-
1
-
-
11944274056
-
-
M. H. Anderson et al., Science 269, 198 (1995).
-
(1995)
Science
, vol.269
, pp. 198
-
-
Anderson, M.H.1
-
2
-
-
4244115335
-
-
K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 3969
-
-
Davis, K.B.1
Mewes, M.-O.2
Andrews, M.R.3
Van Druten, N.J.4
Durfee, D.S.5
Kurn, D.M.6
Ketterle, W.7
-
3
-
-
4243132347
-
-
C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 1687
-
-
Bradley, C.C.1
Sackett, C.A.2
Tollett, J.J.3
Hulet, R.G.4
-
4
-
-
0347318638
-
-
K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000).
-
(2000)
Phys. Rev. Lett.
, vol.84
, pp. 806
-
-
Madison, K.W.1
Chevy, F.2
Wohlleben, W.3
Dalibard, J.4
-
5
-
-
0034298964
-
-
B. P. Anderson, P. C. Haljan, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 85, 2857 (2000).
-
(2000)
Phys. Rev. Lett.
, vol.85
, pp. 2857
-
-
Anderson, B.P.1
Haljan, P.C.2
Wieman, C.E.3
Cornell, E.A.4
-
6
-
-
0035917810
-
-
J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Science 292, 476 (2001).
-
(2001)
Science
, vol.292
, pp. 476
-
-
Abo-Shaeer, J.R.1
Raman, C.2
Vogels, J.M.3
Ketterle, W.4
-
8
-
-
40049094480
-
-
edited by P. G. Kevrekides, D. J. Frantzeskakis, and R. Carretero-González Springer, Heidelberg
-
N. G. Parker, B. Jackson, A. M. Martin, and C. S. Adams, Emergent Nonlinear Phenomena in Bose-Einstein Condensates, edited by P. G. Kevrekides, D. J. Frantzeskakis, and R. Carretero-González (Springer, Heidelberg, 2008).
-
(2008)
Emergent Nonlinear Phenomena in Bose-Einstein Condensates
-
-
Parker, N.G.1
Jackson, B.2
Martin, A.M.3
Adams, C.S.4
-
19
-
-
28844440345
-
-
O. K. Vorov, P. Van Isacker, M. S. Hussein, and K. Bartschat, Phys. Rev. Lett. 95, 230406 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 230406
-
-
Vorov, O.K.1
Van Isacker, P.2
Hussein, M.S.3
Bartschat, K.4
-
20
-
-
0033246313
-
-
F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
-
(1999)
Rev. Mod. Phys.
, vol.71
, pp. 463
-
-
Dalfovo, F.1
Giorgini, S.2
Pitaevskii, L.P.3
Stringari, S.4
-
30
-
-
66049160080
-
-
B. Jackson, N. P. Proukakis, C. F. Barenghi, and E. Zaremba, Phys. Rev. A 79, 053615 (2009).
-
(2009)
Phys. Rev. A
, vol.79
, pp. 053615
-
-
Jackson, B.1
Proukakis, N.P.2
Barenghi, C.F.3
Zaremba, E.4
-
42
-
-
30344432432
-
-
C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 263901
-
-
Connaughton, C.1
Josserand, C.2
Picozzi, A.3
Pomeau, Y.4
Rica, S.5
-
45
-
-
84920427777
-
-
note
-
The projected field ψ(x) is thus not strictly a field in the traditional sense [44]; however, we will retain the usage of the term in this work.
-
-
-
-
46
-
-
0033473107
-
-
G. Bruun, Y. Castin, R. Dum, and K. Burnett, Eur. Phys. J. D 7, 433 (1999).
-
(1999)
Eur. Phys. J. D
, vol.7
, pp. 433
-
-
Bruun, G.1
Castin, Y.2
Dum, R.3
Burnett, K.4
-
55
-
-
84920396248
-
-
note
-
We note that geometry and projector definition of [35] yield a conserved angular momentum about the x axis; however, any nonzero angular momenta in the fields evolved in that work were incidental, and of essentially negligible magnitude, as noted by the authors of that paper.
-
-
-
-
56
-
-
84920443465
-
-
note
-
z to the single-particle Hamiltonian [113] serves only to ensure that the rotating-frame equations of motion faithfully describe the same dynamics as the fundamental inertial-frame equations.
-
-
-
-
59
-
-
84920396449
-
-
Ph.D. thesis, University of Oxford, Oxford, UK
-
M. J. Davis, Ph.D. thesis, University of Oxford, Oxford, UK, 2001.
-
(2001)
-
-
Davis, M.J.1
-
60
-
-
84920369140
-
-
note
-
In practice, we average momentum-space densities taken over consecutive 10 cycle periods. Aside from fluctuations close to the origin k = 0 arising from the vortex precession, we observe the densities to settle to their (fluctuating) values well before t =9000 cyc.
-
-
-
-
61
-
-
84920364459
-
-
note
-
We use the peak density of our principal ground state to estimate the healing length η.
-
-
-
-
62
-
-
0003474751
-
-
Cambridge University Press, Cambridge
-
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992).
-
(1992)
Numerical Recipes in C, 2nd Ed.
