Skip to main content
SpringerLink
Log in

Probing Nonlinear Light–Matter Interaction in Momentum Space: Coherent Multiphoton Photoemission Spectroscopy

  • Chapter
  • First Online:
Nonlinear X-Ray Spectroscopy for Materials Science

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 246))

  • 251 Accesses

Abstract

Optical fields interacting with metal surfaces can drive collective free electron plasma currents and single-particle dipole excitations. The outcome of these coherent interactions is immediately evident in nearly perfect images that appear in metal mirrors. Yet, performing quantum state-resolved measurements and electronic charge/spin actuations of metals is extremely challenging because of interaction-driven decoherence of the polarization of the electronic system. In this chapter, we describe interferometrically time-resolved multiphoton photoemission spectroscopy as a quantum state-resolved method for investigating coherent responses of solids. We perform 3D (energy, momentum, and time)-resolved nonlinear photoelectron spectroscopy to record the coherent response of single crystal surfaces with attosecond accuracy. The measurements resolve the coherent polarization oscillations in response to the driving light field, the resonant frequencies of the metal sample, and the optical field-induced dressing of the electronic band structure. As a model system, we focus on the coherent responses of single crystal silver and copper surfaces to intense ~20 fs laser pulses in the IR-UV spectral range. Noble metals provide well-known band structures, deeply studied attosecond collective responses, and simple surface preparation methods that guide the development of experimental and theoretical extension of coherent nonlinear photoemission spectroscopy to more complex materials. To photoexcite electrons above the vacuum level in a nonlinear manner, the excitation creates Floquet ladders of quasi-energy states up to fifth order in the driving light field, including signatures of above threshold photoemission. Finally, we show that at high driving field amplitudes, electrons follow both the space and optical field-dependent periodic potentials causing non-perturbative modifications of metal crystal electronic structures. Hence, nonlinear interferometric photoelectron spectroscopy enables to quantify, as well as to transiently modify, the coherent responses of solid-state materials.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. D.N. Basov, R.D. Averitt, D. Hsieh, Towards properties on demand in quantum materials. Nat. Mater. 16, 1077 (2017)

    Article  ADS  Google Scholar 

  2. A. de la Torre, D.M. Kennes, M. Claassen, S. Gerber, J.W. McIver, M.A. Sentef, Colloquium: nonthermal pathways to ultrafast control in quantum materials. Rev. Mod. Phys. 93, 041002 (2021)

    Article  ADS  Google Scholar 

  3. D. Fausti et al., Light-induced superconductivity in a stripe-ordered cuprate. Science 331, 189 (2011)

    Article  ADS  Google Scholar 

  4. T. Rohwer et al., Collapse of long-range charge order tracked by time-resolved photoemission at high momenta. Nature 471, 490 (2011)

    Article  ADS  Google Scholar 

  5. C.W. Nicholson, A. Lücke, W.G. Schmidt, M. Puppin, L. Rettig, R. Ernstorfer, M. Wolf, Beyond the molecular movie: Dynamics of bands and bonds during a photoinduced phase transition. Science 362, 821 (2018)

    Article  ADS  Google Scholar 

  6. F. Schmitt et al., Transient electronic structure and melting of a charge density wave in TbTe3. Science 321, 1649 (2008)

    Article  ADS  Google Scholar 

  7. L. Stojchevska, I. Vaskivskyi, T. Mertelj, P. Kusar, D. Svetin, S. Brazovskii, D. Mihailovic, Ultrafast switching to a stable hidden quantum state in an electronic crystal. Science 344, 177 (2014)

    Article  ADS  Google Scholar 

  8. E.J. Sie et al., An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61 (2019)

    Article  ADS  Google Scholar 

  9. F. Mahmood, C.-K. Chan, Z. Alpichshev, D. Gardner, Y. Lee, P.A. Lee, N. Gedik, Selective scattering between Floquet-Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306 (2016)

    Article  Google Scholar 

  10. J.W. McIver, B. Schulte, F.U. Stein, T. Matsuyama, G. Jotzu, G. Meier, A. Cavalleri, Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38 (2020)

    Article  Google Scholar 

  11. M. Reutzel, A. Li, Z. Wang, H. Petek, Coherent multidimensional photoelectron spectroscopy of ultrafast quasiparticle dressing by light. Nat. Commun. 11, 2230 (2020)

