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  • Letter
  • Open Access

Transient nuclear inversion by x-ray free electron laser in a tapered x-ray waveguide

Yu-Hsueh Chen1,2, Po-Han Lin1, Guan-Ying Wang1, Adriana Pálffy3,4,2,*, and Wen-Te Liao1,2,5,6,†

  • 1Department of Physics, National Central University, Taoyuan City 32001, Taiwan
  • 2Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
  • 3Institute of Theoretical Physics and Astrophysics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany
  • 4Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058, Erlangen, Germany
  • 5Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
  • 6Center for Quantum Technology, Hsinchu 30013, Taiwan

  • *adriana.palffy-buss@physik.uni-wuerzburg.de
  • †wente.liao@g.ncu.edu.tw
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Phys. Rev. Research 4, L032007 – Published 11 July, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L032007

Abstract

The enhancement of x-ray-matter interaction by guiding and focusing radiation from x-ray free electron lasers is investigated theoretically. We show that elliptical waveguides using a cladding material with a high atomic number, such as platinum, can maintain an x-ray intensity of up to three orders of magnitude larger than in free space. This feature can be used to place a nuclear sample in the waveguide focal area and drive nuclear Mössbauer transitions up to transient nuclear population inversion. The latter is a long-standing goal related to gamma-ray lasers or nuclear state population control for energy storage. We show that inverted nuclei numbers of up to approximately 2×105 are achievable in the realistic region of longitudinal x-ray-free-electron-laser coherence time ≤10 fs. Our results anticipate the important role of tapered x-ray waveguides and strategically embedded samples in the field of x-ray quantum optics.

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References (79)

