Skip to main content

Part of the book series: Lecture Notes in Physics ((LNP,volume 831))

  • 1579 Accesses

Abstract

The existence of wavy properties associated with material particles is one of the fundamental achievements of quantum mechanics. Thus, the experimental use of single, double, or multiple slits has become a standard test of the universality of matter diffraction phenomena, independently of both the type of diffracted particle (charged or neutral, elementary or composite) and the interaction between particles and diffracting objects (electromagnetic or nuclear). This is confirmed by a large amount of experiments, ranging from tiny objects such as electrons, neutrons, single atoms, or small clusters, to more complex, mesoscopic-sized systems such as fullerenes, large biomolecues or Bose-Einstein condensates. Several effects will also be discussed such as the so-called Talbot effect responsible for displaying carpet-like patterns in the near-field region as well as the Talbot-Beeby effect responsible for the distortion of the corresponding patterns due to the presence of attractive interactions between diffracted particles and gratings.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Badurek, G., Rauch, H., Zeilinger, A. (eds.): Proceedings of the International Workshop on Matter Wave Interferometry, Vienna, 1987. Physica B, vol. 151 (1988)

    Google Scholar 

  2. Berman, P.: Atom Interferometry. Academic Press, San Diego (1997)

    Google Scholar 

  3. Cronin, A.D., Schmiedmayer, J., Pritchard, D.E.: Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051–1129 (2009)

    Article  ADS  Google Scholar 

  4. Arndt, M., Hornberger, K.: Quantum interferometry with complex molecules. In: Schwendimann, P. (ed.) Proceedings of the International School of Physics “Enrico Fermi”, Course CLXXI—“Quantum Coherence in Solid State Systems”. Societá Italiana di Fisica (2008)

    Google Scholar 

  5. Arndt, M., Ekers, A., von Klitzing, W., Ulbricht, H.: Focus on modern frontiers of matte wave optics and interferometry. New J. Phys. 14, 125006(1–9) (2012)

    Article  ADS  Google Scholar 

  6. Jönsson, C.: Electron diffraction at multiple slits. Am. J. Phys. 42, 4–11 (1974)

    Article  ADS  Google Scholar 

  7. Tonomura, A., Endo, J., Matsuda, T., Kawasaki, T., Ezawa, H.: Demonstration of single-electron buildup of an interference. Am. J. Phys. 57, 117–120 (1989)

    Article  ADS  Google Scholar 

  8. Mitchell, D.P., Powers, P.N.: Bragg reflection of slow neutrons. Phys. Rev. 50, 486–487 (1936)

    Article  ADS  Google Scholar 

  9. Shull, C.G.: Observation of Pendellösung fringe structure in neutron diffraction. Phys. Rev. Lett. 21, 1585–1589 (1968)

    Article  ADS  Google Scholar 

  10. Shull, C.G.: Single-slit diffraction of neutrons. Phys. Rev. 179, 752–754 (1969)

    Article  ADS  Google Scholar 

  11. Zeilinger, A., Gähler, R., Shull, G.C., Treimer, W., Mampe, W.: Single- and double-slit diffraction of neutrons. Rev. Mod. Phys. 60, 1067–1073 (1988)

    Article  ADS  Google Scholar 

  12. Estermann, I., Stern, O.: Beugung von Molekularstrahlen. Z. Phys. 61, 95–125 (1930)

    Article  ADS  Google Scholar 

  13. Carnal, O., Mlynek, J.: Young’s double-slit experiment with atoms: A simple atom interferometer. Phys. Rev. Lett. 66, 2689–2692 (1991)

    Article  ADS  Google Scholar 

  14. Keith, D.W., Schattenburg, M.L., Smith, H.I., Pritchard, D.E.: Diffraction of atoms by a transmission grating. Phys. Rev. Lett. 61, 1580–1583 (1988)