    Article  ADS  Google Scholar 

  12. S. Zhou et al., Pseudospin-selective Floquet band engineering in black phosphorus. Nature 614, 75 (2023)

    Article  ADS  Google Scholar 

  13. T. Frigge et al., Optically excited structural transition in atomic wires on surfaces at the quantum limit. Nature 544, 207 (2017)

    Article  ADS  Google Scholar 

  14. J.G. Horstmann, H. Böckmann, B. Wit, F. Kurtz, G. Storeck, C. Ropers, Coherent control of a surface structural phase transition. Nature 583, 232 (2020)

    Article  ADS  Google Scholar 

  15. M. Düvel et al., Far-from-equilibrium electron–phonon interactions in optically excited graphene. Nano Lett. 22, 4897 (2022)

    Article  ADS  Google Scholar 

  16. A. Kogar et al., Light-induced charge density wave in LaTe3. Nat. Phys. 16, 159 (2020)

    Article  Google Scholar 

  17. A. Zong, B.R. Nebgen, S.-C. Lin, J.A. Spies, M. Zuerch, Emerging ultrafast techniques for studying quantum materials. Nat. Rev. Mater. 8, 224 (2023)

    Article  ADS  Google Scholar 

  18. J.A. Sobota, Y. He, Z.-X. Shen, Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021)

    Article  ADS  Google Scholar 

  19. D. Filippetto, P. Musumeci, R.K. Li, B.J. Siwick, M.R. Otto, M. Centurion, J.P.F. Nunes, Ultrafast electron diffraction: visualizing dynamic states of matter. Rev. Mod. Phys. 94, 045004 (2022)

    Article  ADS  Google Scholar 

  20. S. Ghimire, D.A. Reis, High-harmonic generation from solids. Nat. Phys. 15, 10 (2019)

    Article  Google Scholar 

  21. S. Ghimire, A.D. DiChiara, E. Sistrunk, P. Agostini, L.F. DiMauro, D.A. Reis, Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138 (2011)

    Article  Google Scholar 

  22. F. Langer et al., Lightwave-driven quasiparticle collisions on a subcycle timescale. Nature 533, 225 (2016)

    Article  ADS  Google Scholar 

  23. C.P. Schmid et al., Tunable non-integer high-harmonic generation in a topological insulator. Nature 593, 385 (2021)

    Article  ADS  Google Scholar 

  24. C. Heide et al., Probing topological phase transitions using high-harmonic generation. Nat. Photon. 16, 620 (2022)

    Article  ADS  Google Scholar 

  25. J. Freudenstein et al., Attosecond clocking of correlations between Bloch electrons. Nature 610, 290 (2022)

    Article  ADS  Google Scholar 

  26. A. Damascelli, Probing the electronic structure of complex systems by ARPES. Phys. Scr. T109, 61 (2004)

    Article  ADS  Google Scholar 

  27. M. Reutzel, A. Li, H. Petek, Coherent two-dimensional multiphoton photoelectron spectroscopy of metal surfaces. Phys. Rev. X 9, 011044 (2019)

    Google Scholar 

  28. M. Reutzel, A. Li, H. Petek, Above-threshold multiphoton photoemission from noble metal surfaces. Phys. Rev. B 101, 075409 (2020)

    Article  ADS  Google Scholar 

  29. W.S. Fann, R. Storz, J. Bokor, Observation of above-threshold multiphoton photoelectric emission from image-potential surface states. Phys. Rev. B 44, 10980 (1991)

    Article  ADS  Google Scholar 

  30. M. Aeschlimann, C.A. Schmuttenmaer, H.E. Elsayed-Ali, R.J.D. Miller, J. Cao, Y. Gao, D.A. Mantell, Observation of surface enhanced multiphoton photoemission from metal surfaces in the short pulse limit. J. Chem. Phys. 102, 8606 (1995)

    Article  ADS  Google Scholar 

  31. F. Banfi, C. Giannetti, G. Ferrini, G. Galimberti, S. Pagliara, D. Fausti, F. Parmigiani, Experimental evidence of above-threshold photoemission in solids. Phys. Rev. Lett. 94, 037601 (2005)

