Self-similar scaling in the coherent dynamics of ultracold atoms

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 2, 2009, Pages

  Artoni, M ^a,b   La Rocca, G ^c   Ferrari, G ^b,d  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

^c SCUOLA NORMALE SUPERIORE   (Italy)

^d INFN SEZIONE DI FIRENZE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC WAVE PACKETS; BLOCH OSCILLATIONS; COHERENT DYNAMICS; DRIVING PERIODS; ENERGY SPECTRA; HOFSTADTER; OPTICAL-LATTICE POTENTIAL; QUASI-ENERGY; SELF-SIMILAR; SELF-SIMILAR PATTERNS; ULTRA-COLD; ULTRACOLD ATOMS;

ATOMS; MAGNETIC FIELDS;

ATOMIC SPECTROSCOPY;

EID: 69449106641     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.021604     Document Type: Article

References (26)

1. Quantum Chaos Between Order and Disorder, edited by, G. Casati, and, B. Chirikov, (Cambridge University Press, Cambridge, 1995), p. 633.
2. H. J. Stoeckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, 1999).
3. D. Hofstadter, Phys. Rev. B 14, 2239 (1976). 10.1103/PhysRevB.14.2239
4. F. Claro, M. Pacheco, and Z. Barticevic, Phys. Rev. Lett. 64, 3058 (1990). 10.1103/PhysRevLett.64.3058
5. U. Kuhl and H. J. Stockmann, Phys. Rev. Lett. 80, 3232 (1998). 10.1103/PhysRevLett.80.3232
6. O. Richoux and V. Pagneux, Europhys. Lett. 59, 34 (2002). 10.1209/epl/i2002-00156-5
7. D. Jaksch, New J. Phys. 5, 56 (2003). 10.1088/1367-2630/5/1/356
8. J. Wang and J. Gong, Phys. Rev. A 77, 031405 (R) (2008). 10.1103/PhysRevA.77.031405
9. M. Raizen, Phys. Today 50 (7), 30 (1997). 10.1063/1.881845
10. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996). 10.1103/PhysRevLett.76.4508
11. O. Morsch, J. H. Muller, M. Cristiani, D. Ciampini, and E. Arimondo, Phys. Rev. Lett. 87, 140402 (2001). 10.1103/PhysRevLett.87.140402
12. G. Roati, E. de Mirandes, F. Ferlaino, H. Ott, G. Modugno, and M. Inguscio, Phys. Rev. Lett. 92, 230402 (2004). 10.1103/PhysRevLett.92.230402
13. G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, Phys. Rev. Lett. 97, 060402 (2006). 10.1103/PhysRevLett.97.060402
14. V. V. Ivanov, A. Alberti, M. Schioppo, G. Ferrari, M. Artoni, M. L. Chiofalo, and G. M. Tino, Phys. Rev. Lett. 100, 043602 (2008). 10.1103/PhysRevLett.100.043602
15. C. Sias, H. Lignier, Y. P. Singh, A. Zenesini, D. Ciampini, O. Morsch, and E. Arimondo, Phys. Rev. Lett. 100, 040404 (2008). 10.1103/PhysRevLett.100. 040404
16. M. Gluck, Phys. Rep. 366, 103 (2002), e.g., examine in Ch. 7 a Hamiltonian, which can be recovered from Eq. 1 upon a suitable change in variables, giving rise to a seemingly self-similar pattern in the dwell time of a particle in the chaotic region of its trajectory. This is however at variance with the self-similar scaling both in the quasienergies topology and amplitudes which we anticipate here. 10.1016/S0370-1573(02)00142-4
17. G. Wannier, Phys. Rev. 52, 191 (1937). 10.1103/PhysRev.52.191
18. We restrict to widths smaller than the Brillouin zone (2π/a). This affects only the amplitude of the oscillations yet leaving their time-dependent behavior unaltered.
19. Fractional ladders may also be studied by adopting a more involved approach based on Floquet theory as, e.g., in X. G. Zhao, Phys. Lett. A 202, 297 (1995), where an absorption detection scheme has also been envisaged 10.1016/0375-9601(95)00336-2
20. see also Q. Thommen, J. C. Garreau, and V. Zehnle, Phys. Rev. A 65, 053406 (2002) where a detection scheme based instead on Raman stimulated spectroscopy has been suggested. 10.1103/PhysRevA.65.053406
21. Owing to a further symmetry upon reflection of the pattern about T/ T0 =1/2, the same recursive structure can be observed in the remaining part of the spectrum of Fig. 3 spanning rational values of T/ T0 between 1/2 and 1.
22. F. L. Moore, J. C. Robinson, C. Bharucha, P. E. Williams, and M. G. Raizen, Phys. Rev. Lett. 73, 2974 (1994). 10.1103/PhysRevLett.73.2974
23. Nonlinearities, negligible in fermionic atoms and in some cases of cold yet not condensed bosonic atoms, may also be controlled or compensated in other specific cases, see, e.g., M. Salerno, V. V. Konotop, and Y. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008) 10.1103/PhysRevLett.101.030405
24. M. Gustavsson, Phys. Rev. Lett. 100, 080404 (2008) 10.1103/PhysRevLett. 100.080404
25. M. Fattori, Phys. Rev. Lett. 100, 080405 (2008) 10.1103/PhysRevLett.100. 080405
26. and Y. V. Bludov, J. Phys. B 42, 105302 (2009). 10.1088/0953-4075/42/10/ 105302