    Article  ADS  Google Scholar 

  15. Keith, D.W., Ekstrom, C.R., Turchette, Q.A., Pritchard, D.E.: An interferometer for atoms. Phys. Rev. Lett. 66, 2693–2696 (1991)

    Article  ADS  Google Scholar 

  16. Shimizu, F., Shimizu, K., Takuma, H.: Double-slit interference with ultracold metastable neon atoms. Phys. Rev. A 46, R17–R20 (1992)

    Article  ADS  Google Scholar 

  17. Rasel, E.M., Oberthaler, M.K., Batelaan, H., Schmiedmayer, J., Zeilinger, A.: Atom wave interferometry with diffraction gratings of light. Phys. Rev. Lett. 75, 2633–2637 (1995)

    Article  ADS  Google Scholar 

  18. Landragin, A., Cognet, L., Horvath, G.Zs.K., Westbrook, C.I., Westbrook, N., Aspect, A.: A reflection grating for atoms at normal incidence. Europhys. Lett. 39, 485–490 (1997)

    Article  ADS  Google Scholar 

  19. Hegergeldt, G.C., Köhler, T.: Atomic versus molecular diffraction: Influence of breakups and finite size. Phys. Rev. A 57, 2021–2029 (1998)

    Article  ADS  Google Scholar 

  20. Doak, R.B., Grisenti, R.E., Rehbein, S., Schmahl, G., Toennies, J.P., Wöll, Ch.: Towards realization of an atomic de Broglie microscope: Helium atom focusing using Fresnel zone plates. Phys. Rev. Lett. 83, 4229–4232 (1999)

    Article  ADS  Google Scholar 

  21. Grisenti, R.E., Schöllkopf, W., Toennies, J.P., Hegerfeldt, G.C., Köhler, T.: Determination of atom-surface van der Waals potential from transmission-grating diffraction intensities. Phys. Rev. Lett. 83, 1755–1758 (1999)

    Article  ADS  Google Scholar 

  22. Grisenti, R.E., Schöllkopf, W., Toennies, J.P., Manson, J.R., Savas, T.A., Smith, H.I.: He-atom diffraction from nanostructure transmission gratings: The role of imperfections. Phys. Rev. A 61, 033608(1–15) (2000)

    Article  ADS  Google Scholar 

  23. Schöllkopf, W., Toennies, J.P.: Nondestructive mass selection of small van der Waals clusters. Science 266, 1345–1348 (1994)

    Article  ADS  Google Scholar 

  24. Arndt, M., Nairz, O., Vos-Andreae, J., Keller, C., van der Zouw, G., Zeilinger, A.: Wave-particle duality of C60 molecules. Nature 401, 680–682 (1999)

    Article  ADS  Google Scholar 

  25. Brezger, B., Hackermüller, L., Uttenthaler, S., Petschinka, J., Arndt, M., Zeilinger, A.: Matter-wave interferometer for large molecules. Phys. Rev. Lett. 88, 100404(1–4) (2002)

    Article  ADS  Google Scholar 

  26. Viale, A., Vicari, M., Zanghì, N.: Analysis of the loss of coherence in interferometry with macromolecules. Phys. Rev. A 68, 063610(1–18) (2003)

    Article  ADS  Google Scholar 

  27. Hornberger, K., Sipe, J.E., Arndt, M.: Theory of decoherence in a matter wave Talbot-Lau interferometer. Phys. Rev. A 70, 053608(1–18) (2004)

    Article  ADS  Google Scholar 

  28. Gerlich, S., Eibenberger, S., Tomandl, M., Nimmrichter, S., Hornberger, K., Fagan, P.J., Tüxen, J., Mayor, M., Arndt, M.: Quantum interference of large organic clusters. Nat. Commun. 2, 263(1–5) (2011)

    Article  ADS  Google Scholar 

  29. Deng, L., Hagley, E.W., Denschlag, J., Simsarian, J.E., Edwards, M., Clark, C.W., Helmerson, K., Rolston, S.L., Phillips, W.D.: Temporal, matter-wave-dispersion Talbot effect. Phys. Rev. Lett. 83, 5407–5411 (1999)