    Article  ADS  Google Scholar 

  32. F. Bisio, M. Nývlt, J. Franta, H. Petek, J. Kirschner, Mechanisms of high-order perturbative photoemission from Cu(001). Phys. Rev. Lett. 96, 087601 (2006)

    Article  ADS  Google Scholar 

  33. G. Saathoff, L. Miaja-Avila, M. Aeschlimann, M.M. Murnane, H.C. Kapteyn, Laser-assisted photoemission from surfaces. Phys. Rev. A 77, 022903 (2008)

    Article  ADS  Google Scholar 

  34. F. Bisio, A. Winkelmann, C.-T. Chiang, H. Petek, J. Kirschner, Band structure effects in above threshold photoemission. J. Phys. Condens. Matter 23, 485002 (2011)

    Article  Google Scholar 

  35. F. Sirotti, N. Beaulieu, A. Bendounan, M.G. Silly, C. Chauvet, G. Malinowski, G. Fratesi, V. Véniard, G. Onida, Multiphoton k-resolved photoemission from gold surface states with 800-nm femtosecond laser pulses. Phys. Rev. B 90, 035401 (2014)

    Article  ADS  Google Scholar 

  36. P. Dreher, D. Janoschka, A. Neuhaus, B. Frank, H. Giessen, M. Horn-von Hoegen, F.-J. Meyer zu Heringdorf, Quantitative determination of the electric field strength in a plasmon focus from ponderomotive energy shifts. Nanophotonics 11, 3687 (2022)

    Google Scholar 

  37. R. Bormann, M. Gulde, A. Weismann, S.V. Yalunin, C. Ropers, Tip-enhanced strong-field photoemission. Phys. Rev. Lett. 105, 147601 (2010)

    Article  ADS  Google Scholar 

  38. M. Schenk, M. Kruger, P. Hommelhoff, Strong-field above-threshold photoemission from sharp metal tips. Phys. Rev. Lett. 105, 257601 (2010)

    Article  ADS  Google Scholar 

  39. P. Dombi et al., Strong-field nano-optics. Rev. Mod. Phys. 92, 025003 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  40. M. Merschdorf, W. Pfeiffer, A. Thon, S. Voll, G. Gerber, Stimulated emission induced by exciton–exciton scattering in ZnO/ZnMgO multiquantum wells up to room temperature. Appl. Phys. A 71, 547 (2000)

    Article  ADS  Google Scholar 

  41. P. Dombi, A. Hörl, P. Rácz, I. Márton, A. Trügler, J.R. Krenn, U. Hohenester, Ultrafast strong-field photoemission from plasmonic nanoparticles. Nano Lett. 13, 674 (2013)

    Article  ADS  Google Scholar 

  42. M. Dąbrowski, Y. Dai, H. Petek, Ultrafast microscopy: imaging light with photoelectrons on the nano-femto scale. J. Phys. Chem. Lett. 8, 4446 (2017)

    Article  Google Scholar 

  43. M. Sivis, N. Pazos-Perez, R. Yu, R. Alvarez-Puebla, F.J. García de Abajo, C. Ropers, Continuous-wave multiphoton photoemission from plasmonic nanostars. Commun. Phys. 1, 13 (2018)

    Article  Google Scholar 

  44. A. Li, M. Reutzel, Z. Wang, D. Novko, B. Gumhalter, H. Petek, Plasmonic photoemission from single-crystalline silver. ACS Photon. 8, 247 (2021)

    Article  Google Scholar 

  45. H. Petek, A. Li, X. Li, S. Tan, M. Reutzel, Plasmonic decay into hot electrons in silver. Prog. Surf. Sci. 98, 100707 (2023)

    Google Scholar 

  46. A. Damascelli, Z. Hussain, Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473 (2003)

    Article  ADS  Google Scholar 

  47. H. Zhang, T. Pincelli, C. Jozwiak, T. Kondo, R. Ernstorfer, T. Sato, S. Zhou, Angle-resolved photoemission spectroscopy. Nat. Rev. Methods Primers 2, 54 (2022)

    Article  Google Scholar 

  48. S. Hüfner, Photoelectron Spectroscopy: Principles and Applications (Springer, Berlin, 2003)

    Book  Google Scholar 

  49. M. Reutzel, A. Li, B. Gumhalter, H. Petek, Nonlinear plasmonic photoelectron response of Ag(111). Phys. Rev. Lett. 123, 017404 (2019)