  1. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, Ph. Hering, Z. Huang et al., First lasing and operation of an angstrom-wavelength free-electron laser, Nature Photon 4, 641 (2010).
  2. C. Pellegrini, A. Marinelli, and S. Reiche, The physics of x-ray free-electron lasers, Rev. Mod. Phys. 88, 015006 (2016).
  3. B. W. Adams, C. Buth, S. M. Cavaletto, J. Evers, Z. Harman, C. H. Keitel, A. Pálffy, A. Picón, R. Röhlsberger, Y. Rostovtsev, and K. Tamasaku, X-ray quantum optics, J. Mod. Opt. 60, 2 (2013).
  4. A. I. Chumakov, A. Q. R. Baron, I. Sergueev, C. Strohm, O. Leupold, Y. Shvyd'ko, G. V. Smirnov, R. Rüffer, Y. Inubushi, M. Yabashi et al., Superradiance of an ensemble of nuclei excited by a free electron laser, Nat. Phys. 14, 261 (2018).
  5. G. C. Baldwin and J. C. Solem, Recoilless gamma-ray lasers, Rev. Mod. Phys. 69, 1085 (1997).
  6. P. Walker and G. Dracoulis, Energy traps in atomic nuclei, Nature (London) 399, 35 (1999).
  7. G. V. Smirnov, U. van Bürck, A. I. Chumakov, A. Q. R. Baron, and R. Rüffer, Synchrotron mössbauer source, Phys. Rev. B 55, 5811 (1997).
  8. V. Potapkin, A. I. Chumakov, G. V. Smirnov, J.-P. Celse, R. Rüffer, C. McCammon, and L. Dubrovinsky, The Fe57 Mössbauer Source at the ESRF, J. Synchrotron Rad. 19, 559 (2012).
  9. Yu. V. Shvyd'ko, T. Hertrich, U. van Bürck, E. Gerdau, O. Leupold, J. Metge, H. D. Rüter, S. Schwendy, G. V. Smirnov, W. Potzel, and P. Schindelmann, Storage of Nuclear Excitation Energy through Magnetic Switching, Phys. Rev. Lett. 77, 3232 (1996).
  10. G.-Y. Wang and W.-T. Liao, Generation of Short Hard-X-Ray Pulses of Tailored Duration Using a Mössbauer Source, Phys. Rev. Applied 10, 014003 (2018).
  11. G. V. Smirnov, U. van Bürck, J. Arthur, S. L. Popov, A. Q. R. Baron, A. I. Chumakov, S. L. Ruby, W. Potzel, and G. S. Brown, Nuclear Exciton Echo Produced by Ultrasound in Forward Scattering of Synchrotron Radiation, Phys. Rev. Lett. 77, 183 (1996).
  12. F. Vagizov, V. Antonov, Y.V. Radeonychev, R. N. Shakhmuratov, and O. Kocharovskaya, Coherent control of the waveforms of recoilless γ-ray photons, Nature (London) 508, 80 (2014).
  13. U. van Burck, R. L. Mossbauer, G. V. Smirnov, and H. J. Maurus, Enhanced nuclear resonance scattering in dynamical diffraction of gamma rays, J. Phys. C 13, 4511 (1980).
  14. E. Gerdau, R. Rüffer, H. Winkler, W. Tolksdorf, C. P. Klages, and J. P. Hannon, Nuclear Bragg Diffraction of Synchrotron Radiation in Yttrium Iron Garnet, Phys. Rev. Lett. 54, 835 (1985).
  15. E. Gerdau, R. Rüffer, R. Hollatz, and J. P. Hannon, Quantum Beats from Nuclei Excited by Synchrotron Radiation, Phys. Rev. Lett. 57, 1141 (1986).
  16. U. van Bürck, R. L. Mössbauer, E. Gerdau, R. Rüffer, R. Hollatz, G. V. Smirnov, and J. P. Hannon, Nuclear Bragg Scattering of Synchrotron Radiation with Strong Speedup of Coherent Decay, Measured On Antiferromagnetic FeBO573, Phys. Rev. Lett. 59, 355 (1987).
  17. Y. V. Shvyd'ko and U. Van Bürck, Hybrid forms of beat phenomena in nuclear forward scattering of synchrotron radiation, Hyperfine Interact. 123/124, 511 (1999).
  18. J. P. Hannon and G. T. Trammell, Coherent γ-ray optics, Hyperfine Interact. 123/124, 127 (1999).
  19. G. V. Smirnov, U. van Bürck, W. Potzel, P. Schindelmann, S. L. Popov, E. Gerdau, Yu. V. Shvyd'ko, H. D. Rüter, and O. Leupold, Propagation of nuclear polaritons through a two-target system: Effect of inversion of targets, Phys. Rev. A 71, 023804 (2005).
  20. R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, Collective lamb shift in single-photon superradiance, Science 328, 1248 (2010).