    Article  ADS  Google Scholar 

  30. Romero-Isart, O., Juan, M.L., Quidant, R., Cirac, J.I.: Toward quantum superposition of living organisms. New J. Phys. 12, 033015(1–16) (2010)

    Article  ADS  Google Scholar 

  31. Romero-Isart, O., Pflanzer, A.C., Blaser, F., Kaltenbaek, R., Kiesel, N., Aspelmeyer, M., Cirac, J.I.: Large quantum superpositions and interference of massive nanometer-sized objects. Phys. Rev. Lett. 107, 020405(1–4) (2011)

    Article  ADS  Google Scholar 

  32. Romero-Isart, O.: Quantum superposition of massive objects and collapse models. Phys. Rev. A 84, 052121(1–17) (2011)

    Article  ADS  Google Scholar 

  33. Omnès, R.: Consistent interpretations of quantum mechanics. Rev. Mod. Phys. 64, 339–382 (1992)

    Article  ADS  Google Scholar 

  34. Rauch, H., Treimer, W., Bonse, U.: Test of a single crystal neutron interferometer. Phys. Lett. A 47, 369–371 (1974)

    Article  ADS  Google Scholar 

  35. Gould, P.L., Ruff, G.A., Pritchard, D.E.: Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect. Phys. Rev. Lett. 56, 827–830 (1986)

    Article  ADS  Google Scholar 

  36. Kapitza, P.L., Dirac, P.A.M.: The reflection of electrons from standing light waves. Proc. Camb. Philol. Soc. 29, 297–300 (1933)

    Article  ADS  Google Scholar 

  37. Freimund, D.L., Aflatooni, K., Batelaan, H.: Observation of the Kapitza-Dirac effect. Nature 413, 142–143 (2001)

    Article  ADS  Google Scholar 

  38. Clauser, J.F., Li, S.: Talbot-vonLau atom interferometry with cold slow potassium. Phys. Rev. A 49, R2213–R2216 (1994)

    Article  ADS  Google Scholar 

  39. Clauser, J.F., Reinsch, M.W.: New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry. Appl. Phys. B 54, 380–395 (1992)

    Article  ADS  Google Scholar 

  40. Talbot, H.F.: Facts relating to optical science. Philos. Mag. 9, 401–407 (1836)

    Google Scholar 

  41. Rayleigh, L.: On copying diffraction-gratings, and some phenomena connected therewith. Philos. Mag. 11, 196–205 (1881)

    Article  Google Scholar 

  42. Winthrop, J.T., Worthington, C.R.: Theory of Fresnel Images. I. Plane periodic objects in monochromatic light. J. Opt. Soc. Am. 55, 373–381 (1965)

    Article  ADS  Google Scholar 

  43. Latimer, P., Crouse, R.F.: Talbot effect reinterpreted. Appl. Opt. 31, 80–89 (1992)

    Article  ADS  Google Scholar 

  44. Lau, E.: Beugungserscheinungen an Doppelrastern. Ann. Phys. 6, 417–423 (1948)

    Article  Google Scholar 

  45. Jahns, J., Lohmann, A.W.: The Lau effect: A diffraction experiment with incoherent illumination. Opt. Commun. 28, 263–267 (1979)

    Article  ADS  Google Scholar 

  46. Sudol, R., Thompson, B.J.: Lau effect: Theory and experiment. Appl. Opt. 20, 1107–1116 (1981)

    Article  ADS  Google Scholar 

  47. Hornberger, K., Gerlich, S., Haslinger, P., Nimmrichter, S., Arndt, M.: Colloquium: Quantum interference of clusters and molecules. Rev. Mod. Phys. 84, 157–173 (2012)

