Light scattering by ultracold atoms in an optical lattice

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 1, 2010, Pages

  Rist, Stefan ^a   Menotti, Chiara ^b   Morigi, Giovanna ^a,c  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF TRENTO   (Italy)

^c SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ATOM-PHOTON INTERACTION; ATOMIC SITES; ATOMIC STATE; BRAGG SCATTERING; BRAGG SPECTROSCOPY; LINEAR REGIME; MATTER WAVES; MOTT INSULATORS; OPTICAL LATTICES; PHOTON RECOILS; SCATTERING CROSS SECTION; SUPERFLUID PHASE; THEORETICAL RESULT; TIME OF FLIGHT MEASUREMENTS; ULTRACOLD ATOMS;

ATOMIC SPECTROSCOPY; ATOMS; CRYSTAL LATTICES; LIGHT; LIGHT SCATTERING; OPTICAL MATERIALS; PHASE TRANSITIONS; PHOTONS; QUANTUM THEORY; REFRACTION;

SCATTERING;

EID: 73649116001     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.013404     Document Type: Article

References (75)

1. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976).
2. W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenkovic, X.-P. Huang, and D. J. Wineland, Science SCIEAS 0036-8075 10.1126/science.279.5351.686 279, 686 (1998).
3. M. Weidemüller, A. Hemmerich, A. Görlitz, T. Esslinger, and T. W. Hänsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.4583 75, 4583 (1995).
4. G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.2823 75, 2823 (1995).
5. G. Grynberg and C. Robilliard, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00017-5 355, 335 (2001).
6. L. Guidoni, C. Triché, P. Verkerk, and G. Grynberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3363 79, 3363 (1997).
7. S. Slama, C. von Cube, A. Ludewig, M. Kohler, C. Zimmermann, and Ph. W. Courteille, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.031402 72, 031402 (R) (2005);
8. S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann, and Ph. W. Courteille, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.193901 94, 193901 (2005);
9. S. Slama, C. von Cube, M. Kohler, C. Zimmermann, and Ph. W. Courteille, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.023424 73, 023424 (2006).
10. J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4569 82, 4569 (1999);
11. D. M. Stamper-Kurn, A. P. Chikkatur, A. Görlitz, S. Inouye, S. Gupta, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2876 83, 2876 (1999).
12. R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77.187 77, 187 (2005).
13. D. Clément, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.155301 102, 155301 (2009).
14. S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062317 68, 062317 (2003).
15. J. I. Cirac, R. Blatt, A. S. Parkins, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.48.2169 48, 2169 (1993);
16. Ch. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.538 85, 538 (2000).
17. S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.137901 90, 137901 (2003).
18. G. Morigi, J. Eschner, S. Mancini, and D. Vitali, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.023601 96, 023601 (2006).
19. I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, and W. D. Phillips, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.1394 52, 1394 (1995).
20. M. Weidemüller, A. Görlitz, T. W. Hänsch, and A. Hemmerich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.4647 58, 4647 (1998).
21. B. Nagorny, Th. Elsässer, and A. Hemmerich, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.153003 91, 153003 (2003);
22. D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.183601 91, 183601 (2003).
23. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
24. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108 81, 3108 (1998).
25. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen De, and U. Sen, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730701223200 56, 243 (2007).
26. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature NATUAS 0028-0836 10.1038/415039a 415, 39 (2002).
27. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.130403 92, 130403 (2004).
28. M. Krämer, C. Tozzo, and F. Dalfovo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.061602 71, 061602 (R) (2005).
29. A. M. Rey, P. B. Blakie, G. Pupillo, C. J. Williams, and C. W. Clark, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.023407 72, 023407 (2005).
30. A. Brunello, F. Dalfovo, L. Pitaevskii, S. Stringari, and F. Zambelli, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.063614 64, 063614 (2001).
31. C. Menotti, M. Krämer, L. Pitaevskii, and S. Stringari, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.053609 67, 053609 (2003).
32. H. W. Chan, A. T. Black, and V. Vuletic, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.063003 90, 063003 (2003);
33. A. T. Black, H. W. Chan, and V. Vuletic, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.203001 91, 203001 (2003).
34. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, Nature (London) NATUAS 0028-0836 10.1038/nature06120 450, 268 (2007);
35. F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, Science SCIEAS 0036-8075 10.1126/science.1163218 322, 235 (2008).
36. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, Nature (London) NATUAS 0028-0836 10.1038/nature06331 450, 272 (2007).
37. S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.213601 99, 213601 (2007);
