Abstract
This paper gives a summary of the experimental production and the theoretical description of a gaseous Bose-Einstein condensate. We present the standard procedure to obtain a condensate: laser cooling, followed by evaporative cooling in a magnetic trap. We then turn to the theoretical treatment of an interacting Bose- Einstein condensate. We justify the use of a contact potential to describe atom interactions and we outline the derivation of the Gross-Pitaevskii equation. We then discuss experiments revealing the coherence properties of a single condensate, and the relative coherence between two independent condensates. Finally, we address the problem of the superfluidity of a condensate, by focussing on its rotational properties and the nucleation of quantized vortices.
Unité de Recherche de l’Ecole normale supérieure et de l’Université Pierre et Marie Curie, associée au CNRS.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Pais: Subtle is the Lord (Oxford University Press, Oxford 1982)
S.N. Bose: Z. Phys. 26, 178 (1924)
A. Einstein: Sitzber. Klg. Preuss. Akad. Wiss. 261 (1924)
A. Einstein: Sitzber. Klg. Preuss. Akad. Wiss. 3 (1925)
P. Kapitza, Nature 141, 74 (1938)
J.F. Allen, A.D. Misener, Nature 141, 75 (1938)
F. London: Nature 141, 643 (1938)
M. Inguscio, S. Stringari, C.E. Wieman: Proceedings of the International School of Physics Enrico Fermi, Course CXL, Bose-Einstein Condensation in Atomic Gases (IOS Press, Amsterdam 1999)
J.P. Wolfe, J.L. Lin, D.W. Snoke: ‘Bose-Einstein Condensation of a Nearly Ideal Gas: Excitons in Cu20’. In Bose-Einstein Condensation, ed. by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, Cambridge 1995) pp. 281–329
A. Mysyrowicz: ‘Bose-Einstein Condensation of Excitonic Particles in Semiconductors’. In Bose-Einstein Condensation, ed. by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, Cambridge 1995) pp. 330–354
D.G. Fried, T. C. Killian, L. Willmann, D. Landhuis, S.C. Moss, D. Kleppner, T.J. Greytak: Phys. Rev. Lett. 81, 3811 (1998)
A. Robert, O. Sirjean, A. Browaeys, J. Poupard, S. Nowak, D. Boiron, C.I. Westbrook, A. Aspect: Science 292, 461 (2001)
F. Pereira Dos Santos, J. Léonard, Junmin Wang, C. J. Barrelet, F. Perales, E. Rasel, C. S. Unnikrishnan, M. Leduc, C. Cohen-Tannoudji: Phys. Rev. Lett. 86, 3459 (2001)
C.C. Bradley, C.A. Sackett, R.G. Hulet: Phys. Rev. Lett. 78, 985 (1997) See also C.C. Bradley, C.A. Sackett, J.J. Tollett, R. G. Hulet: Phys. Rev. Lett. 75, 1687 (1995)
K.B. Davis, M.O. Mewes, N. Van Druten, D. Durfee, D. Kurn, W. Ketterle: Phys. Rev. Lett. 75, 3969 (1995)
G. Modugno, G. Ferrari, G. Roati, R. J. Brecha, A. Simoni, M. Inguscio: Science 294, 1320–1322 (2001)
M.H. Anderson, J. Ensher, M. Matthews, C. Wieman, E. Cornell: Science 269, 198 (1995)
S. Chu: Rev. Mod. Phys. 70, 685 (1998)
C. Cohen-Tannoudji: Rev. Mod. Phys. 70, 707 (1998)
W.D. Phillips: Rev. Mod. Phys. 70, 721 (1998)
W. Ketterle, N.J. Van Druten: Advances in Atomic, Molecular, and Optical Physics, 37, 181 (1996)
M.R. Andrews, D.M. Kurn, H.-J. Miesner, D.S. Durfee, C.G. Townsend, S. Inouye, W. Ketterle: Phys. Rev. Lett. 79, 553 (1997)
F. Dalfovo, S. Giorgini, l.P. Pitaevskii, S. Stringari: Rev. Mod. Phys. 71, 463 (1999)
L.D. Landau, E. M. Lifshitz: Quantum Mechanics, § 131 (Pergamon Press, Oxford 1977)
C.J. Joachain: Quantum collision theory (North-Holland, Amsterdam 1983)
J. Dalibard: ‘Collisional dynamics of ultra-cold atomic gases’. In: Proceedings of the International School of Physics Enrico Fermi, Course CXL, Bose-Einstein Condensation in Atomic Gases, ed. by M. Inguscio, S. Stringari, C.E. Wieman (IOS Press, Amsterdam 1999) pp. 321–350
See the contribution of G. Kurizki to the present book and refs. in
K. Huang: Statistical Mechanics (Wiley, New York 1987)
E.M. Lifshitz, L.P. Pitaevskii: Statistical Physics, Part 2 (Butterworth-Heinemann, Oxford 1980)