    Article  ADS  Google Scholar 

  48. Juffmann, T., Milic, A., Müllneritsch, M., Asenbaum, P., Tsukernik, A., Tüxen, J., Mayor, M., Cheshnovsky, O., Arndt, M.: Real-time single-molecule imaging of quantum interference. Nat. Nanotechnol. 7, 297–300 (2012)

    Article  ADS  Google Scholar 

  49. Carnal, O., Faulstich, A., Mlynek, J.: Diffraction of metastable helium atoms by a transmission grating. Appl. Phys. B 53, 88–91 (1991)

    Article  ADS  Google Scholar 

  50. Feynman, R.P.: Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20, 367–387 (1948)

    Article  MathSciNet  ADS  Google Scholar 

  51. Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley, Reading (1965)

    MATH  Google Scholar 

  52. Comsa, G.: Dynamics of Gas–Surface Interactions. Springer Series in Chemical Physics, vol. 21. Springer, Berlin (1982)

    Google Scholar 

  53. Sanz, A.S., Miret-Artés, S.: A causal look into the quantum Talbot effect. J. Chem. Phys. 126, 234106(1–11) (2007)

    Article  ADS  Google Scholar 

  54. Beeby, J.L.: The scattering of helium atoms from surfaces. J. Phys. C 4, L359–L361 (1971)

    Article  ADS  Google Scholar 

  55. Elmore, W.C., Heald, M.A.: Physics of Waves. Dover Publications, New York (1985)

    Google Scholar 

  56. Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Saunders College, Philadelphia (1976)

    Google Scholar 

  57. Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965)

    MATH  Google Scholar 

  58. Heller, E.J.: Time-dependent approach to semiclassical dynamics. J. Chem. Phys. 62, 1544–1555 (1975)

    Article  ADS  Google Scholar 

  59. Tannor, D.J.: Introduction to Quantum Mechanics: A Time-Dependent Perspective. University Science Books, Sausalito (2006)

    Google Scholar 

  60. Sanz, A.S., Borondo, F., Miret-Artés, S.: Causal trajectories description of atom diffraction by surfaces. Phys. Rev. B 61, 7743–7751 (2000)

    Article  ADS  Google Scholar 

  61. Sanz, A.S., Borondo, F., Miret-Artés, S.: Particle diffraction studied using quantum trajectories. J. Phys. Condens. Matter 14, 6109–6145 (2002)

    Article  ADS  Google Scholar 

  62. Arsenović, D., Božić, M., Sanz, A.S., Davidović, M.: Evolution of the wave function of an atom hit by a photon in a three-grating interferometer. Phys. Scr. T 135, 014025(1–5) (2009)

    Article  ADS  Google Scholar 

  63. Božić, M., Arsenović, D., Sanz, A.S., Davidović, M.: On the influence of resonance photon scattering on atom interference. Phys. Scr. T 140, 014017(1–5) (2010)

    ADS  Google Scholar 

  64. Davidović, M., Sanz, A.S., Božić, M., Arsenović, D.: Coherence loss and revivals in atomic interferometry: A quantum-recoil analysis. J. Phys. A, Math. Theor. 45, 165303(1–17) (2012)

    Article  ADS  Google Scholar 

  65. Sanz, A.S., Miret-Artés, S.: A trajectory-based understanding of quantum interference. J. Phys. A 41, 435303(1–23) (2008)

    Article  MathSciNet  ADS  Google Scholar 

  66. Chapman, M.S., Hammond, T.D., Lenef, A., Schmiedmayer, J., Rubenstein, R.A., Smith, E., Pritchard, D.E.: Photon scattering from atoms in an atom interferometer: Coherence lost and regained. Phys. Rev. Lett. 75, 3783–3787 (1995)

    Article  ADS  Google Scholar 

  67. Sanz, A.S.: A Bohmian approach to quantum fractals. J. Phys. A, Math. Gen. 38, 6037–6050 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  68. Sbitnev, V.I.: N-slit interference: Fractals in near-field region, Bohmian trajectories. arXiv:0907.4638 (2009)

