Two mode theory of Bose-Einstein condensates: Interferometry and the Josephson model

Journal of Modern Optics

Volumn 59, Issue 4, 2012, Pages 287-353

  Dalton, B J ^a   Ghanbari, S ^a  

^a SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

interferometry; Josephson model; two mode Bose Einstein condensates

Indexed keywords

AMPLITUDE EQUATION; ANGULAR MOMENTUM THEORY; ATOMIC GAS; BLOCH EQUATION; BLOCH SPHERE; BLOCH VECTORS; BOSE-EINSTEIN CONDENSATES; COHERENCE PROPERTIES; COHERENT STATE; DECOHERENCE EFFECTS; DEPHASING EFFECTS; DOUBLE WELL; DOUBLE-WELL TRAP; DYNAMICAL BEHAVIOURS; DYNAMICAL EFFECTS; EIGENSTATES; ELLIPTIC FUNCTIONS; FIELD OPERATORS; GROSS-PITAEVSKII EQUATION; HEISENBERG; INTERFERENCE PATTERNS; JOSEPHSON; MAGNETIC QUANTUM NUMBER; MATHEMATICAL DERIVATION; MATRIX; MECHANICS EQUATION; MODE EXPANSION; MODE THEORY; MODEL DYNAMICS; NEAR-ZERO TEMPERATURE; ONLINE SUPPLEMENTARY MATERIAL; PHASE SPACES; PROBABILITY AMPLITUDE; QUANTUM CORRELATIONS; QUANTUM FLUCTUATION; QUANTUM NUMBERS; QUANTUM REGIMES; QUANTUM SYSTEM; RELATIVE PHASE; SINGLE MODE; SINGLE PARTICLE STATE; SINGLE WELL; SPIN OPERATORS; SPIN SQUEEZING; SPIN STATE; TRAP POTENTIALS; TWO-COMPONENT; TWO-MODE STATE; UNITARY ROTATION; VARIATIONAL PRINCIPLES;

ANGULAR MOMENTUM; BIOELECTRIC PHENOMENA; BOSE-EINSTEIN CONDENSATION; BOSONS; COVARIANCE MATRIX; DESCRIBING FUNCTIONS; DYNAMICAL SYSTEMS; INTERFEROMETRY; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; QUANTUM ELECTRONICS; QUANTUM OPTICS; SPHERES; STATISTICAL MECHANICS; STEAM CONDENSERS; VARIATIONAL TECHNIQUES; VECTORS;

HAMILTONIANS;

EID: 84855935647     PISSN: 09500340     EISSN: 13623044     Source Type: Journal    
DOI: 10.1080/09500340.2011.632100     Document Type: Review

References (64)

