
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Other (3)

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University, 1995).

Phasing of 1H data was done as in [30]. For higher harmonic data, the frequency dependent phase shift of detection electronics was corrected in addition. More details will be published elsewhere.

A Kramida, Yu Ralchenko, J Reader, and ASD NIST Team, “NIST Atomic Spectra Database,” (ver. 5.3),” [Online]. Available: http://physics.nist.gov/asd [2015, July 21]. National Institute of Standards and Technology, Gaithersburg, MD. (2014).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of the optical setup. Collinear phase-modulated pump-probe pulses of the fundamental frequency are generated in an optical interferometer. A nonlinear crystal (NLC) followed by an optical filter is placed behind the interferometer to generate collinear second harmonic pulses. A monochromator is used to construct the reference signal for harmonic lock-in demodulation of the fluorescence signal. (b) Harmonic lock-in detection scheme using an external reference signal.
Fig. 2
Fig. 2 (a) Model three-level system with one- and two-photon transition. (b) Collinear pump-probe pulses induce second harmonic pulses in a nonlinear crystal (NLC). SHG1 and SHG2 denote the SHG pulses of individual incident pump and probe pulses and SFG denotes the SFG pulse occurring during pump-probe overlap. (c) Double-sided Feynman diagrams for SQC and DQC pathways involving interactions with one SHG pump and probe pulse (1 and 2) and for interactions with the SFG and either of the SHG pulses (3 and 4).
Fig. 3
Fig. 3 Obtained signals for first and second harmonic laser pulses exciting an alkali-metal vapor mixture containing potassium (K), rubidium (Rb) and cesium (Cs). (a) shows the relevant NIR and UV transitions in the alkali atoms. (b)-(e) show the first and second harmonic time- and frequency-domain data, denoted 1H, 2H TD and 1H, 2H FD, respectively. Black dashed lines indicate transitions frequencies taken from [42].
Fig. 4
Fig. 4 Excitation of the 5S1/2 → 6P3/2,1/2 transitions in a rubidium vapor for the laser wavelength 420.8 nm (23764 cm−1). The excitation scheme is shown in (a). (c), (e) show the time domain data for 2H and 1H lock-in demodulation and (b), (d), (f) the discrete Fourier transforms of 4H, 2H and 1H signals. In (b) the collective excitation 5S1/2 →6P3/2 and 5S1/2 → 6P1/2 is hidden in the noise floor. Black dashed lines show transition frequencies taken from [42].
Fig. 5
Fig. 5 Excitation of the 5S1/2 → 6P3/2,1/2 transitions in a rubidium vapor for laser center wavelengths between 417.8 and 424.2 nm. (a) shows the second harmonic time-domain (2H TD) data and (b) and (c) show the second (2H FD) and first harmonic (1H FD) frequency-domain spectra. In (a), oscillation frequencies differ among data runs which is due to changes of the monochromator wavelength. In (c), simulated signals are included as discussed in the text. Gray vertical lines indicate the laser center frequency and black dashed lines show transition frequencies taken from [42].

Equations (10)

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S n ( t , τ ) = A n [ 1 + β cos ( ω n g τ ϕ 21 ( t ) ) ] ,
R ( τ , t ) = R 0 [ 1 + β cos ( ω ref τ Ω 21 t ) ] ,
R n ( t , τ ) cos ( n ω ref τ n Ω 21 t ) ] .
S ( τ ) = A n β cos [ ( ω n g n ω ref ) τ ] .
S 1 QSHG | μ e g | 2 2 E ˜ 2 ( ω e g ) cos ( ω e g τ 2 Ω 21 t ) ,
S 2 QSHG | μ e g | 2 | μ f e | 2 4 E ˜ 2 ( ω e g ) E ˜ 2 ( ω f e ) cos ( ω f g τ 4 Ω 21 t ) ,
S 1 QSFG | μ e g | 2 2 g ( τ , 2 Δ t ) E ˜ 2 ( ω e g ) cos ( ω e g τ / 2 Ω 21 t ) ,
S 2 QSFG | μ e g | 2 | μ f e | 2 4 g ( τ , Δ t ) E ˜ 2 ( ω e g ) E ˜ 2 ( ω f e ) cos ( ω f g τ / 2 2 Ω 21 t ) .
S CC ( τ , t ) = ( A 1 3 A 2 + A 1 A 2 3 ) π 4 ln 2 Δ t g ( τ , 2 3 Δ t ) cos [ ω 0 τ Ω 21 t ] ,
S AC ( τ , t ) = A 1 2 A 2 2 2 π 4 ln 2 Δ t g ( τ , Δ t ) cos [ 2 ω 0 τ Ω 21 t ] ,

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