Interaction of excited states in two-species Bose-Einstein condensates: A case study

SIAM Journal on Applied Dynamical Systems

Volumn 9, Issue 1, 2010, Pages 34-61

  Kapitula, Todd ^a   Law, Kody J H ^b   Kevrekidis, Panayotis G ^b  

^a CALVIN COLLEGE   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Bose Einstein condensates; Existence; Multicomponent systems; Nonlinear Schr dinger equations; Stability

Indexed keywords

BOSE-EINSTEIN CONDENSATES; DINGER EQUATION; LEADING ORDERS; LINEAR COMBINATIONS; LYAPUNOV-SCHMIDT REDUCTION; MAGNETIC TRAP; MULTI-COMPONENT SYSTEMS; NONLINEAR INTERACTIONS; SPECTRAL STABILITY;

EXCITED STATES; PLASMA CONFINEMENT; STATISTICAL MECHANICS; STEAM CONDENSERS; SYSTEM STABILITY;

NONLINEAR EQUATIONS;

EID: 74049143592     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/080742002     Document Type: Article

References (49)

1. F. ABDULLAEV AND R. KRAENKEL, Coherent atomic oscillations and resonances between coupled Bose-Einstein condensates with time-dependent trapping potential, Phys. Rev. A, 62 (2000), paper 023613.
2. J. R. ABO-SHAEER, C. RAMAN, J. M. VOGELS, AND W. KETTERLE, Observation of vortex lattices in Bose-Einstein condensates, Science, 292 (2001), pp. 476-479.
3. B. ANDERSON, K. DHOLAKIA, AND E. WRIGHT, Atomic-phase interference devices based on ring-shaped Bose-Einstein condensates: Two-ring case, Phys. Rev. A, 67 (2003), paper 033601.
4. B. ANDERSON, P. HALJAN, C. REGAL, D. FEDER, L. COLLINS, C. CLARK, AND E. CORNELL, Watching dark solitons decay into vortex rings in a Bose-Einstein condensate, Phys. Rev. Lett., 86 (2001)
5. P. AO AND S. T. CHUI, Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases, Phys. Rev. A, 58 (1997), pp. 4836-4840.
6. R. BATTYE, N. COOPER, AND P. SUTCLIFFE, Stable Skyrmions in two-component Bose-Einstein condensates, Phys. Rev. Lett., 88 (2002), paper 080401.
7. C. BECKER, S. STELLMER, P. SOLTAN-PANAHI, S. DÖRSCHER, M. BAUMERT, E.-M. RICHTER, J. KRONJÄGER, K. BONGS, AND K. SENGSTOCK, Oscillations and interactions of dark and darkbright solitons in Bose-Einstein condensates, Nature Phys., 4 (2008), pp. 496-501.
8. R. BRADLEY, B. DECONINCK, AND J. KUTZ, Exact nonstationary solutions to the mean-field equations of motion for two-component Bose-Einstein condensates in periodic potentials, J. Phys. A., 38 (2005), pp. 1901-1916.
9. S. BURGER, K. BONGS, S. DETTMER, W. ERTMER, K. SENGSTOCK, A. SANPERA, G. SHLYAPNIKOV, AND M. LEWENSTEIN, Dark solitons in Bose-Einstein condensates, Phys. Rev. Lett., 83 (1999), pp. 5198-5201.
10. Th. BUSCH, J. I. CIRAC, V. M. PEREZ-GARCIA, AND P. ZOLLER, Stability and collective excitations of a two-component condensed gas: A moment approach, Phys. Rev. A, 56 (1997), pp. 2978-2983.
11. P. CHOSSAT AND R. LAUTERBACH, Methods in Equivariant Bifurcations and Dynamical Systems, Adv. Ser. Nonlinear Dynam. 15, World Scientific, River Edge, NJ, 2000.
12. J. DENSCHLAG, J. SIMSARIAN, D. FEDER, C. CLARK, L. COLLINS, J. CUBIZOLLES, L. DENG, E. HAGLEY, K. HELMERSON, W. REINHARDT, S. ROLSTON, B. SCHNEIDER, AND W. PHILLIPS, Generating solitons by phase engineering of a Bose-Einstein condensate, Science, 287 (2000), pp. 97-101.