    Article  ADS  Google Scholar 

  50. B. Krömker, M. Escher, D. Funnemann, D. Hartung, H. Engelhard, J. Kirschner, Development of a momentum microscope for time resolved band structure imaging. Rev. Sci. Instrum. 79, 053702 (2008)

    Article  ADS  Google Scholar 

  51. K. Medjanik et al., Direct 3D mapping of the fermi surface and fermi velocity. Nat. Mat. 16, 615 (2017)

    Article  Google Scholar 

  52. A. Li et al., Multidimensional multiphoton momentum microscopy of the anisotropic Ag(110) surface. Phys. Rev. B 105, 075105 (2022)

    Article  ADS  Google Scholar 

  53. M. Keunecke et al., Electromagnetic dressing of the electron energy spectrum of Au(111) at high momenta. Phys. Rev. B 102, 161403 (2020)

    Article  ADS  Google Scholar 

  54. J. Maklar et al., A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments. Rev. Sci. Ins. 91, 123112 (2020)

    Article  ADS  Google Scholar 

  55. B. Schönhense et al., Multidimensional photoemission spectroscopy—the space-charge limit. New J. Phys. 20, 033004 (2018)

    Article  ADS  Google Scholar 

  56. G. Schönhense et al., Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens. Rev. Sci. Instrum. 92, 053703 (2021)

    Article  ADS  Google Scholar 

  57. E. Rotenberg, A. Bostwick, microARPES and nanoARPES at diffraction-limited light sources: opportunities and performance gains. J. Synch. Radiati. 21, 1048 (2014)

    Article  Google Scholar 

  58. K. Giesen, F. Hage, F.J. Himpsel, H.J. Riess, W. Steinmann, Two-photon photoemission via image-potential states. Phys. Rev. Lett. 55, 300 (1985)

    Article  ADS  Google Scholar 

  59. W. Steinmann, Magneto-optical Kerr effect and perpendicular magnetic anisotropy of evaporated and sputtered Co/Pt multilayer structures. Appl. Phys. A 49, 365 (1989)

    Article  ADS  Google Scholar 

  60. H. Petek, S. Ogawa, Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals. Prog. Surf. Sci. 56, 239 (1997)

    Article  ADS  Google Scholar 

  61. M. Wolf, Femtosecond dynamics of electronic excitations at metal surfaces. Surf. Sci. 377–379, 343 (1997)

    Article  ADS  Google Scholar 

  62. M. Bauer, A. Marienfeld, M. Aeschlimann, Hot electron lifetimes in metals probed by time-resolved two-photon photoemission. Prog. Surf. Sci. 90, 319 (2015)

    Article  ADS  Google Scholar 

  63. U. Höfer, I.L. Shumay, C. Reuss, U. Thomann, W. Wallauer, T. Fauster, Time-resolved coherent photoelectron spectroscopy of quantized electronic states on metal surfaces. Science 277, 1480 (1997)

    Article  Google Scholar 

  64. U. Bovensiepen, H. Petek, M. Wolf, Dynamics at Solid State Surfaces and Interfaces, Vol. 1: Current Developments (Wiley-VCH Verlag Gmbh & Co., Weinheim, 2010), Vol. 1: Current developments

    Google Scholar 

  65. U. Bovensiepen, H. Petek, M. Wolf, Dynamics at Solid State Surfaces and Interfaces, Vol. 2: Fundamentals (Wiley-VCH Verlag Gmbh & Co., Weinheim, 2012), Vol. 2: Fundamentals

    Google Scholar 

  66. P.M. Echenique, R. Berndt, E.V. Chulkov, T. Fauster, A. Goldmann, U. Höfer, Decay of electronic excitations at metal surfaces. Surf. Sci. Rep. 52, 219 (2004)

    Article  ADS  Google Scholar 

  67. T. Fauster, M. Weinelt, U. Höfer, Quasi-elastic scattering of electrons in image-potential states. Prog. Surf. Sci. 82, 224 (2007)

