Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow

SIAM Journal on Scientific Computing

Volumn 30, Issue 4, 2007, Pages 1925-1948

  Bao, Weizhu ^a   Lim, Fong Yin ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Backward forward Euler sine pseudospectral method; Coupled Gross Pitaevskii equations; Ground state; Normalized gradient flow; Spin 1 Bose Einstein condensate

Indexed keywords

BOSE-EINSTEIN CONDENSATION; EQUATIONS OF STATE; NUMERICAL METHODS; STATISTICAL MECHANICS;

BACKWARD-FORWARD EULER SINE-PSEUDOSPECTRAL METHOD; BOSE-EINSTEIN CONDENSATES; CONDITION; COUPLED GROSS-PITAEVSKII EQUATION; GRADIENT FLOW; GROSS-PITAEVSKII EQUATION; NORMALIZED GRADIENT; NORMALIZED GRADIENT FLOW; PSEUDOSPECTRAL METHODS; SPIN-1 BOSE-EINSTEIN CONDENSATE;

GROUND STATE;

EID: 53349177418     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070698488     Document Type: Article

References (35)

1. A. AFTALION AND Q. DU, Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime, Phys. Rev. A, 64 (2001), 063603.
2. M. H. ANDERSON, J. R. ENSHER, M. R. MATTHEWA, C. E. WIEMAN, AND E. A. CORNELL, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, 269 (1995), pp. 198-201.
3. W. BAO, Ground states and dynamics of multicomponent Bose-Einstein condensates, Multiscale Model. Simul., 2 (2004), pp. 210-236.
4. W. BAO AND M. H. CHAI, A uniformly convergent numerical method for singularly perturbed nonlinear eigenvalue problems, Commun. Comput. Phys., 4 (2008), pp. 135-160.
5. W. BAO, 1-L CHERN, AND F. Y. LIM, Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates, J. Comput. Phys., 219 (2006), pp. 836-854.
6. W. BAO AND Q. DU, Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow, SIAM J. Sci. Comput., 25 (2004), pp. 1674-1697.
7. W. BAO, D. JAKSCH, AND P. A. MARKOWICH, Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation, J. Comput. Phys., 187 (2003), pp. 318-342.
8. W. BAO, F. Y. LIM, AND Y. ZHANG, Energy and chemical potential asymptotics for the ground state of Bose-Einstein condensates in the semiclassical regime, Bull. Inst. Math. Acad. Sinica, 2 (2007), pp. 495-532.
9. W. BAO AND W. TANG, Ground state solution of trapped interacting Bose-Einstein condensate by directly minimizing the energy functional, J. Comput. Phys., 187 (2003), pp. 230-254.
10. W. BAO AND H. WANG, A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates, SIAM J. Numer. Anal., 45 (2007), pp. 2177-2200.
11. M. D. BARRETT, J. A. SAUER, AND M. S. CHAPMAN, All-optical formation of an atomic Bose-Einstein condensate, Phys. Rev. Lett., 87 (2001), 010404.
12. C. C. BRADLEY, C. A. SAOKETT, J. J. TOLLETT, AND R. G. HULET, Evidence of Bose-Einstein condensation in an atomic gas with attractive interaction, Phys. Rev. Lett., 75 (1995), pp. 1687-1690.
13. S.-L. CHANG, C.-S. CHIEN, AND B.-W. JENG, Liapunov-Schmidt reduction and continuation for nonlinear Schrödinger equations, SIAM J. Sci. Comput., 29 (2007), pp. 729-755.
14. S.-L. CHANG, C.-S. CHIEN, AND B. W. JENG, Computing wave functions of nonlinear Schrodinger equations: A time independent approach, J. Comput. Phys., 226 (2007), pp. 104-130.
15. S. M. CHANG, W. W. LIN, AND S. F. SHIEH, Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate, J. Comput. Phys., 202 (2005), pp. 367-390.
16. M. L. CHIOPALO, S. SUCCI, AND M. P. TOSI, Ground state of trapped interacting Bose-Einstein condensates by an explicit imaginary-time algorithm, Phys. Rev. E, 62 (2000), 007438.
17. B. J. DABROWSKA-WÜSTER, E. A. OSTROVSKAYA, T. J. ALEXANDER, AND Y. S. KIVSHAR, Multicomponent gap solitons in spinor Bose Einstein condensates, Phys. Rev. A, 75 (2007), 023617.
18. F. DALFOVO, S. GIORGINI, L. P. PITAEVSKII, AND S. STRINGARI, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys., 71 (1999), pp. 463-512.
19. 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.
20. A. GÖRLITZ, T. L. GUSTAVSON, A. E. LEANHARDT, E. Löw, A. P. CHIKKATUR, S. GUPTA, S. INOUYE, D. E. PRITCHARD, AND W. KETTERLE, Sodium Bose-Einstein condensates in the F = 2 state in a large-volume optical trap, Phys. Rev. Lett., 90 (2003), 090401.
21. E. P. GROSS, Structure of a quantized vortex in boson systems, Nuovo Cimento, 20 (1961), pp. 454-477.
22. T. L. HO, Spinor Bose condensates in optical traps, Phys. Rev. Lett., 81 (1998), pp. 742-745.
23. C. K. LAW, H. PU, AND N. P. BIGELOW, Quantum spins mixing in spinor Bose-Einstein condensates, Phys. Rev. Lett., 81 (1998) pp. 5257-5261.
24. 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.
25. T. OHMI AND K. MACHIDA, Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, J. Phys. Soc. Japan, 67 (1998), pp. 1822-1825.
26. L. P. PITAEVSKII, Vortex lines in an imperfect Bose gas, Soviet Phys. JETP, 13 (1961), pp. 451-454.
27. L. P. PITAEVSKII AND S. STRINGARI, Bose-Einstein Condensation, Clarendon Press, Oxford, 2003.
28. L. SIMON, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math., 118 (1983), pp. 525-571.
29. D. M. STAMPER-KURN, M. R. ANDREWS, A. P. 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.
30. D. M. STAMPER-KURN AND W. KETTERLE, Spinor condensates and light scattering from Bose-Einstein condensates, in Proceedings of the Les Houches 1999 Summer School (Session LXXII), in Coherent Atomic Matter Waves, Les Houches 1999 Summer School (Session LXXII) in 1999, R. Kaiser, C. Westbrook, and F. David, eds., Springer, New York, 2001, pp. 137-217.
31. J. STENGER, S. INOUYE, D. M. STAMPER- KURN, H.-J. MIESNER, A. P. CHIKKATUR, AND W. KETTERLE, Spin domains in ground state Bose-Einstein condensates, Nature, 396 (1998), pp. 345-348.
32. S. YI, Ö. E. MÜSTECAPLIOǦLU, C. P. SUN, AND L. YOU, Single-mode approximation in a spinor-1 atomic condensate, Phys. Rev. A, 66 (2002), 011601.
33. W. ZHANG, S. YI, AND L. YOU, Mean field ground state of a spin-1 condensate in a magnetic field, New J. Phys., 5 (2003), pp. 77-89.
34. W. ZHANG, S. YI, AND L. YOU, Bose-Einstein condensation of trapped interacting spin-1 atoms, Phys. Rev. A, 70 (2004), 043611.
35. W. ZHANG AND L. YOU, An effective quasi-one-dimensional description of a spin-1 atomic condensate, Phys. Rev. A, 71 (2005), 025603.