13. Z. DUTTON, M. BUDDE, C. SLOWE, AND L. V. HAU, Observation of quantum shock waves created with ultra-compressed slow light pulses in a Bose-Einstein condensate, Science, 293 (2001), pp. 663-668.
14. B. EIERMANN, T. ANKER, M. ALBIEZ, M. TAGLIEBER, P. TRERTLEIN, K.-P. MARZLIN, AND M. OBERTHALER, Bright Bose-Einstein gap solitons of atoms with repulsive interactions, Phys. Rev. Lett., 92 (2004), paper 230401.
15. P. ENGELS, I. CODDINGTON, P. C. HALJAN, AND E. A. CORNELl, Nonequilibrium effects of anisotropic compression applied to vortex lattices in Bose-Einstein condensates, Phys. Rev. Lett., 89 (2002), paper 100403.
16. B. D. ESRY AND C. H. GREENE, Low-lying excitations of double Bose-Einstein condensates, Phys. Rev. A, 57 (1998), pp. 1265-1271.
17. B. D. ESRY, C. H. GREENE, J. P. BURKE, AND J. L. BOHN, Hartree-Fock theory for double condensates, Phys. Rev. Lett., 78 (1997), pp. 3594-3597.
18. E. V. GOLDSTEIN AND P. MEYSTRE, Quasiparticle instabilities in multicomponent atomic condensates, Phys. Rev. A, 55 (1997), pp. 2935-2940.
19. R. GRAHAM AND D. WALLS, Collective excitations of trapped binary mixtures of Bose-Einstein gases, Phys. Rev. A, 57 (1998), pp. 484-487.
20. D. HALL, M. MATTHEWS, J. ENSHER, C. WIEMAN, AND E. CORNELL, Dynamics of component separation in a binary mixture of Bose-Einstein condensates, Phys. Rev. Lett., 81 (1998), pp. 1539-1542.
21. M. HǍRǍGUŞ AND T. KAPITULA, On the spectra of periodic waves for infinite-dimensional Hamiltonian systems, Phys. D, 237 (2008), pp. 2649-2671.
22. T.-L. HO AND V. SHENOY, Binary mixtures of Bose condensates of alkali atoms, Phys. Rev. Lett., 77 (1996), pp. 3276-3279.
23. T. KAPITULA, P. KEVREKIDIS, AND B. SANDSTEDE, Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems, Phys. D, 195 (2004), pp. 263-282.
24. T. KAPITULA, P. KEVREKIDIS, AND B. SANDSTEDE, Addendum: Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems, Phys. D, 201 (2005), pp. 199-201.
25. T. KAPITULA, P. G. KEVREKIDIS, AND Z. CHEN, Three is a crowd: Solitary waves in photorefractive media with three potential wells, SIAM J. Appl. Dyn. Sys., 5 (2006), pp. 598-633.
26. T. KAPITULA, P. KEVREKIDIS, AND R. CARRETERO-GONZÁLEZ, Rotating matter waves in Bose-Einstein condensates, Phys. D, 233 (2007), pp. 112-137.
27. K. KASAMATSU, M. TSUBOTA, AND M. UEDA, Quadrupole and scissors modes and nonlinear mode coupling in trapped two-component Bose-Einstein condensates, Phys. Rev. A, 69 (2004), paper 043621.
28. P. G. KEVREKIDIS, D. J. FRANTZESKAKIS, AND R. CARRETERO-GONZÁLEZ, Emergent Nonlinear Phenomena in Bose-Einstein Condensates, Springer-Verlag, New York, Berlin, 2008.
29. P. KEVREKIDIS, H. NISTAZAKIS, D. FRANTZESKAKIS, B. MALOMED, AND R. CARRETERO-GONZÁLEZ, Families of matter-waves in two-component Bose-Einstein condensates, Eur. Phys. J. D, 28 (2004), pp. 181-185.
30. L. KHAYKOVICH, F. SCHRECK, G. FERRARI, T. BOURDELAND, J. CUBIZOLLES, L. CARR, Y. CASTIN, AND C. SALOMON, Formation of a matter-wave bright soliton, Science, 296 (2002), pp. 1290-1293.
