Abstract.
Tomographic-probability representation for soliton solutions of Gross-Pitaevskii equation is introduced. Tomograms of the wavefunction describing bright soliton states of Bose-Einstein condensate are obtained in the presence of a quadratic external potential.
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S. De Nicola, R. Fedele, M.A. Man’ko and V.I. Man’ko, J. Opt. B: Quantum and Semiclass. Opt. 5, 95 (2003)
S. Mancini, V.I. Man’ko, P. Tombesi, Quantum Semiclass. Opt. 7, 615 (1995)
E.P. Gross, Nuovo Cim. 20, 454 (1961) L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)
F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringary, Rev. Mod. Phys. 71, 463 (1989)
Ph. Noziéres, D. Pines, The Theory of Quantum Liquids (Reading MA: Addison-Wesley, 1990), Vol. II
S. Mancini, V.I. Man’ko, P. Tombesi, Phys. Lett. A 213, 1 (1996)
J. Von Neumann, Mathematische Grundlagen der Quantummechanik (Springer, Berlin, 1932)
M.H. Anderson, J.R. Ensher, M.R. Matthews, G.E. Wieman, E.A. Cornell, Science 269, 198 (1995)
K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 95, 3969 (1995)
C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1997) C.C. Bradley, C.A. Sackett, R.G. Hulet, Phys. Rev. Lett. 78, 985, (1995) C.A. Sackett, C.C. Bradley, M. Welling, R.G. Hulet, Appl Phys. B: Lasers Opt. 65, 433 (1997) J.M. Gerton, D. Strekalov, I. Prodan, R.G. Hulet, Nature (London) 408, 692 (2000)
W. Hai, Ch. Lee, G. Chong, Propagation, breathing and transition of mattar-wave packet trains, arXiv:quant-ph/0301112v1 (2003)
V.Y.F. Leung, A.G. Truscott, K.G.H. Baldwin, Phys. Rev. A 66, 061602 (2002)
L.D. Carr, Y. Castin, Phys. Rev. A 66, 063602 (2002)
D.L. Feder, M.S. Pindzola, L.A. Collins, B.I. Schneider, C.W. Clark, Phys. Rev. A 62, 053606 (2002)
A. Muryshev, G.V. Shlyapnikov, W. Ertmer, K. Sengstock, M. Lewenstein, Phys. Rev. Lett. 89, 110401 (2002)
J. Dziarmaga, Z.P. Karkuszewski, K. Sacha, Images of the dark soliton in a depleted condensate, arXiv:cond-mat/0212492v2 (2003)
V.A. Brazhnyi, A.M. Kamchatnov, V.V. Konotop, On creation and evolution of dark solitons in Bose-Einstein condensate arXiv:quant-ph/0301319v1 (2003)
S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, Phys. Rev. Lett. 83, 5198 (1999)
V.V. Dodonov, S. Mizrahi, Ann. Phys. NY 237, 226 (1995)
E.P. Wigner, Phys. Rev. 40, 749 (1932)
J.E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949)
R. Fedele, D. Anderson D, J. Opt. B: Quantum Semiclass. Opt. 2, 207 (2000)
R. Fedele, D. Anderson, M. Lisak Physica Scripta T 84, 27 (2000)
I.E. Alber, Proc. Royal Soc. London A 636, 525 (1978)
B. Hall, M. Lisak, D. Anderson, R. Fedele, V.E. Semenov, Phys. Rev. E 65, 035602(R) (2002)
R. Fedele, P.K. Shukla, M. Onorato, D. Anderson, M. Lisak, Phys. Lett. A 303, 61 (2002)
V.I. Man’ko, R.V. Mendes, Phys. Lett. A 263, 53 (1999)
V.I. Man’ko, R.V. Mendes, Physica D 145, 330 (2000)
O.V. Man’ko, V.I. Man’ko, J. Russ. Laser Res. 18, 411 (1997)
Z.P. Karkuszewski, K. Sacha, J. Zakrzewski, Phys. Rev. A 63, 061601(R) (2001)
L. Khaykovich, F. Schreck, G. Ferrari, Science 290, 1290 (2003)
P.O. Fedichev, A.E. Muryshev, G.V. Shlyapnikov, Phys. Rev. A 60, 3220 (1999)
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Received: 18 September 2003, Published online: 23 December 2003
PACS:
03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 03.65.Wj State reconstruction, quantum tomography - 42.65.-k Nonlinear optics
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Nicola, S.D., Fedele, R., Man’ko, M.A. et al. Tomographic-probability description of solitons in Bose-Einstein condensates. Eur. Phys. J. B 36, 385–390 (2003). https://doi.org/10.1140/epjb/e2003-00357-2
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DOI: https://doi.org/10.1140/epjb/e2003-00357-2