S. Inouye, M.R. Andrews, J. Stenger, H.-J. Miesner, D.M. Stamper-Kurn, W. Ketterle: Nature 392, 151 (1998)
I. Bloch, T. W. Hänsch, T. Esslinger: Nature 403, 166 (2000)
I. Bloch, T.W. Hänsch, T. Esslinger: Phys. Rev. Lett. 82, 3008 (1999).
P.W. Anderson: ‘Measurement in Quantum Theory and the Problem of Complex Systems’. In The Lesson of Quantum Theory, ed. by J. de Boer, E. Dal, O. Ulfbeck (Elsevier, Amsterdam 1986) pp. 23–34
A. J. Leggett, F. Sols: Found. of Physics 21, 353 (1991)
J. Javanainen, S.M. Yoo: Phys. Rev. Lett. 76, 161 (1996)
J.I. Cirac, C.W. Gardiner, M. Narschewski, P. Zoller: Phys. Rev. A 54, R3714 (1996)
Y. Castin, J. Dalibard: Phys. Rev. A 55, 4330 (1997)
M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn, W. Ketterle: Science 275, 637 (1997)
R.J. Donnelly: Quantized Vortices in Helium II (Cambridge University Press, Cambridge 1991)
D. Guéry-Odelin, S. Stringari: Phys. Rev. Lett. 83, 4452 (1999)
O.M. Maragò, S.A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, C. J. Foot: Phys. Rev. Lett. 84, 2056 (2000)
C. Raman, M. Köhl, R. Onofrio, D. S. Durfee, C.E. Kuklewicz, Z. Hadzibabic, W. Ketterle: Phys. Rev. Lett. 83, 2502 (1999)
A.P. Chikkatur, A. Gorlitz, D.M. Stamper-Kurn, S. Inouye, S. Gupta, W. Ketterle: Phys. Rev. Lett. 85, 483 (2000)
R. Onofrio, C. Raman, J.M. Vogels, J. Abo-Shaeer, A.P. Chikkatur, W. Ketterle: Phys. Rev. Lett. 85, 2228 (2000)
A. Fetter, A Svidzinsky: J. Phys. Condens. Matter 13, 135 (2001)
L. Onsager: Nuovo Cimento 6,suppl. 2, 249 (1949)
R.P. Feynman: ‘Application of Quantum Mechanics to Liquid Helium’. In Progress in Low Temperature Physics, vol. 1, ed. by C. J. Gorter (North-Holland, Amsterdam, 1955) pp. 17–53
A.A. Abrikosov: JETP 32, 1442 (1957)
H. Träuble, U. Essmann: J. Appl. Phys. 25, 273 (1968)
N.V. Sarma: Philos. Mag. 17, 1233 (1968)
E.J. Yarmchuk, M.J.V. Gordon, R.E. Packard: Phys. Rev. Lett. 43, 214 (1979)
M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell: Phys. Rev. Lett. 83, 2498 (1999)
B.P. Anderson, P.C. Haljan, C.E. Wieman, E.A. Cornell: Phys. Rev. Lett. 85, 2857 (2000)
B.P. Anderson, P.C. Haljan, C.A. Regal, D.L. Feder, L.A. Collins, C.W. Clark, E.A. Cornell: Phys. Rev. Lett. 86, 2926 (2001)
K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard: Phys. Rev. Lett. 84, 806 (2000)
J.R. Abo-Shaeer, C. Raman, J.M. Vogels, W. Ketterle: Science 292, 476 (2001)
C. Raman, J.R. Abo-Shaeer, J.M. Vogels, K. Xu, W. Ketterle: Phys. Rev. Lett. 87, 210402 (2001)
P.C. Haljan, I. Coddington, P. Engels, E.A. Cornell: Phys. Rev. Lett. 87, 210403 (2001)
E. Hodby, G. Hechenblaikner, S.A. Hopkins, O.M. Maragò, C.J. Foot: Phys. Rev. Lett. 88, 010405 (2002)
P. Rosenbusch, D.S. Petrov, S. Sinha, F. Chevy, V. Bretin, Y. Castin, G. Shlyapnikov, J. Dalibard: Phys. Rev. Lett. 88, 250403 (2002)
Y. Castin, R. Dum: Phys. Rev. Lett. 77, 5315 (1996)
E. Lundh, C.J. Pethick, H. Smith: Phys. Rev. A 58, 4816 (1998)
F. Dalfovo, M. Modugno: Phys. Rev. A 61, 023605 (2000)
M. Modugno, L. Pricoupenko, Y. Castin: cond-mat/02033597.
P. Engels, I. Coddington, P. C. Haljan, E. A. Cornell: cond-mat/0204449
E. Mandonnet, A. Minguzzi, R. Dum, I. Carusotto, Y. Castin, J. Dalibard: Eur. Phys. J. D 10, 9 (2000)
P. Cren, C.F. Roos, A. Aclan, J. Dalibard, D. Guéry-Odelin: to be published in Eur. Phys. J. D (2002)
A.N. Chikkatur (MIT group), private communication
J.J. García-Ripoll, V.M. Pérez-García: Phys. Rev. A 63, 041603 (2001)
J.J. García-Ripoll, V.M. Pérez-García: Phys. Rev. A 64, 053611 (2001)
A. Aftalion, T. Riviere: Phys. Rev. A 64, 04s3611 (2001)
A. Aftalion, R. L. Jerrard: cond-mat/0204475
P.O. Fedichev, G.V. Shlyapnikov: Phys. Rev. A 60, R1779 (1999)
P.O. Fedichev, A.E. Muryshev: cond-mat/0004264
B. DeMarco, D.S. Jin: Science 285, 1703 (1999)
A.G. Truscott, K.E. Strecker, W.I. McAlexander, G.B. Partridge, R.G. Hulet: Science 291, 2570 (2001)
F. Schreck, L. Khaykovich, K.L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, C. Salomon: Phys. Rev. Lett. 87, 080403 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dalibard, J. (2002). Coherence and Superfluidity of Gaseous Bose-Einstein Condensates. In: Dauxois, T., Ruffo, S., Arimondo, E., Wilkens, M. (eds) Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics, vol 602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45835-2_9
Download citation
DOI: https://doi.org/10.1007/3-540-45835-2_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44315-5
Online ISBN: 978-3-540-45835-7
eBook Packages: Springer Book Archive