Quantum interference experiments with large molecules

American Journal of Physics

Volumn 71, Issue 4, 2003, Pages 319-325

  Nairz, Olaf ^a,b   Arndt, Markus ^a   Zeilinger, Anton ^a  

^a INSTITUT FÜR EXPERIMENTALPHYSIK   (Austria)

^b UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037391010     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1531580     Document Type: Article

References (47)

1. M. Planck, "Zur Theorie des Gesetzes der Energieverteilung im Normalenspektrum," Verh. Dtsch. Phys. Ges. 2, 237 (1900); English translation: "On the theory of the energy distribution law of the normal spectrum," in The Old Quantum Theory, edited by D. ter Haar (Pergamon, New York, 1967), p. 82.
2. M. Planck, "Zur Theorie des Gesetzes der Energieverteilung im Normalenspektrum," Verh. Dtsch. Phys. Ges. 2, 237 (1900); English translation: "On the theory of the energy distribution law of the normal spectrum," in The Old Quantum Theory, edited by D. ter Haar (Pergamon, New York, 1967), p. 82.
3. P. Lenard, "Über die lichtelektrische Wirkung," Ann. Phys. (Leipzig) 8, 149-198 (1902).
4. A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Ann. Phys. (Leipzig) 17, 132-148 (1905); English translation: A. Arons and M. Peppard, "Concerning an heuristic point of view toward the emission and transformation of light," Am. J. Phys. 33, 367-374 (1965).
5. A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Ann. Phys. (Leipzig) 17, 132-148 (1905); English translation: A. Arons and M. Peppard, "Concerning an heuristic point of view toward the emission and transformation of light," Am. J. Phys. 33, 367-374 (1965).
6. L. de Broglie, "Waves and quanta," Nature (London) 112, 540-540 (1923).
7. C. Davisson and L. Germer, "The scattering of electrons, by a single crystal of nickel," Nature (London) 119, 558-560 (1927).
8. A student, having been taught some elementary statistical physics, would be tempted to answer the second one by analogy with the Galton board. Also there, the trajectory of the single particle appears to be undetermined and still the count rate in each channel would be in agreement with the deterministic laws of classical statistics. But we should note, first of all, that the apparent randomness in this example is only due to the ill-defined initial conditions when we release the ball. Second, if we were to perform such a Galton experiment with two different starting positions, the probability distributions of these experiments would simply add up and interference would never be observed.
9. C. Brukner and A. Zeilinger, "Young's experiment and the finiteness of information," Philos. Trans. R. Soc. London, Ser. A 360, 1061-1069 (2002).
10. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
11. I. Estermann and O. Stern, "Beugung von Molekularstrahlen," Z. Phys. 61, 95-125 (1930).
12. H. v. Halban Jnr. and P. Preiswerk, "Preuve Expérimentale de la Diffraction Des Neutrons," C. R. Acad. Sci. Paris 203, 73-75 (1936).
13. R. Gähler and A. Zeilinger, "Wave-optical experiments with very cold neutrons," Am. J. Phys. 59, 316-324 (1991).
14. C. Jönsson, "Electron diffraction at multiple slits," Am. J. Phys. 42, 4-11 (1974).
15. A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single- and double-dlit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
16. O. Carnal and J. Mlynek, "Young's, double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 66, 2689-2692 (1991).
17. W. Schöllkopf and J. P. Toennies, "Nondestructive mass selection of small van der Waals clusters," Science 266, 1345-1348 (1994).
18. W. Schöllkopf and J. Toennies, "The nondestructive detection of the Helium dimer and trimer," J. Chem. Phys. 104, 1155-1158 (1996).
19. T. W. Hänsch and A. L. Schawlow, "Cooling of gases by laser radiation," Opt. Commun. 13, 68-69 (1975).
20. + mono-ion oscillator III (side band cooling)," Bull. Am. Phys. Soc. 20, 637-637 (1975).
21. S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
22. C. N. Cohen-Tannoudji, "Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
23. W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
24. M. H, Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
25. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Bose-Einstein condensation in a gas of Sodium atoms," Phys. Rev. Lett. 75, 3969-3973 (1995).
26. M. R. Andrews, C. Townsend, H. Miesner, D. Durfee, D. Kurn, and W. Ketterle, "Observation of interference between two Bose condensates," Science 275, 637-641 (1997).
27. C. Bordé, N. Courtier, F. D. Burck, A. Goncharov, and M. Gorlicki, "Molecular interferometry experiments," Phys. Lett. A 188, 187-197 (1994).
28. 2 molecule," Eur. Phys. J. D 12, 235-240 (2000).
29. 2 molecules," Phys. Rev. Lett. 74, 4783-4786 (1995).
30. See comment by J. Clauser in Atom Interferometry, edited by P. R. Herman (Academic, New York, 1997), p. 143.
31. R. E. Grisenti, W. Schollkopf, J. P. Toennies, G. C. Hegerfeldt, T. Kohler, and M. Stoll, "Determination of the bond length and binding energy of the Helium dimer by diffraction from a transmission grating," Phys. Rev. Lett. 85, 2284-2287 (2000).
32. L. Saffaro, "Cosmoids, fullerenes and continuous polygons," in Proceedings of the First Italian Workshop on Fullerenes: Status and Perspectives, edited by C. Taliani, G. Ruani, and R. Zamboni (World Scientific, Singapore, 1992), Vol. 2, p. 55.
33. R. W. Marks, The Dymaxion World of Buckminster Fuller (Southern Illinois U.P., Carbondale, 1960).
34. H. Kroto, J. Heath, S. O'Brian, R. Curl, and R. Smalley, "C60: Buckmin-sterfullerene," Nature (London) 318, 162-166 (1985).
35. It is interesting to compare the de Broglie wavelength of the fullerene with its actual size: The buckyball has a diameter of about 1 nm, which is 350 times larger than its de Broglie wavelength. Our interference experiments clearly show that the concept of the de Broglie wavelength is not merely academic for objects with dimensions much larger than their wavelengths but can actually be demonstrated.
36. Our gratings were provided by Professor Henry Smith and Dr. Tim Savas of MIT.
37. 60 molecules," Nature (London) 401, 680-682 (1999); O. Nairz, M. Arndt, and A. Zeilinger, "Experimental challenges in fullerene interferometry," J. Mod. Opt. 47, 2811-2821 (2000).
38. 60 molecules," Nature (London) 401, 680-682 (1999); O. Nairz, M. Arndt, and A. Zeilinger, "Experimental challenges in fullerene interferometry," J. Mod. Opt. 47, 2811-2821 (2000).
39. For the original work see P. V. Cittert, "Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene," Physica (Amsterdam) 1, 201-210 (1934), and F. Zernike, "The concept of degree of coherence and its application to optical problems," ibid. 5, 785-795 (1938). A textbook with a detailed account of the theorem is M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1993).
40. For the original work see P. V. Cittert, "Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene," Physica (Amsterdam) 1, 201-210 (1934), and F. Zernike, "The concept of degree of coherence and its application to optical problems," ibid. 5, 785-795 (1938). A textbook with a detailed account of the theorem is M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1993).
41. For the original work see P. V. Cittert, "Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene," Physica (Amsterdam) 1, 201-210 (1934), and F. Zernike, "The concept of degree of coherence and its application to optical problems," ibid. 5, 785-795 (1938). A textbook with a detailed account of the theorem is M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1993).
42. L. Bergmann and C. Schaefer, Optics: Of Waves and Particles (de Gruyter, New York, 1999).
43. E. Hecht, Optics (Addison-Wesley, Reading, MA, 2002), 4th ed.
44. This effect has also been described in the context of He diffraction in R. E. Grisenti, W. Schöllkopf, J. P. Toennies, G. C. Hegerfeldt, and T. Köhler, "Determination of atom-surface van der Waals potentials from transmission-grating diffraction intensities," Phys. Rev. Lett. 83, 1755-1758 (1999).
45. -4 behavior at distances beyond 20 nm, due to the finite (retarded) signaling time between the molecule and its mirror image; see also H. B. G. Casimir and D. Polder, "The influence of retardation on the London-van der Waals forces," Phys. Rev. 73, 360-372 (1948).
46. 60," J. Chem. Phys. 103, 2445-2453 (1995).
47. K. Hansen and E. Campbell, "Thermal radiation from small particles," Phys. Rev. E 58, 5477-5482 (1998).