An introduction to quantum interferometry: Young's experiment with fock and coherent states
H. Sanabriaª and B.M. Rodríguez–Larab
ª Department of Neurobiology and Anatomy, University of Texas Medical School at Houston, Houston, TX 77030, USA, e–mail: Hugo.Sanabria@uth.tmc.edu
b Facultad de Ingeniería Arturo Narro Siller, Universidad Autónoma de Tamaulipas, 89 330 Tampico, México, e–mail: bmlara@uat.edu.mx
Recibido el 31 de julio de 2006 ]]> Aceptado el 18 de enero de 2007
Abstract
Quantum interferometry uses the quantum properties of light to surpass the Rayleigh diffraction limit inherent in classical interferometry. We have used Fock and coherent states, which describe the electromagnetic input field, a multi–photon counting apparatus, and an operator–based approach to a multi–slit Young's experiment to present the principles behind quantum interferometry. Our calculations show interference fringes that depend on the wavelength of the source λ, the number of slits in the Young's screen—both characteristics present in the classical scheme—, and the number of photons m, that the measurement apparatus detects. The latter dependence generates an effective de Broglie wavelength, λ/m, a phenomenon that can only be observed by taking advantage of the quantum properties of light.
Keywords: Quantum interferometry; Young experiment; photon states; diffraction limit.
Resumen
La interferometría cuántica utiliza las propiedades no clásicas de la luz para rebasar el límite de difracción de Rayleigh presente en interferometría clásica. Usando estados de Fock y estados coherentes, que describen el campo electromagnético de la fuente de luz, un detector dependiente del número de fotones presentes en el campo, y una descripción operacional del experimento de Young generalizado a múltiples aperturas, presentamos los principios básicos de interferometría cuántica. Los resultados obtenidos muestran franjas de interferencia que dependen de la longitud de onda de la luz λ, del número de aperturas en la pantalla de Young—ambas características presentes en el caso clásico— y del número de fotones m que puede detectar el aparato de medición. Esta última dependencia genera una longitud de onda efectiva de de Broglie dada por λ/m, un fenómeno que sólo puede ser observado utilizando las propiedades cuánticas de la luz.
Descriptores: Interferometría cuántica; experimento de Young; estados de fotones; límite de difracción.
]]> PACS: 01.40.–d; 03.65.Ta; 42.25.Hz
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References
1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999). [ Links ]
2. K.T. Hecht, Quantum Mechanics (Springer, 2005). [ Links ]
3. C. Roychoudhuri and R. Roy, Opt. Photonics News 14 (2003) S1. [ Links ]
4. M.O. Scully and M.S. Zubairy, Quantum optics, 1st ed. (Cambridge Universite, Press, Cambridge, 1997). [ Links ]
5. P. Meystre and M. Sargent III, Elements of quantum optics, 3rd ed. (Springer–Verlag, Berlin, 1998). [ Links ]
6. R. Loudon, The quantum theory of light, 2nd ed. (Oxford University Press, 1983). [ Links ]
7. M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge Univ. Press, 2000). [ Links ]
8. D. Bowmeester and A. Zeilinger, The physics of quantum information: quantum cryptography, quantum teleportation, quantum computation (Springer–Verlag, Berlin, 2000). [ Links ]
9. A. Muthukrishnan, M. Scully, and M. Zubairy, J. Opt. B 6 (2004) S575. [ Links ]
10. G. Bjork, J. Soderholm, and L.L. Sanchez–Soto, J. Opt. Soc. Am. B 6 (2004) S478. [ Links ]
11. A. Boto et al., Phys. Rev. Lett. 85 (2000) 2733. [ Links ]
12. A. Zeilinger, Rev. Mod. Phys. 71 (1999) 288. [ Links ]
13. E. Fonseca, P. Souto Ribeiro, A. Padua, and C. Monken, Phys. Rev. A 60 (1999) 1530. [ Links ]
14. J. Perina, B. Saleh, and M. Teich, Rev. Rev. A 49 (1998) 3972. [ Links ]
15. M. Mitchell, J. Lundeen, and A Steinberg, Nature 429 (2004) 161. [ Links ]
16. P. Walther et al., Nature 429 (2004) 158. [ Links ]
17. M. D'Angelo, M. Chekhova, and Y. Shih, Phys. Rev. Lett. 87 (2001) 013602. [ Links ]
18. R. Bennink, S. Bentley, and R. Boyd, Phys. Rev. Lett. 89 (2002) 113601. [ Links ]
19. M. D'Angelo, Y.–H. Kim, S.P Kulik, and Y Shih, Phys. Rev. Lett. 92 (2004) 233601. [ Links ]
20. M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge, 1999). [ Links ]
21. R.P. Feynman, R.B. Leighton, and M. Sands, The Feyman lectures on physics III: quantum mechanics (Addison–Wesley, Massachusetts, 1965). [ Links ]
22. L. Allen and J. Eberly, Optical resonace and two–level atoms (Wyley, New York, 1975). [ Links ]
23. R. Glauber, Phys. Rev. 130 (1963) 2529. [ Links ]
24. J. Kim, S. Takeuchi, and Y Yamamoto, Appl. Phys. Lett. 74 (1999) 902. [ Links ]
25. D. Lincoln, Nucl. Inst. Meth. A 453 (2000) 177. [ Links ]
26. G. Khouty, H. Eisenberg, E. Fonseca, and D. Bouwmeester, quant–ph/0601104 p. 0601104 (2006). [ Links ]
27. E.R. Floyd, quant–ph/0605120 (2006). [ Links ]
28. E.R. Floyd, quant–ph/0605121 (2006). [ Links ]
29. S.W. Hell, Nat. Biotechnol. 21 (2003) 1347. [ Links ]
30. M.G.L. Gustasfsson, J. Microsc. 298 (2000) 82. [ Links ] ]]>