-
-
Press, W.H.1
Teukolsky, S.A.2
Vetterling, W.T.3
Flannery, B.P.4
-
64
-
-
84920447119
-
-
note
-
v} before calculating the power spectrum presented in Fig. 2(b).
-
-
-
-
66
-
-
84920472178
-
-
note
-
This property of the many-body system persists in the classical-field model [67], but note, however, the effect of the projector on large dipole oscillations [58].
-
-
-
-
68
-
-
84920368311
-
-
note
-
Vortices may of course occur in all such simulations; we use the phrase "vortex free" here to refer to simulations in which any appearance of vortices is incidental and sufficiently transient as to not affect the statistics under consideration significantly.
-
-
-
-
70
-
-
0346405503
-
-
Y. Castin and C. Herzog, C. R. Acad. Sci., Ser. IV: Phys., Astrophys. 2, 419 (2001).
-
(2001)
C. R. Acad. Sci., Ser. IV: Phys., Astrophys.
, vol.2
, pp. 419
-
-
Castin, Y.1
Herzog, C.2
-
73
-
-
66049121814
-
-
T. Yamada et al., Phys. Rev. C 79, 054314 (2009).
-
(2009)
Phys. Rev. C
, vol.79
, pp. 054314
-
-
Yamada, T.1
-
74
-
-
84920371500
-
-
edited by I. Beltita, G. Nenciu, and R. Purice World Scientific, Singapore
-
R. Seiringer, in Mathematical Results in Quantum Mechanics: Proceedings of the Qmath10 Conference, edited by I. Beltita, G. Nenciu, and R. Purice (World Scientific, Singapore, 2008).
-
(2008)
Mathematical Results in Quantum Mechanics: Proceedings of the Qmath10 Conference
-
-
Seiringer, R.1
-
75
-
-
0003653383
-
-
edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji Gordon and Breach, New York
-
R. J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965).
-
(1965)
Quantum Optics and Electronics
-
-
Glauber, R.J.1
-
77
-
-
84920480594
-
-
note
-
We adopt here the convention for Bogoliubov-mode component labeling of [47,78].
-
-
-
-
81
-
-
0000822986
-
-
R. J. Dodd, K. Burnett, M. Edwards, and C. W. Clark, Phys. Rev. A 56, 587 (1997).
-
(1997)
Phys. Rev. A
, vol.56
, pp. 587
-
-
Dodd, R.J.1
Burnett, K.2
Edwards, M.3
Clark, C.W.4
-
83
-
-
84920488836
-
-
note
-
4(x) have the form of vortex modes with charges q=+3 and q=-1, respectively. These circulations correspond, respectively, to those of the u and v ( components of the linear excitation of the GP vortex with angular momentum m =+2 relative to the GP state [84].
-
-
-
-
84
-
-
1642282590
-
-
T. Mizushima, Y. Kawaguchi, K. Machida, T. Ohmi, T. Isoshima, and M. M. Salomaa, Phys. Rev. Lett. 92, 060407 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.92
, pp. 060407
-
-
Mizushima, T.1
Kawaguchi, Y.2
Machida, K.3
Ohmi, T.4
Isoshima, T.5
Salomaa, M.M.6
-
86
-
-
84920474135
-
-
note
-
ij [35].
-
-
-
-
89
-
-
84920486697
-
-
note
-
Note that the Goldstone mode only happens to be the second most highly occupied mode in the present case as its spurious "population" is larger than that of all other noncondensate modes.
-
-
-
-
91
-
-
84920389226
-
-
note
-
It could indeed be said that this is the definitive distinction of interpretation between the time-dependent GP theory and the time-dependent classical-field theory.
-
-
-
-
93
-
-
84920411086
-
-
unpublished
-
T. M. Wright et al. (unpublished).
-
-
-
Wright, T.M.1
-
94
-
-
84920404782
-
-
note
-
cin an effective least-squares sense [95].
-
-
-
-
95
-
-
84920434217
-
-
private communication
-
C. Fox (private communication).
-
-
-
Fox, C.1
-
96
-
-
84920449162
-
-
note
-
iθ) is also broken by any condensate mode that forms. This symmetry is of course the classical precursor to the so-called gauge symmetry associated with particle-number conservation in the corresponding secondquantized field theory [88]. However, the global phase of the classical field has no effect on the density-matrix calculations we perform here.
-
-
-
-
101
-
-
84920484480
-
-
note
-
0 (x) as comprising the noncondensate field here.
-
-
-
-
105
-
-
0035914836
-
-
P. C. Haljan, I. Coddington, P. Engels, and E. A. Cornell, Phys. Rev. Lett. 87, 210403 (2001).
-
(2001)
Phys. Rev. Lett.
, vol.87
, pp. 210403
-
-
Haljan, P.C.1
Coddington, I.2
Engels, P.3
Cornell, E.A.4
-
106
-
-
84920454119
-
-
note
-
r, which we associate with a persistent dipole excitation of the field.
-
-
-
-
109
-
-
84920491921
-
-
note
-
0 dominates to such an extent that this is of no concern for the indicative representation we seek here.
-
-
-
-
111
-
-
84920410436
-
-
Ph.D. thesis, Victoria University of Wellington
-
A. S. Bradley, Ph.D. thesis, Victoria University of Wellington, 2006.
-
(2006)
-
-
Bradley, A.S.1
|