Bose-Einstein condensates in super-lattices

SIAM Journal on Applied Dynamical Systems

Volumn 4, Issue 4, 2005, Pages 783-807

  Porter, Mason A ^a   Kevrekidis, P G ^b  

^a California Institute of Technology   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Bose Einstein condensates; Hamiltonian systems; Multiple scale perturbation theory

Indexed keywords

BOSE-EINSTEIN CONDENSATES; HAMILTONIAN SYSTEMS; MULTIPLE SCALE PERTURBATION THEORY;

COMPUTER SIMULATION; HAMILTONIANS; PERTURBATION TECHNIQUES; RESONANCE; SUPERLATTICES;

QUANTUM THEORY;

EID: 33644685994     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040610611     Document Type: Article

References (62)

1. M. ABRAMOWITZ AND I. STEGUN, EDS., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series 55, National Bureau of Standards, Washington, DC, 1964.
2. G. L. ALFIMOV, P. G. KEVREKIDIS, V. V. KONOTOP, AND M. SALERNO, Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential, Phys. Rev. E, 66 (2002), paper 046608.
3. B. P. ANDERSON AND M. A. KASEVICH, Macroscopic quantum interference from atomic tunnel arrays, Science, 282 (1998), pp. 1686-1689.
4. 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 (1995), pp. 198-201.
5. T. ANKER, M. ALBIEZ, R. GATI, S. HUNSMANN, B. EIERMANN, A. TROMBETTONI, AND M. K. OBERTHALER, Nonlinear self-trapping of matter waves in periodic potentials, Phys. Rev. Lett., 94 (2005), paper 020403.
6. N. W. ASHCROFT AND N. D. MERMIN, Solid State Physics, Brooks/Cole, South Melbourne, Australia, 1976.
7. B. B. BAIZAKOV, V. V. KONOTOP, AND M. SALERNO, Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability, J. Phys. B, 35 (2002), pp. 5105-5119.
8. Y. B. BAND, I. TOWERS, AND B. A. MALOMED, Unified semiclassical approximation for Bose-Einstein condensates: Application to a BEC in an optical potential, Phys. Rev. A, 67 (2003), paper 023602.
9. C. M. BENDER AND S. A. ORSZAG, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978.
10. K. BERG-SØRENSEN AND K. MØLMER, Bose-Einstein condensates in spatially penodic potentials, Phys. Rev. A, 58 (1998), pp. 1480-1484.
11. V. A. BRAZHNYI AND V. V. KONOTOP, Theory of nonlinear matter waves in optical lattices, Modern Phys. Lett. B, 18 (2004), pp. 627-651.
12. J. C. BRONSKI, L. D. CARR, R. CARRETERO-GONZÁLEZ, B. DECONINCK, J. N. KUTZ, AND K. PROMIS-LOW, Stability of attractive Bose-Einstein condensates in a periodic potential, Phys. Rev. E, 64 (2001), paper 056615.
13. J. C. BRONSKI, L. D. CARR, B. DECONINCK, AND J. N. KUTZ, Bose-Einstein condensates in standing waves: The cubic nonlinear Schrödinger equation with a periodic potential, Phys. Rev. Lett., 86 (2001), pp. 1402-1405.
14. J. C. BRONSKI, L. D. CARR, B. DECONINCK, J. N. KUTZ, AND K. PROMISLOW, Stability of repulsive Bose-Einstein condensates in a periodic potential, Phys. Rev. E, 63 (2001), paper 036612.
15. L. BRUSCH, A. TORCINI, M. VAN HECKE, M. G. ZIMMERMANN, AND M. BÄR, Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation, Phys. D, 160 (2001), pp. 127-148.
16. L. BRUSCH, M. G. ZIMMERMANN, M. VAN HECKE, M. BÄR, AND A. TORCINI, Modulated amplitude waves and the transition from phase to defect chaos, Phys. Rev. Lett., 85 (2000), pp. 86-89.
17. K. BURNETT, M. EDWARDS, AND C. W. CLARK, The theory of Bose-Einstein condensation of dilute gases, Physics Today, 52 (1999), pp. 37-42.
18. R. CARRETERO-GONZÁLEZ AND K. PROMISLOW, Localized breathing oscillations of Bose-Einstein condensates in periodic traps, Phys. Rev. A, 66 (2002), paper 033610.