31. C. K. LAW, H. PU, N. P. BIGELOW, AND J. H. EBERLY, Stability signature in two-species dilute Bose-Einstein condensates, Phys. Rev. Lett., 79 (1997), pp. 3105-3108.
32. R. MACKAY, Stability of equilibria of Hamilto nian systems, in Hamiltonian Dynamical Systems, R. MacKay and J. Meiss, eds., Adam Hilger, London, 1987, pp. 137-153.
33. K. W. MADISON, F. CHEVY, W. WOHLLEBEN, AND J. DALIBARD, Vortices formation in a stirred Bose-Einstein condensate, Phys. Rev. Lett., 84 (2000), pp. 806-809.
34. M. MATTHEWS, B. ANDERSON, P. HALJAN, D. HALL, C. WIEMAN, AND E. CORNELL, Vortices in a Bose-Einstein condensate, Phys. Rev. Lett., 83 (1999), pp. 2498-2501.
35. K. MERTES, J. W. MERRILL, R. CARRETERO- GONZÁLEZ, D. J. FRANTZESKAKIS, P. G. KEVREKIDIS, AND D. S. HALL, Nonequilibrium dynamics and superfluid ring excitations in binary Bose-Einstein condensates, Phys. Rev. Lett., 99 (2007), paper 190402.
36. H.-J. MIESNER, D. M. STAMPER-KURN, J. STENGER, S. INOUYE, A. P. CHIKKATUR, AND W. KETTERLE, Observation of metastable states in spinor Bose-Einstein condensates, Phys. Rev. Lett., 82 (1999), pp. 2228-2231.
37. C. MYATT, E. BURT, R. GHRIST, E. CORNELL, AND C. WIEMAN, Production of two overlapping Bose-Einstein condensates by sympathetic cooling, Phys. Rev. Lett., 78 (1997), pp. 586-589.
38. S. B. PAPP, J. M. PINO, AND C. E. WIEMAN, Tunable miscibility in a dual-species Bose-Einstein condensate, Phys. Rev. Lett., 101 (2008), paper 040402.
39. D. PELINOVSKY AND J. YANG, Instabilities of multihump vector solitons in coupled nonlinear Schrödinger equations, Stud. Appl. Math., 115 (2005), pp. 109-137.
40. V. M. PÉREZ-GARCÍA AND J. BELMONTE- BEITIA, Symbiotic solitons in heteronuclear multicomponent Bose-Einstein condensates, Phys. Rev. A, 72 (2005), paper 033620.
41. C. PETHICK AND H. SMITH, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge, UK, 2002.
42. L. PITAEVSKII AND S. STRINGARI, Bose-Einstein Condensation, Oxford University Press, Oxford, UK, 2003.
43. H. PU AND N. P. BIGELOW, Collective excitations, metastability and nonlinear response of a trapped two-species Bose-Einstein condensate, Phys. Rev. Lett., 80 (1998), pp. 1134-1137.
44. V. SCHWEIKHARD, I. CODDINGTON, P. ENGELS, S. TUNG, AND E. CORNELL, Vortex-lattice dynamics in rotating spinor Bose-Einstein condensates, Phys. Rev. Lett., 93 (2004), paper 210403.
45. D. STAMPER-KURN, M. ANDREWS, A. CHIKKATUR, S. INOUYE, H.-J. MIESNER, J. STENGER, AND W. KETTERLE, Optical confinement of a Bose-Einstein condensate, Phys. Rev. Lett., 80 (1998), pp. 2027-2030.
46. J. STENGER, S. INOUYE, D. M. STAMPER-KURN, H.-J. MIESNER, A. P. CHIKKATUR, AND W. KETTERLE, Spin domains in ground state spinor Bose-Einstein condensates, Phys. Rev. Lett., 396 (1998), pp. 345-348.
47. K. STRECKER, G. PARTRIDGE, A. TRUSCOTT, AND R. HULET, Formation and propagation of matter-wave soliton trains, Nature, 417 (2002), pp. 150-153.
48. L. N. TREFETHEN, Spectral Methods in MATLAB, Software Environ. Tools 10, SIAM, Philadelphia, 2000.
49. M. TRIPPENBACH, K. GÓRAL, K. RZAZEWSKI, B. MALOMED, AND Y. B. BAND, Structure of binary Bose-Einstein condensates, J. Phys. B., 33 (2000), pp. 4017-4031.