1. Pitaevskii, L.; Stringari, S. Bose-Einstein Condensation; Clarendon Press: Oxford, UK, 2003.
2. Kasevich, M.A. Science 2002, 298, 1363-1368.
3. Cronin, A.D.; Schmeidmayer, J.; Pritchard, D.E. Rev. Mod. Phys. 2009, 81, 1051-1129.
4. Gross, E.P. Nuovo Cimento 1961, 20, 454.
5. Pitaevskii, L.P. Zh. Eksp. Teor. Fiz. 1961, 40, 646.
6. Leggett, A.J. Rev. Mod. Phys. 2001, 73, 307-356.
7. Dalton, B.J. J. Mod. Opt. 2007, 54, 615-637.
8. Dalton, B.J. Ann. Phys. 2011, 326, 668-720.
9. Ostrovskaya, E.A.; Kivshar, Y.S.; Lisak, M.; Hall, B.; Cattani, F.; Anderson, D. Phys. Rev. A 2000, 61, 031601.
10. Ananikian, D.; Bergeman, T. Phys. Rev. A 2006, 73, 013604.
11. Dziarmaga, J.; Sacha, K. Phys. Rev. A 2003, 67, 033608.
12. Steel, M.J.; Olsen, M.K.; Plimak, L.I.; Drummond, P.D.; Tan, S.M.; Collett, M.J.; Walls, D.F.; Graham, R. Phys. Rev. A 1998, 58, 4824-4835.
13. Bouyer, P.; Kasevich, M.A. Phys. Rev. A 1997, 56, R1083-R1086.
14. Dunningham, J.A.; Burnett, K.; Barnett, S.M. Phys. Rev. Lett. 2002, 89, 150401.
15. Anderson, R.P.; Ticknor, C.; Sidorov, A.I.; Hall, B.V. Phys. Rev. A 2009, 80, 023603.
16. Gati, R.; Oberthaler, M.K. J. Phys. B: At. Mol. Opt. Phys. 2007, 40, R61-R89.
17. Shin, Y.; Saba, M.; Pasquini, T.A.; Ketterle, W.; Pritchard, D.E.; Leanhardt, A.E. Phys. Rev. Lett. 2004, 92, 050405.
18. Schumm, T.; Hofferberth, S.; Andersson, L.M.; Wildermuth, S.; Groth, S.; Bar-Joseph, I.; Kruger, P. Nat. Phys. 2005, 1, 57-62.
19. Dunningham, J.A.; Burnett, K. Phys. Rev. A 2004, 70, 033601.
20. Schumm, T.; Manz, S.; Bucker, R.; Smith, D.A.; Schmeidmayer, J. Interferometry with Bose-Einstein Condensates on Atom Chips. In Atom Chips; Reichel, J., Vuletic, V., Eds.; Wiley: New York, 2011; p 211.
21. Gross, C.; Zibold, T.; Nicklas, E.; Esteve, J.; Oberthaler, M.K. Nature 2010, 464, 1165-1169.
22. Riedel, M.F.; Bohl, P.; Li, Y.; Hansch, T.W.; Sinatra, A.; Treutlein, P. Nature 2010, 464, 1170-1173.
23. Jo, G.-B.; Shin, Y.; Will, S.; Pasquini, T.A.; Saba, M.; Ketterle, W.; Pritchard, D.E.; Vengalattore, M.; Prentiss, M. Phys. Rev. Lett. 2007, 98, 030407.
24. Baumgartner, F.; Sewell, R.J.; Eriksson, S.; Llorente-Garcia, I.; Dingjan, J.; Cotter, J.P.; Hinds, E.A. Phys. Rev. Lett. 2010, 105, 243003.
25. Zobay, O.; Garraway, B.M. Phys. Rev. Lett. 2001, 86, 1195-1198.
26. Esteve, J.; Gross, C.; Weller, A.; Giovanazzi, S.; Oberthaler, M.K. Nature 2008, 455, 1216-1219.
27. Milburn, G.J.; Corney, J.; Wright, E.M.; Walls, D.F. Phys. Rev. A 1997, 55, 4318-4324.
28. Menotti, C.; Anglin, J.R.; Cirac, J.I.; Zoller, P. Phys. Rev. A 2001, 63, 023601.
29. Jaaskelainen, M.; Meystre, P. Phys. Rev. A 2006, 73, 013602.
30. Rose, M.E. Elementary Theory of Angular Momentum; Wiley: New York, 1957.
31. Arecchi, F.T.; Courtens, E.; Gilmore, R.; Thomas, H. Phys. Rev. A 1972, 6, 2211-2237.
32. Steel, M.J.; Collett, M.J. Phys. Rev. A 1998, 57, 2920-2930.
33. Micheli, A.; Jaksch, D.; Cirac, J.I.; Zoller, P. Phys. Rev. A 2003, 67, 013607.
34. Pegg, D.T.; Barnett, S.M. Phys. Rev. A 1989, 39, 1665-1675.
35. Bach, R.; Rzazewski, K. Phys. Rev. Lett. 2004, 92, 200401.
36. Bach, R.; Rzazewski, K. Phys. Rev. A 2004, 70, 063622.
37. Gardiner, C.W. Phys. Rev. A 1997, 56, 1414-1423.
38. Castin, Y.; Dum, R. Phys. Rev. A 1998, 57, 3008-3021.
39. Javanainen, J.; Yoo, S.M. Phys. Rev. Lett. 1996, 76, 161-164.
40. Wong, T.; Collett, M.J.; Walls, D.F. Phys. Rev. A 1996, 54, R3718-R3721.
41. Cirac, J.I.; Gardiner, C.W.; Narachewski, M.; Zoller, P. Phys. Rev. A 1996, 54, R3714-R3717.
42. Horak, P.; Barnett, S.M. J. Phys. B: At. Mol. Opt. Phys. 1999, 32, 3421-3436.
43. Andrews, M.R.; Townsend, C.G.; Miesner, H.-J.; Durfee, D.S.; Kurn, D.M.; Ketterle, W. Science 1997, 275, 637-641.
44. Kitagawa, M.; Ueda, M. Phys. Rev. A 1993, 47, 5138-5143.
45. Dirac, P.A.M. Proc. Cambridge Philos. Soc. 1930, 26, 376.
46. Frenkel, J. Wave Mechanics; Oxford University Press: Oxford, UK, 1934.
47. Spekkens, R.W.; Sipe, J.E. Phys. Rev. A 1999, 59, 3868-3877.
48. Alon, O.E.; Streltsov, A.J.; Cederbaum, L.S. Phys. Rev. A 2008, 77, 033613.
49. Li, Y.; Treutlein, P.; Reichel, J.; Sinatra, A. Euro. Phys. J. B 2009, 68, 365-381.
50. Sinatra, A.; Castin, Y. Euro. Phys. J. D 2000, 8, 319-332.
51. Blakie, P.B.; Ballagh, R.J.; Gardiner, C.W. J. Opt. B: Quantum Semiclass. Opt. 1999, 1, 378-382.
52. Streltsov, A.J.; Alon, O.E.; Cederbaum, L.S. Phys. Rev. Lett. 2007, 99, 030402.
53. Streltsov, A.J.; Alon, O.E.; Cederbaum, L.S. Phys. Rev. A 2006, 73, 063626.
54. Grond, J.; von Winkel, G.; Schmeidmayer, J.; Hohenester, U. Phys. Rev. A 2009, 80, 053625.
55. D'Agosta, R.; Presilla, C. Phys. Rev. A 2002, 65, 043609.
56. Jaksch, D.; Bruder, C.; Cirac, J.I.; Gardiner, C.W.; Zoller, P. Phys. Rev. Lett. 1998, 81, 3108-3111.
57. Carr, L.D.; Duncan-Frazer, D.R.; Garcia-March, M.A. Euro. Phys. Lett. 2010, 90, 10005.
58. Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S.R. Phys. Rev. A 1999, 59, 620-633.
59. Sidorov, A.I.; Dalton, B.J.; Whitlock, S.M.; Scharnberg, F. Phys. Rev. A 2006, 74, 023612.
60. Gradsteyn, I.S.; Ryzhik, I.M. Tables of Integrals Series and Products; Academic Press: New York, 1965.
61. Grimm, R.; Weidensmuller, M.; Ovchinnikov, Y.B. Adv. At. Mol. Opt. Phys. 2000, 42, 95-170.
62. Gardiner, C.W.; Zoller, P. Phys. Rev. A 1998, 58, 536-556.
63. Dalton, B.J. J. Phys. Conf. Ser. 2007, 67, 012059.
64. Hoffmann, S.E.; Corney, J.F.; Drummond, P.D. Phys. Rev. A 2008, 78, 013622.