  69. Sbitnev, V.I.: N-slit interference: Path integrals, Bohmian trajectories. arXiv:1001.0661 (2010)

  70. Sbitnev, V.I.: Matter waves in the Talbot-Lau interferometry. arXiv:1005.0890 (2010)

  71. Davidović, M., Arsenović, D., Božić, M., Sanz, A.S., Miret-Artés, S.: Should particle trajectories comply with the transverse momentum distribution? Eur. Phys. J. Spec. Top. 160, 95–104 (2008)

    Article  Google Scholar 

  72. Chapman, M.S., Ekstrom, C.R., Hammond, T.D., Schmiedmayer, J., Tannian, B.E., Wehinger, S., Pritchard, D.E.: Near-field imaging of atom diffraction gratings: The atomic Talbot effect. Phys. Rev. A 51, R14–R17 (1995)

    Article  ADS  Google Scholar 

  73. Berry, M., Marzoli, I., Schleich, W.: Quantum carpets, carpets of light. Phys. World 14(6), 39–46 (2001)

    Google Scholar 

  74. Wójcik, D., Bialynicki-Birula, I., Zyczkowski, K.: Time evolution of quantum fractals. Phys. Rev. Lett. 85, 5022–5025 (2000)

    Article  ADS  Google Scholar 

  75. Berry, M.: Quantum fractal in boxes. J. Phys. A 29, 6617–6630 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  76. Hall, M.J.W., Reineker, M.S., Schleich, W.P.: Unravelling quantum carpets: A travelling-wave approach. J. Phys. A 32, 8275–8292 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  77. Amanatidis, E.J., Katsanos, D.E., Evangelou, S.N.: Fractal noise in quantum ballistic and diffusive lattice systems. Phys. Rev. B 69, 195107(1–8) (2004)

    Article  ADS  Google Scholar 

  78. Guantes, R., Sanz, A.S., Margalef-Roig, J., Miret-Artés, S.: Atom-surface diffraction: A trajectory description. Surf. Sci. Rep. 53, 199–330 (2004)

    Article  ADS  Google Scholar 

  79. Sanz, A.S., Miret-Artés, S.: Selective adsorption resonances: Quantum and stochastic approaches. Phys. Rep. 451, 37–154 (2007)

    Article  ADS  Google Scholar 

  80. Born, M., Wolf, E.: Principles of Optics. Pergamon Press, New York (1980)

    Google Scholar 

  81. Kaplan, A.E., Marzoli, I., Lamb, W.E. Jr., Schleich, W.P.: Multimode interference: Highly regular pattern formation in quantum wave-packet evolution. Phys. Rev. A 61, 032101(1–6) (2000)

    Article  ADS  Google Scholar 

  82. Nest, M.: Quantum carpets and correlated dynamics of several fermions. Phys. Rev. A 73, 023613(1–6) (2006)

    Article  ADS  Google Scholar 

  83. Sanz, A.S., Miret-Artés, S.: Comment on “Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics” [J. Chem. Phys. 125, 231103 (2006)]. J. Chem. Phys. 127, 197101(1–3) (2007)

    Article  ADS  Google Scholar 

  84. Sanz, A.S., Miret-Artés, S.: Aspects of nonlocality from a quantum trajectory perspective: A WKB approach to Bohmian mechanics. Chem. Phys. Lett. 445, 350–354 (2007)

    Article  ADS  Google Scholar 

  85. Sanz, A.S., Borondo, F., Miret-Artés, S.: On the classical limit in atom-surface diffraction. Europhys. Lett. 55, 303–309 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sanz, Á.S., Miret-Artés, S. (2014). Interference and Interferometry. In: A Trajectory Description of Quantum Processes. II. Applications. Lecture Notes in Physics, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17974-7_3

Download citation

Publish with us

Policies and ethics