19. F. S. CATALIOTTI, L. FALLANI, F. FERLAINO, C. FORT, P. MADDALONI, AND M. INGUSCIO, Superfluid current disruption in a chain of weakly coupled Bose-Einstein condensates, New J. Phys., 5 (2003), pp. 71.1-71.7.
20. D.-I. CHOI AND Q. NIU, Bose-Einstein condensates in an optical lattice, Phys. Rev. Lett., 82 (1999), pp. 2022-2025.
21. F. DALFOVO, S. GIORGINI, L. P. PITAEVSKII, AND S. STRINGARI, Theory of Bose-Einstein condensation on trapped gases, Rev. Modern Phys., 71 (1999), pp. 463-512.
22. 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 (1995), pp. 3969-3973.
23. L. A. DMITRIEVA AND Y. A. KUPERIN, Spectral modelling of quantum superlattice and application to the Mott-Peierls simulated transitions, cond-mat/0311468, 2003.
24. E. A. DONLEY, N. R. CLAUSSEN, S. L. CORNISH, J. L. ROBERTS, E. A. CORNELL, AND C. E. WEIMAN, Dynamics of collapsing and exploding Bose-Einstein condensates, Nature, 412 (2001), pp. 295-299.
25. Y. EKSIOGLU, P. VIGNOLO, AND M. P. TOSI, Matter-wave interferometry in periodic and quasi-periodic arrays, Optics Comm., 243 (2004), pp. 175-181.
26. N. GEMELKE, E. SARAJLIC, Y. BIDEL, S. HONG, AND S. CHU, Period-doubling instability of Bose-Einstein condensates induced in periodically translated optical lattices, cond-mat/0504311, 2005.
27. H. GOLDSTEIN, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA, 1980.
28. M. GREINER, O. MANDEL, T. ESSLINGER, T. MÄNSCH, AND I. BLOCH, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, 415 (2002), pp. 39-44.
29. E. W. HAGLEY, L. DENG, M. KOZUMA, J. WEN, K. HELMERSON, S. L. ROLSTON, AND W. D. PHILLIPS, A well-collimated quasi-continuous atom laser, Science, 283 (1999), pp. 1706-1709.
30. W. KETTERLE, Experimental studies of Bose-Einstein condensates, Physics Today, 52 (1999), pp. 30-35.
31. P. G. KEVREKIDIS, R. CARRETERO-GONZÁLEZ, D. J. FRANTZESKAKIS, AND I. KEVREKIDIS, Vortices in Bose-Einstein condensates: Some recent developments, Modern Phys. Lett. B, 18 (2004), pp. 1481-1505.
32. P. G. KEVREKIDIS AND D. J. FRANTZESKAKIS, Pattern forming dynamical instabilities of Bose-Einstein condensates, Modern Phys. Lett. B, 18 (2004), pp. 173-202.
33. P. G. KEVREKIDIS, D. J. FRANTZESKAKIS, B. A. MALOMED, A. R. BISHOP, AND I. G. KEVREKIDIS, Dark-in-bright solitons in Bose-Einstein condensates with attractive interactions, New J. Phys., 5 (2003), pp. 64.1-64.17.
34. P. G. KEVREKIDIS, G. THEOCHARIS, D. J. FRANTZESKAKIS, AND B. A. MALOMED, Feshbach resonance management for Bose-Einstein condensates, Phys. Rev. Lett., 90 (2003), paper 230401.
35. T. KÖHLER, Three-body problem in a dilute Bose-Einstein condensate, Phys. Rev. Lett., 89 (2002), paper 210404.
36. D. F. LAWDEN, Elliptic Functions and Applications, Appl. Math. Sci. 80, Springer-Verlag, New York, 1989.
37. P. J. Y. LOUIS, E. A. OSTROVSKAYA, AND Y. S. KIVSHAR, Matter-wave dark solitons in optical lattices, J. Opt. B Quantum Semiclassical Opt., 6 (2004), pp. S309-S317.
38. P. J. Y. LOUIS, E. A. OSTROVSKAYA, C. M. SAVAGE, AND Y. S. KIVSHAR, Bose-Einstein condensates in optical lattices: Band-gap structure and solitons, Phys. Rev. A, 67 (2003), paper 013602.
39. M. MACHHOLM, A. NICOLIN, C. J. PETHICK, AND H. SMITH, Spatial period-doubling in Bose-Einstein condensates in an optical lattice, Phys. Rev. A, 69 (2004), paper 043604.
40. M. MACHHOLM, C. J. PETHICK, AND H. SMITH, Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential, Phys. Rev. A, 67 (2003), paper 053613.