  21. R. Röhlsberger, H. C. Wille, K. Schlage, and B. Sahoo, Electromagnetically induced transparency with resonant nuclei in a cavity, Nature (London) 482, 199 (2012).
  22. K. P. Heeg, H.-C. Wille, K. Schlage, T. Guryeva, D. Schumacher, I. Uschmann, K. S. Schulze, B. Marx, T. Kämpfer, G. G. Paulus, R. Röhlsberger, and J. Evers, Vacuum-Assisted Generation and Control of Atomic Coherences at X-Ray Energies, Phys. Rev. Lett. 111, 073601 (2013).
  23. K. P. Heeg, J. Haber, D. Schumacher, L. Bocklage, H.-C. Wille, K. S. Schulze, R. Loetzsch, I. Uschmann, G. G. Paulus, R. Rüffer, R. Röhlsberger, and J. Evers, Tunable Subluminal Propagation of Narrow-band X-Ray Pulses, Phys. Rev. Lett. 114, 203601 (2015).
  24. K. P. Heeg, C. Ott, D. Schumacher, H.-C. Wille, R. Röhlsberger, T. Pfeifer, and J. Evers, Interferometric Phase Detection at X-Ray Energies Via Fano Resonance Control, Phys. Rev. Lett. 114, 207401 (2015).
  25. K. P. Heeg, A. Kaldun, C. Strohm, P. Reiser, C. Ott, R. Subramanian, D. Lentrodt, J. Haber, H.-C. Wille, S. Goerttler, R. Rüffer, C. H. Keitel, R. Röhlsberger, T. Pfeifer, and J. Evers, Spectral narrowing of x-ray pulses for precision spectroscopy with nuclear resonances, Science 357, 375 (2017).
  26. J. Haber, X. Kong, C. Strohm, S. Willing, J. Gollwitzer, L. Bocklage, R. Rüffer, A. Pálffy, and R. Röhlsberger, Rabi oscillations of x-ray radiation between two nuclear ensembles, Nat. Photonics 11, 720 (2017).
  27. K. P. Heeg, A. Kaldun, C. Strohm, C. Ott, R. Subramanian, D. Lentrodt, J. Haber, H.-C. Wille, S. Goerttler, R. Rüffer, C H Keitel, R. Röhlsberger, T. Pfeifer, and J. Evers, Coherent x-ray-optical control of nuclear excitons with zeptosecond phase-stability, Nature (London) 590, 401 (2021).
  28. J. Haber, K. S. Schulze, K. Schlage, R. Loetzsch, L. Bocklage, T. Gurieva, H. Bernhardt, H.-C. Wille, R. Rüffer, I. Uschmann et al., Collective strong coupling of x-rays and nuclei in a nuclear optical lattice, Nat. Photonics 10, 445 (2016).
  29. Y. V. Shvyd'ko, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, High-reflectivity high-resolution x-ray crystal optics with diamonds, Nat. Phys. 6, 196 (2010).
  30. Y. Shvyd'Ko, S. Stoupin, V. Blank, and S. Terentyev, Near-100% bragg reflectivity of x-rays, Nat. Photonics 5, 539 (2011).
  31. K. P. Heeg, C. H. Keitel, and J. Evers, Inducing and detecting collective population inversions of mössbauer nuclei, arXiv:1607.04116.
  32. D. H. Bilderback, S. A. Hoffman, and D. J. Thiel, Nanometer spatial resolution achieved in hard imaging and laue diffraction experiments, Science 263, 201 (1994).
  33. R. Huang and D. H. Bilderback, Single-bounce monocapillaries for focusing synchrotron radiation: Modeling, measurements and theoretical limits, J. Synchrotron Radiat. 13, 74 (2006).
  34. X. Zeng, F. Duewer, M. Feser, C. Huang, A. Lyon, A. Tkachuk, and W. Yun, Ellipsoidal and parabolic glass capillaries as condensers for x-ray microscopes, Appl. Opt. 47, 2376 (2008).
  35. C. G. Schroer and B. Lengeler, Focusing Hard X Rays to Nanometer Dimensions by Adiabatically Focusing Lenses, Phys. Rev. Lett. 94, 054802 (2005).
  36. M.J Zwanenburg, J. H. H Bongaerts, J. F Peters, D. Riese, and J. F van der Veen, Focusing of coherent x-rays in a tapered planar waveguide, Phys. B: Condens. Matter 283, 285 (2000).
  37. F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, Two-dimensional x-ray waveguides and point sources, Science 297, 230 (2002).
  38. A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, Two-Dimensional Hard X-Ray Beam Compression by Combined Focusing and Waveguide Optics, Phys. Rev. Lett. 94, 074801 (2005).