    Article  ADS  Google Scholar 

  68. M. Weinelt, Time-resolved two-photon photoemission from metal surfaces. J. Phys. Condens. Matter 14, R1099 (2002)

    Article  ADS  Google Scholar 

  69. D. Schmitt et al., Formation of moiré interlayer excitons in space and time. Nature 608, 499 (2022)

    Article  ADS  Google Scholar 

  70. R. Wallauer et al., Tracing orbital images on ultrafast time scales. Science 371, 1056 (2021)

    Article  ADS  Google Scholar 

  71. J. Madéo et al., Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors. Science 370, 1199 (2020)

    Article  ADS  Google Scholar 

  72. J.C. Johannsen et al., Direct view of hot carrier dynamics in graphene. Phys. Rev. Lett. 111, 027403 (2013)

    Article  ADS  Google Scholar 

  73. I. Gierz et al., Snapshots of non-equilibrium Dirac carrier distributions in graphene. Nat. Mater. 12, 1119 (2013)

    Article  ADS  Google Scholar 

  74. J. Lehmann, M. Merschdorf, W. Pfeiffer, A. Thon, S. Voll, G. Gerber, Surface plasmon dynamics in silver nanoparticles studied by femtosecond time-resolved photoemission. Phys. Rev. Lett. 85, 2921 (2000)

    Article  ADS  Google Scholar 

  75. H. Petek, A.P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, S. Ogawa, Optical phase control of coherent electron dynamics in metals. Phys. Rev. Lett. 79, 4649 (1997)

    Article  ADS  Google Scholar 

  76. X. Cui, C. Wang, A. Argondizzo, S. Garrett-Roe, B. Gumhalter, H. Petek, Transient excitons at metal surfaces. Nat. Phys. 10, 505 (2014)

    Article  Google Scholar 

  77. H. Petek, H. Nagano, S. Ogawa, Hole decoherence of d bands in copper. Phys. Rev. Lett. 83, 832 (1999)

    Article  ADS  Google Scholar 

  78. J. Güdde, M. Rohleder, T. Meier, S.W. Koch, U. Höfer, Time-resolved investigation of coherently controlled electric currents at a metal surface. Science 318, 1287 (2007)

    Article  ADS  Google Scholar 

  79. T. Eul, E. Prinz, M. Hartelt, B. Frisch, M. Aeschlimann, B. Stadtmüller, Coherent response of the electronic system driven by non-interfering laser pulses. Nat. Commun. 13, 3324 (2022)

    Article  ADS  Google Scholar 

  80. M. Bauer, S. Pawlik, M. Aeschlimann, Decay dynamics of photoexcited alkali chemisorbates: real-time investigations in the femtosecond regime. Phys. Rev. B 60, 5016 (1999)

    Article  ADS  Google Scholar 

  81. A. Kubo, N. Pontius, H. Petek, Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface. Nano Lett. 7, 470 (2007)

    Article  ADS  Google Scholar 

  82. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F.J. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, F. Steeb, Adaptive subwavelength control of nano-optical fields. Nature 446, 301 (2007)

    Article  ADS  Google Scholar 

  83. S. Ogawa, H. Nagano, H. Petek, A.P. Heberle, Optical dephasing in Cu(111) measured by interferometric two-photon time-resolved photoemission. Phys. Rev. Lett. 78, 1339 (1997)

    Article  ADS  Google Scholar 

  84. M. Merschdorf, C. Kennerknecht, W. Pfeiffer, Collective and single-particle dynamics in time-resolved two-photon photoemission. Phys. Rev. B 70, 193401 (2004)

    Article  ADS  Google Scholar 

  85. H. Petek, M.J. Weida, H. Nagano, S. Ogawa, Real-time observation of adsorbate atom motion above a metal surface. Science 288, 1402 (2000)

    Article  ADS  Google Scholar 

  86. S. Ogawa, H. Nagano, H. Petek, Phase and energy relaxation in an antibonding surface state: Cs/Cu(111). Phys. Rev. Lett. 82, 1931 (1999)

    Article  ADS  Google Scholar 

  87. M. Aeschlimann et al., Observation of optical coherence in a disordered metal-molecule interface by coherent optical two-dimensional photoelectron spectroscopy. Phys. Rev. B 105, 205415 (2022)

    Article  ADS  Google Scholar 

  88. M. Dabrowski, Y. Dai, H. Petek, Ultrafast photoemission electron microscopy: imaging plasmons in space and time. Chem. Rev. 120, 6247 (2020)