38. K. W. Murch, K. L. Moore, S. Gupta, and D. M. Stamper-Kurn, Nature Phys. NATUAS 1745-2473 10.1038/nphys965 4, 561 (2008).
39. P. Cañizares, T. Görler, J. P. Paz, G. Morigi, and W. P. Schleich, Laser Phys. LAPHEJ 1054-660X 10.1134/S1054660X0707002X 17, 903 (2007).
40. I. B. Mekhov, C. Maschler, and H. Ritsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.100402 98, 100402 (2007);
41. I. B. Mekhov, C. Maschler, and H. Ritsch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.053618 76, 053618 (2007).
42. W. Chen, D. Meiser, and P. Meystre, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.023812 75, 023812 (2007).
43. I. B. Mekhov, C. Maschler, and H. Ritsch, Nature Phys. PLRAAN 1745-2473 10.1038/nphys571 3, 319 (2007).
44. J. Larson, B. Damski, G. Morigi, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.050401 100, 050401 (2008).
45. I. B. Mekhov and H. Ritsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.020403 102, 020403 (2009).
46. J. Ruostekoski, C. J. Foot, and A. B. Deb, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.170404 103, 170404 (2009).
47. J. Javanainen and J. Ruostekoski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.150404 91, 150404 (2003);
48. J. Ruostekoski, J. Javanainen, and G. V. Dunne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.013603 77, 013603 (2008).
49. M. Lewenstein, L. You, J. Cooper, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.50.2207 50, 2207 (1994).
50. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, New York, 2004).
51. M. Saba, T. A. Pasquini, C. Sanner, Y. Shin, W. Ketterle, and D. E. Pritchard, Science SCIEAS 0036-8075 10.1126/science.1108801 307, 1945 (2005).
52. A. M. Rey, Ph.D. thesis, University of Maryland, 2004 (http://jilawww.colorado.edu/~arey/papers/thesis.pdf).
53. L. Pitaevski and S. Stringari, Bose-Einstein Condensation (Oxford Science, Oxford, UK, 2003).
54. Equation (44) is reported with the density of states at the value of the laser frequency ωL. This approximation is justified, as the range of frequencies of the final states is of the order of the recoil frequency (from few to tens KHz), while the laser frequency is in the optical regime. The same approximation will be applied to the vacuum coupling strengths Cλ, Eq. (6), entering the interaction Hamiltonian Hint', Eq. (8).
55. While in general the use of the Gaussian ansatz in place of Wannier functions should be handled with care, as Wannier functions decay exponentially at infinity [see, e.g., W. Kohn, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.115.809 115, 809 (1959)], the precise form of the ansatz is not important for the purpose of this estimate.
56. The linewidth of the excitations is essentially determined by the spontaneous decay rate of the excited state. In this treatment, we are assuming γ'T 1, where γ' is the rate of incoherent scattering and is of the order γ'~γCLα2/Δ2.
57. T. D. Kühner, S. R. White, and H. Monien, Phys. Rev. B PHRVAO 1098-0121 10.1103/PhysRevB.61.12474 61, 12474 (2000).
58. K. Sengupta and N. Dupuis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.033629 71, 033629 (2005).
59. S. Konabe, T. Nikuni, and M. Nakamura, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.033621 73, 033621 (2006).
60. Y. Ohashi, M. Kitaura, and H. Matsumoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.033617 73, 033617 (2006).
61. S. D. Huber, E. Altman, H. P. Büchler, and G. Blatter, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.75.085106 75, 085106 (2007).
62. C. Menotti and N. Trivedi, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.77.235120 77, 235120 (2008).
63. S. Guibal, C. Mennerat-Robilliard, D. Larousserie, C. Triche, J. Y. Courtois, and G. Grynberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.4709 78, 4709 (1997).
64. D. V. van Coevorden, R. Sprik, A. Tip, and A. Lagendijk, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.2412 77, 2412 (1996).
65. P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/63/4/201 63, 455 (2000).
66. M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E RPPHAG 1539-3755 10.1103/PhysRevE.72.046604 72, 046604 (2005).
67. Y. D. Chong, D. E. Pritchard, and M. Soljacic, Phys. Rev. B RPPHAG 1098-0121 10.1103/PhysRevB.75.235124 75, 235124 (2007).
68. I. Carusotto, M. Antezza, F. Bariani, S. De Liberato, and C. Ciuti, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.063621 77, 063621 (2008);
69. F. Bariani and I. Carusotto, J. Eur. Opt. Soc. PLRAAN 1990-2573 10.2971/jeos.2008.08005 3, 08005 (2008).
70. S. Rist, P. Vignolo, and G. Morigi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053822 79, 053822 (2009).
71. M. Antezza and Y. Castin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.013816 80, 013816 (2009).
72. S. Rist, J. Eschner, M. Hennrich, and G. Morigi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.013808 78, 013808 (2008).
73. K. Ekert, O. Romero Isart, M. Rodriguez, M. Lewenstein, E. Polzik, and A. Sanpera, Nature Phys. PLRAAN 1745-2473 10.1038/nphys776 4, 50 (2008).
74. V. B. Braginsky and F. Y. Khalili, in Quantum Measurement, edited by, K. S. Thorne, (Cambridge University, New York, 1995).
75. P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.043003 96, 043003 (2006).