  39. S. P. Krüger, H. Neubauer, M. Bartels, S. Kalbfleisch, K. Giewekemeyer, P. J. Wilbrandt, M. Sprung, and T. Salditt, Sub-10 nm beam confinement by x-ray waveguides: Design, fabrication and characterization of optical properties, J. Synchrotron Radiat. 19, 227 (2012).
  40. H.-Y. Chen, S. Hoffmann, and T. Salditt, X-ray beam compression by tapered waveguides, Appl. Phys. Lett. 106, 194105 (2015).
  41. T. Salditt, S. Hoffmann, M. Vassholz, J. Haber, M. Osterhoff, and J. Hilhorst, X-Ray Optics on a Chip: Guiding X Rays in Curved Channels, Phys. Rev. Lett. 115, 203902 (2015).
  42. S. Hoffmann-Urlaub, P. Höhne, M. Kanbach, and T. Salditt, Advances in fabrication of x-ray waveguides, Microelectron. Eng. 164, 135 (2016).
  43. E. A. Stern, Z. Kalman, A. Lewis, and K. Lieberman, Simple method for focusing x rays using tapered capillaries, Appl. Opt. 27, 5135 (1988).
  44. E. I. Denisov, V. I. Glebov, and N. K. Zhevago, Focusing of x-rays using tapered waveguides, Nucl. Instrum. Methods Phys. Res., Sect. A 308, 400 (1991).
  45. C. Bergemann, H. Keymeulen, and J. F. van der Veen, Focusing X-Ray Beams to Nanometer Dimensions, Phys. Rev. Lett. 91, 204801 (2003).
  46. A. Iida and K. Hirano, Kirkpatrick-baez optics for a sub-m synchrotron x-ray microbeam and its applications to x-ray analysis, Nucl. Instrum. Methods Phys. Res., Sect. B 114, 149 (1996).
  47. National nuclear data center, https://www.nndc.bnl.gov/ensdf/.
  48. Lawrence berkeley national laboratory, https://henke.lbl.gov/optical_constants/asf.html.
  49. T. Pfeifer, Y. Jiang, S. Düsterer, R. Moshammer, and J. Ullrich, Partial-coherence method to model experimental free-electron laser pulse statistics, Opt. Lett. 35, 3441 (2010).
  50. J. Feldhaus, E. L. Saldin, J. R. Schneider, E. A. Schneidmiller, and M. V. Yurkov, Possible application of x-ray optical elements for reducing the spectral bandwidth of an x-ray sase fel, Opt. Commun. 140, 341 (1997).
  51. J. Amann, W. Berg, V. Blank, F.-J. Decker, Y. Ding, P. Emma, Y. Feng, J. Frisch, D. Fritz, J. Hastings et al., Demonstration of self-seeding in a hard-x-ray free-electron laser, Nat. Photonics 6, 693 (2012).
  52. S. Serkez, Self-seeding xfels: Operation principle and challenges, Synchrotron Radiation News 29, 10 (2016).
  53. C. Emma, A. Lutman, M. W. Guetg, J. Krzywinski, A. Marinelli, J. Wu, and C. Pellegrini, Experimental demonstration of fresh bunch self-seeding in an x-ray free electron laser, Appl. Phys. Lett. 110, 154101 (2017).
  54. I. Inoue, T. Osaka, T. Hara, T. Tanaka, T. Inagaki, T. Fukui, S. Goto, Y. Inubushi, H. Kimura, R. Kinjo et al., Generation of narrow-band x-ray free-electron laser via reflection self-seeding, Nat. Photonics 13, 319 (2019).
  55. I. Nam et al., High-brightness self-seeded x-ray free-electron laser covering the 3.5 kev to 14.6 kev range, Nat. Photonics 15, 435 (2021).
  56. K.-J. Kim, Y. Shvyd'ko, and S. Reiche, A Proposal for an X-Ray Free-Electron Laser Oscillator with an Energy-Recovery Linac, Phys. Rev. Lett. 100, 244802 (2008).
  57. J. Zemella et al., Numerical simulations of an xfelo for the european xfel driven by a spent beam, in Proceedings of the 32th International Free-Electron Laser Conference (JACoW, Geneva, Switzerland, 2012), pp. 429.
  58. B. Adams, G. Aeppli, T. Allison, Alfred QR Baron, P. Bucksbaum, A. I. Chumakov, C. Corder, S. P. Cramer, S. DeBeer, Y. Ding et al., Scientific opportunities with an x-ray free-electron laser oscillator, arXiv:1903.09317.
  59. Y. Shvyd'ko, Output coupling from x-ray free-electron laser cavities with intracavity beam splitters, Phys. Rev. Accel. Beams 22, 100703 (2019).
  60. P. Rauer, I. Bahns, W. Hillert, J. Roßbach, W. Decking, and H. Sinn, Integration of an xfelo at the european xfel facility, in Proceedings of the 39th International Free-Electron Laser Conference (JACoW, Geneva, Switzerland, 2019), pp. 62.