    Article  Google Scholar 

  89. Y. Dai, Z. Zhou, A. Ghosh, R.S.K. Mong, A. Kubo, C.-B. Huang, H. Petek, Plasmonic topological quasiparticle on the nanometre and femtosecond scales. Nature 588, 616 (2020)

    Article  ADS  Google Scholar 

  90. Y. Dai, Z. Zhou, A. Ghosh, S. Yang, C.-B. Huang, H. Petek, Ultrafast nanofemto photoemission electron microscopy of vectorial plasmonic fields. MRS Bull. 46, 738 (2021)

    Article  ADS  Google Scholar 

  91. E. Prinz, M. Hartelt, G. Spektor, M. Orenstein, M. Aeschlimann, Orbital angular momentum in nanoplasmonic vortices. ACS Photon. 10, 340 (2023)

    Article  Google Scholar 

  92. P. Dreher, D. Janoschka, B. Frank, H. Giessen, F.-J. Meyer zu Heringdorf, Focused surface plasmon polaritons coherently couple to electronic states in above-threshold electron emission. Commun. Phys. 6, 15 (2023)

    Google Scholar 

  93. G. Spektor et al., Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices. Science 355, 1187 (2017)

    Article  ADS  Google Scholar 

  94. G. Spektor, D. Kilbane, A.K. Mahro, M. Hartelt, E. Prinz, M. Aeschlimann, M. Orenstein, Mixing the light spin with plasmon orbit by nonlinear light-matter interaction in gold. Phys. Rev. X 9, 021031 (2019)

    Google Scholar 

  95. B. Huber et al., Space- and time-resolved UV-to-NIR surface spectroscopy and 2D nanoscopy at 1 MHz repetition rate. Rev. Sci. Ins. 90, 113103 (2019)

    Article  ADS  Google Scholar 

  96. J. Réhault, M. Maiuri, A. Oriana, G. Cerullo, Two-dimensional electronic spectroscopy with birefringent wedges. Rev. Sci. Ins. 85, 123107 (2014)

    Article  ADS  Google Scholar 

  97. C.M. Heyl, J. Güdde, A. L’Huillier, U. Höfer, High-order harmonic generation with μJ laser pulses at high repetition rates. J. Phys. B 45, 074020 (2012)

    Article  ADS  Google Scholar 

  98. C.-T. Chiang, A. Blättermann, M. Huth, J. Kirschner, W. Widdra, High-order harmonic generation at 4 MHz as a light source for time-of-flight photoemission spectroscopy. Appl. Phys. Lett. 101, 071116 (2012)

    Article  ADS  Google Scholar 

  99. S. Hädrich, A. Klenke, J. Rothhardt, M. Krebs, A. Hoffmann, O. Pronin, V. Pervak, J. Limpert, A. Tünnermann, High photon flux table-top coherent extreme-ultraviolet source. Nat. Photon. 8, 779 (2014)

    Article  ADS  Google Scholar 

  100. M. Puppin et al., Time- and angle-resolved photoemission spectroscopy of solids in the extreme ultraviolet at 500 kHz repetition rate. Rev. Sci. Instrum. 90, 023104 (2019)

    Article  ADS  Google Scholar 

  101. M. Keunecke et al., Time-resolved momentum microscopy with a 1 MHz high-harmonic extreme ultraviolet beamline. Rev. Sci. Instrum. 91, 063905 (2020)

    Article  ADS  Google Scholar 

  102. A. Kunin et al., Momentum-resolved exciton coupling and valley polarization dynamics in monolayer WS2. Phys. Rev. Lett. 130, 046202 (2023)

    Article  ADS  Google Scholar 

  103. X. Li, M.A.R. Reber, C. Corder, Y. Chen, P. Zhao, T.K. Allison, High-power ultrafast Yb:fiber laser frequency combs using commercially available components and basic fiber tools. Rev. Sci. Instrum. 87, 093114 (2016)

    Article  ADS  Google Scholar 

  104. A. Li, N.A. James, T. Wang, Z. Wang, H. Petek, M. Reutzel, Towards full surface Brillouin zone mapping by coherent multi-photon photoemission. New J. Phys. 22, 073035 (2020)

