Quantum interference in a driven washboard potential

American Journal of Physics

Volumn 72, Issue 8, 2004, Pages 1017-1025

  Thommen, Quentin ^a   Garreau, Jean Claude ^a   Zehnlé, Véronique ^a  

^a UNIVERSITÉ DES SCIENCES ET TECHNOLOGIES DE LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344670284     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1757446     Document Type: Article

References (32)

1. F. Bloch, "Über die Quantenmechanik der Elektronen in Kristallgittern," Z. Phys. 52, 555-600 (1928).
2. C. Zener, "A theory of electrical breakdown of solid dielectrics," Proc. R. Soc. London, Ser. A 145, 523-529 (1934).
3. G. H. Wannier, "Wave functions and effective Hamiltonian for Bloch electrons in an electric field," Phys. Rev. 117, 432-439 (1960).
4. E. E. Mendez, F. Agulló-Rueda, and J. M. Hong, "Stark localization in GaAs-GaAlAs superlattices under an electric field," Phys. Rev. Lett. 60, 2426-2429 (1988).
5. P. Voisin, J. Bleuse, C. Bouche, S. Gaillard, C. Alibert, and A. Regreny, "Observation of the Wannier-Stark quantization in a semiconductor superlattice," Phys. Rev. Lett. 61, 1639-1642 (1988).
6. C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
7. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, "Bloch oscillations of atoms in an optical potential," Phys. Rev. Lett. 76, 4508-4511 (1996).
8. S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, "Observation of atomic Wannier-Stark ladders in an accelerating optical potential," Phys. Rev. Lett. 76, 4512-4515 (1996).
9. Q. Niu, X. G. Zhao, G. A. Georgakis, and M. G. Raizen, "Atomic Landau-Zener tunneling and Wannier-Stark ladders in optical potentials," Phys. Rev. Lett. 76, 4504-4507 (1996).
10. B. P. Anderson and M. Kasevich, "Microscopic quantum interference from atomic tunnel arrays," Science 282, 1686-1689 (1998).
11. O. Morsch, J. H. Mueller, M. Cristiani, D. Ciampini, and E. Arimondo, "Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices," Phys. Rev. Lett. 87, 1404021-1404024 (2001).
12. M. G. Raizen, C. Salomon, and Q. Niu, "New light on quantum transport," Phys. Today 50 (7), 30-34 (1997).
13. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons et Atomes: Processus d'Interaction (InterEditions, Paris, 1988); English translation: Photon and Atoms: Basic Processes and Applications (Wiley, New York, 1997).
14. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons et Atomes: Processus d'Interaction (InterEditions, Paris, 1988); English translation: Photon and Atoms: Basic Processes and Applications (Wiley, New York, 1997).
15. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, Berlin, 1999).
16. P. Meystre, Atom Optics (Springer-Verlag, Berlin, 2001).
17. Q. Thommen, J. C. Garreau, and V. Zehnlé, "Theoretical analysis of quantum dynamics in one-dimensional lattices: Wannier-Stark description," Phys. Rev. A 65, 0534061-0534068 (2002).
18. Several simple Maple programs for visualization of the results are available from 〉http://www.phlam.univ-lillel.fr/atfr/cq〈
19. N. W. Ashkroft and N. D. Mermin, Solid State Physics (Saunders College, Fort Worth, TX, 1976).
20. We suppose that the system is enclosed in a large bounding box (containing many wells L ≫ 1000) and consider the bulk properties that are not altered by boundary effects.
21. 0,0 + n does depend on n.
22. B.
23. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).
24. E. Merzbacher, Quantum Mechanics 3rd ed. (Wiley, New York, 1998).
25. This approximation is not necessary, but it simplifies the calculations with out any loss of physical effects. For a treatment without this approximation, see Q. Thommen, J. C. Garreau, and V. Zehnlé, "Atomic motion in tilted optical lattices," Arxiv quant-ph/0307118 (2003).
26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
27. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
28. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
29. G. Monsivais, M. D. Castillo-Mussot, and F. Claro, "Stark-ladder reso nances in the propagation of electromagnetic waves," Phys. Rev. Lett. 64, 1433-1436 (1990).
30. Readers unfamiliar with the properties of Fourier series can find good accounts in M. R. Spiegel, Schaum's Outline of Fourier Analysis with Applications to Boundary Value Problems (McGraw-Hill, Columbus, OH, 1974); E. Butkov, Mathematical Physics (Addison-Wesley, Reading, MA, 1973), for example.
31. Readers unfamiliar with the properties of Fourier series can find good accounts in M. R. Spiegel, Schaum's Outline of Fourier Analysis with Applications to Boundary Value Problems (McGraw-Hill, Columbus, OH, 1974); E. Butkov, Mathematical Physics (Addison-Wesley, Reading, MA, 1973), for example.
32. Q. Thommen, J. C. Garreau, and V. Zehnlé, "Atomic motion in tilted optical lattices: an analytical approach," J. Opt. B: Quantum Semiclass. Opt. 6, 301-308 (2004).