  61. G. Marcus, A. Halavanau, Z. Huang, J. Krzywinski, J. MacArthur, R. Margraf, T. Raubenheimer, and D. Zhu, Refractive Guide Switching a Regenerative Amplifier Free-Electron Laser for High Peak and Average Power Hard X Rays, Phys. Rev. Lett. 125, 254801 (2020).
  62. K. Li, J. Yan, C. Feng, M. Zhang, and H. Deng, High brightness fully coherent x-ray amplifier seeded by a free-electron laser oscillator, Phys. Rev. Accel. Beams 21, 040702 (2018).
  63. G. Paraskaki, S. Ackermann, B. Faatz, G. Geloni, V. Grattoni, W. Hillert, C. Lechner, M. Mehrjoo, S. Serkez, and T. Tanikawa, Study of a seeded oscillator-amplifier fel, in 39th Free Electron Laser Conf.(FEL'19), Hamburg, Germany, 26-30 August 2019 (JACOW Publishing, Geneva, Switzerland, 2019), pp. 234–237.
  64. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 2006).
  65. G. S. Agarwal, Quantum Optics (Cambridge University Press, Cambridge, 2012).
  66. A. Pálffy, J. Evers, and C. H. Keitel, Electric-dipole-forbidden nuclear transitions driven by super-intense laser fields, Phys. Rev. C 77, 044602 (2008).
  67. W.-T. Liao, A. Pálffy, and C. H. Keitel, Nuclear coherent population transfer with x-ray laser pulses, Phys. Lett. B 705, 134 (2011).
  68. W.-T. Liao, A. Pálffy, and C. H. Keitel, Coherent Storage and Phase Modulation of Single Hard-X-Ray Photons Using Nuclear Excitons, Phys. Rev. Lett. 109, 197403 (2012).
  69. Yu. V. Shvyd'ko, U. van Bürck, W. Potzel, P. Schindelmann, E. Gerdau, O. Leupold, J. Metge, H. D. Rüter, and G. V. Smirnov, Hybrid beat in nuclear forward scattering of synchrotron radiation, Phys. Rev. B 57, 3552 (1998).
  70. C. Fuhse and T. Salditt, Finite-difference field calculations for two-dimensionally confined x-ray waveguides, Appl. Opt. 45, 4603 (2006).
  71. X. Kong, W.-T. Liao, and A. Pálffy, Field control of single x-ray photons in nuclear forward scattering, New J. Phys. 16, 013049 (2014).
  72. I. Bukreeva, A. Popov, D. Pelliccia, A. Cedola, S. B. Dabagov, and S. Lagomarsino, Wave-Field Formation in a Hollow X-Ray Waveguide, Phys. Rev. Lett. 97, 184801 (2006).
  73. W.-T. Liao, A. Pálffy, and C. H. Keitel, Three-beam setup for coherently controlling nuclear-state population, Phys. Rev. C 87, 054609 (2013).
  74. T. J. Bürvenich, J. Evers, and C. H. Keitel, Nuclear Quantum Optics with X-Ray Laser Pulses, Phys. Rev. Lett. 96, 142501 (2006).
  75. M. Osterhoff and T. Salditt, Real structure effects in x-ray waveguide optics: The influence of interfacial roughness and refractive index profile on the near-field and far-field distribution, Opt. Commun. 282, 3250 (2009).
  76. A. Zamkovskaya, E. Maksimova, I. Nauhatsky, and M. Shapoval, X-ray diffraction investigations of the thermal expansion of iron borate FeBO3 crystals, J. Phys.: Conf. Ser. 929, 012030 (2017).
  77. P. A. Markovin, A. M. Kalashnikova, R. V. Pisarev, and Th. Rasing, Optical study of the electronic structure and magnetic ordering in a weak ferromagnet FeBO3, JETP Lett. 86, 712 (2008).
  78. J. Gunst, Y. A. Litvinov, C. H. Keitel, and A. Pálffy, Dominant Secondary Nuclear Photoexcitation with the X-Ray Free-Electron Laser, Phys. Rev. Lett. 112, 082501 (2014).
  79. Y. Wu, J. Gunst, C. H. Keitel, and A. Pálffy, Tailoring Laser-Generated Plasmas for Efficient Nuclear Excitation by Electron Capture, Phys. Rev. Lett. 120, 052504 (2018).

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Phys. Rev. Research 4, L032007– Published 11 July, 2022
  • Received 5 July 2021
  • Accepted 16 June 2022
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