41. B. A. MALOMED, Z. H. WANG, P. L. CHU, AND G. D. PENG, Multichannel switchable system for spatial solitons, J. Opt. Soc. Amer. B Opt. Phys., 16 (1999), pp. 1197-1203.
42. O. MORSCH, J. H. MÜLLER, M. CHRISTIANI, D. CIAMPINI, AND E. ARIMONDO, Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices, Phys. Rev. Lett., 87 (2001), paper 140402.
43. E. J. MUELLER, Superfluidity and mean-field energy loops; Hysteretic behavior in Bose-Einstein condensates, Phys. Rev. A, 66 (2002), paper 063603.
44. A. H. NAYFEH AND D. T. MOOK, Nonlinear Oscillations, John Wiley & Sons, New York, 1995.
45. C. ORZEL, A. K. TUCHMAN, M. L. FENSELAU, M. YASUDA, AND M. A. KASEVICH, Squeezed states in a Bose-Einstein condensate, Science, 291 (2001), pp. 2386-2389.
46. P. PEDRI, L. PITAEVSKII, S. STRINGARI, C. FORT, S. BURGER, F. S. CATALIOTII, P. MADDALONI, F. MINARDI, AND M. INGUSCIO, Expansion of a coherent array of Bose-Einstein condensates, Phys. Rev. Lett., 87 (2001), paper 220401.
47. S. PEIL, J. V. PORTO, B. LABURTHE TOLRA, J. M. OBRECHT, B. E. KING, M. SUBBOTIN, S. L. ROLSTON, AND W. D. PHILLIPS, Patterned loading of a Bose-Einstein condensate into an optical lattice, Phys. Rev. A, 67 (2003), paper 051603(R).
48. C. J. PETHICK AND H. SMITH, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge, UK, 2002.
49. M. A. PORTER AND P. CVITANOVIĆ, Modulated amplitude waves in Bose-Einstein condensates, Phys. Rev. E, 69 (2004), paper 047201.
50. M. A. PORTER AND P. CVITANOVIĆ, A perturbative analysis of modulated amplitude waves in Bose-Einstein condensates, Chaos, 14 (2004), pp. 739-755.
51. M. A. PORTER, P. G. KEVREKIDIS, AND B. A. MALOMED, Resonant and non-resonant modulated amplitude waves for binary Bose-Einstein condensates in optical lattices, Phys. D, 196 (2004), pp. 106-123.
52. J. V. PORTO, S. ROLSTON, B. LABURTHE TOLRA, C. J. WILLIAMS, AND W. D. PHILLIPS, Quantum information with neutral atoms as qubits, Philos. Trans. Math. Phys. Eng. Sci., 361 (2003), pp. 1417-1427.
53. R. H. RAND, Lecture Notes on Nonlinear Vibrations, online book available at http://www.tam.cornell.edu/randdocs/nlvibe45.pdf, 2003.
54. A. M. REY, B. L. HU, E. CALZETTA, A. ROURA, AND C. CLARK, Nonequilibrium dynamics of optical lattice-loaded BEC atoms: Beyond HFB approximation, Phys. Rev. A, 69 (2004), paper 033610.
55. L. SALASNICH, A. PAROLA, AND L. REATTO, Periodic quantum tunnelling and parametric resonance with cigar-shaped Bose-Einstein condensates, J. Phys. B, 35 (2002), pp. 3205-3216.
56. A. SMERZI, A. TROMBETTONI, P. G. KEVREKIDIS, AND A. R. BISHOP, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates, Phys. Rev. Lett., 89 (2002), paper 170402.
57. S. STRINGARI AND L. PITAEVSKII, Bose-Einstein Condensation, Oxford University Press, Oxford, UK, 2003.
58. K. G. H. VOLLBRECHT, E. SOLANO, AND J. L. CIRAC, Ensemble quantum computation with atoms in periodic potentials, Phys. Rev. Lett., 93 (2004), paper 220502.
59. E. T. WHITTAKER AND G. N. WATSON, A Course of Modern Analysis, 4th ed., Cambridge University Press, Cambridge, UK, 1927.
60. R. S. ZOUNES AND R. H. RAND, Global behavior of a nonlinear quasiperiodic Mathieu equation, in Proceedings of the 2001 ASME Design Engineering Technical Conferences, Pittsburgh, PA, 2001, ASME, New York, 2001, VIB-21595.
61. R. S. ZOUNES AND R. H. RAND, Global behavior of a nonlinear quasiperiodic Mathieu equation, Nonlinear Dynam., 27 (2002), pp. 87-105.
62. R. S. ZOUNES AND R. H. RAND, Subharmonic resonance, in the non-linear Mathieu equation, Internat. J. Non-Linear Mech., 37 (2002), pp. 43-73.