    Article  ADS  Google Scholar 

  105. A. Gerlach, G. Meister, R. Matzdorf, A. Goldmann, High-resolution photoemission study of the Ȳ surface state on Ag(110). Surf. Sci. 443, 221 (1999)

    Article  ADS  Google Scholar 

  106. S.T. Cundiff, S. Mukamel, Optical multidimensional coherent spectroscopy. Phys. Today 66, 44 (2013)

    Article  Google Scholar 

  107. S. Mukamel, Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations. Annu. Rev. Phys. Chem. 51, 691 (2000)

    Article  ADS  Google Scholar 

  108. T. Klamroth, P. Saalfrank, U. Höfer, Open-system density-matrix approach to image-potential dynamics of electrons at Cu(100): energy- and time-resolved two-photon photoemission spectra. Phys. Rev. B 64, 035420 (2001)

    Article  ADS  Google Scholar 

  109. M.J. Weida, S. Ogawa, H. Nagano, H. Petek, Ultrafast interferometric pump–probe correlation measurements in systems with broadened bands or continua. J. Opt. Soc. Am. B 17, 1443 (2000)

    Article  ADS  Google Scholar 

  110. S. Dong et al., Direct measurement of key exciton properties: energy, dynamics, and spatial distribution of the wave function. Nat. Sci. 1, e10010 (2021)

    Article  Google Scholar 

  111. N. Pontius, V. Sametoglu, H. Petek, Simulation of two-photon photoemission from the bulk sp-bands of Ag(111). Phys. Rev. B. 72, 115105 (2005). http://link.aps.org/abstract/PRB/v72/e115105

  112. J. Mauritsson et al., Attosecond electron spectroscopy using a novel interferometric pump-probe technique. Phys. Rev. Lett. 105, 053001 (2010)

    Article  ADS  Google Scholar 

  113. S. Tan, Y. Dai, S. Zhang, L. Liu, J. Zhao, H. Petek, Coherent electron transfer at the Ag/graphite heterojunction interface. Phys. Rev. Lett. 120, 126801 (2018)

    Article  ADS  Google Scholar 

  114. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer US, New York, 2000)

    Book  Google Scholar 

  115. A. Anderson, K.S. Deryckx, X.G. Xu, G. Steinmeyer, M.B. Raschke, Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating. Nano Lett. 10, 2519 (2010)

    Article  ADS  Google Scholar 

  116. M. Mascheck, S. Schmidt, M. Silies, T. Yatsui, K. Kitamura, M. Ohtsu, D. Leipold, E. Runge, C. Lienau, Observing the localization of light in space and time by ultrafast second-harmonic microscopy. Nat. Photon. 6, 293 (2012)

    Article  ADS  Google Scholar 

  117. H. Strauch, Georg-August-Universität Göttingen (2022)

    Google Scholar 

  118. S. Tan, A. Argondizzo, J. Ren, L. Liu, J. Zhao, H. Petek, Plasmonic coupling at a metal/semiconductor interface. Nat. Photon. 11, 806 (2017)

    Article  ADS  Google Scholar 

  119. D. Podbiel, P. Kahl, F.-J. Meyer zu Heringdorf, Analysis of the contrast in normal-incidence surface plasmon photoemission microscopy in a pump–probe experiment with adjustable polarization. Appl. Phys. B 122, 90 (2016)

    Google Scholar 

  120. A. Ghosh, S. Yang, Y. Dai, Z. Zhou, T. Wang, C.-B. Huang, H. Petek, A topological lattice of plasmonic merons. Appl. Phys. Rev. 8, 041413 (2021)

    Article  ADS  Google Scholar 

  121. Y. Dai, Z. Zhou, A. Ghosh, K. Kapoor, M. Dąbrowski, A. Kubo, C.-B. Huang, H. Petek, Ultrafast microscopy of a twisted plasmonic spin skyrmion. Appl. Phys. Rev. 9, 011420 (2022)

    Article  ADS  Google Scholar 

  122. T. J. Davis, D. Janoschka, P. Dreher, B. Frank, F.-J. Meyer zu Heringdorf, H. Giessen, Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution. Science 368, eaba6415 (2020)

    Google Scholar 

  123. R.R. Freeman, P.H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, M.E. Geusic, Above-threshold ionization with subpicosecond laser pulses. Phys. Rev. Lett. 59, 1092 (1987)

    Article  ADS  Google Scholar 

  124. W. Becker, F. Grasbon, R. Kopold, D.B. Milošević, G.G. Paulus, H. Walther, in Advances in Atomic, Molecular, and Optical Physics. ed. by B. Bederson, H. Walther (Academic Press, New York, 2002), p.35

    Google Scholar 

  125. J.H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979 (1965)

    Article  ADS  Google Scholar 

  126. T. Oka, S. Kitamura, Floquet engineering of quantum materials. Ann. Rev. Condens. Matter Phys. 10, 387 (2019)

    Article  ADS  Google Scholar 

  127. O.D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F.X. Kärtner, Signatures of carrier-wave Rabi flopping in GaAs. Phys. Rev. Lett. 87, 057401 (2001)

    Article  ADS  Google Scholar 

  128. Q.T. Vu, H. Haug, O.A. Mücke, T. Tritschler, M. Wegener, G. Khitrova, H.M. Gibbs, Light-induced gaps in semiconductor band-to-band transitions. Phys. Rev. Lett. 92, 217403 (2004)

    Article  ADS  Google Scholar 

  129. M. Fleischhauer, A. Imamoglu, J.P. Marangos, Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633 (2005)

    Article  ADS  Google Scholar 

  130. S.H. Autler, C.H. Townes, Stark effect in rapidly varying fields. Phys. Rev. 100, 703 (1955)

    Article  ADS  Google Scholar 

  131. W.H. Knox, Dispersion measurements for femtosecond-pulse generation and applications. Appl. Phys. B 58, 225 (1994)

    Article  ADS  Google Scholar 

  132. V.M. Silkin, P. Lazić, N. Došlić, H. Petek, B. Gumhalter, Ultrafast electronic response of Ag(111) and Cu(111) surfaces: from early excitonic transients to saturated image potential. Phys. Rev. B 92, 155405 (2015)

    Article  ADS  Google Scholar 

  133. F. Reinert, G. Nicolay, S. Schmidt, D. Ehm, S. Hüfner, Direct measurements of the L-gap surface states on the (111) face of noble metals by photoelectron spectroscopy. Phys. Rev. B 63, 115415 (2001)

    Article  ADS  Google Scholar 

  134. B. Gumhalter, D. Novko, H. Petek, Electron emission from plasmonically induced Floquet bands at metal surfaces. Phys. Rev. B 106, 035422 (2022)

    Article  ADS  Google Scholar 

  135. Y. Dai, A. Ghosh, S. Yang, Z. Zhou, C.-B. Huang, H. Petek, Poincaré engineering of surface plasmon polaritons. Nat. Rev. Phys. 4, 562 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge fruitful discussions with Namitha Ann James. M. R. acknowledges support through the Alexander von Humboldt Foundation for his Feodor Lynen PostDoc fellowship at the University of Pittsburgh in the group of H.P. In addition, M.R. acknowledges funding through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—217133147/SFB 1073, project B10, and inspiring discussions with the newly established ITR-mPP team in Göttingen: Hannah Strauch, Marco Merboldt, and Stefan Mathias. H.P. thanks partial financial support from the National Science Foundation Grant No. CHE-2102601, and promotion of ITR-mPP methods by Shijing Tan.

Author information

Authors and Affiliations

  1. I. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany

    Marcel Reutzel

  2. Department of Physics and Astronomy and IQ Initiative, University of Pittsburgh, Pittsburgh, PA, USA

    Andi Li, Zehua Wang & Hrvoje Petek

Authors
  1. Marcel Reutzel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zehua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hrvoje Petek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Marcel Reutzel or Hrvoje Petek .

Editor information

Editors and Affiliations

  1. The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba, Japan

    Iwao Matsuda

  2. Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, Japan

    Ryuichi Arafune

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Reutzel, M., Li, A., Wang, Z., Petek, H. (2023). Probing Nonlinear Light–Matter Interaction in Momentum Space: Coherent Multiphoton Photoemission Spectroscopy. In: Matsuda, I., Arafune, R. (eds) Nonlinear X-Ray Spectroscopy for Materials Science. Springer Series in Optical Sciences, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-99-6714-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-6714-8_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-6713-1

  • Online ISBN: 978-981-99-6714-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation