DOI: 10.1126/science.1138807. Critical Behavior of a Trapped Interacting Bose Gas

Critical Behavior of a Trapped Interacting Bose Gas

10.1126/science.1138807

Crossref journal-article

American Association for the Advancement of Science (AAAS)

Science (221)

Abstract

The phase transition of Bose-Einstein condensation was studied in the critical regime, where fluctuations extend far beyond the length scale of thermal de Broglie waves. We used matter-wave interference to measure the correlation length of these critical fluctuations as a function of temperature. Observations of the diverging behavior of the correlation length above the critical temperature enabled us to determine the critical exponent of the correlation length for a trapped, weakly interacting Bose gas to be ν = 0.67 ± 0.13. This measurement has direct implications for the understanding of second-order phase transitions.

Bibliography

Donner, T., Ritter, S., Bourdel, T., OÌttl, A., KoÌhl, M., & Esslinger, T. (2007). Critical Behavior of a Trapped Interacting Bose Gas. Science, 315(5818), 1556â1558.

Authors 6

T. Donner (first)
S. Ritter (additional)
T. Bourdel (additional)
A. Öttl (additional)
M. Köhl (additional)
T. Esslinger (additional)

References 30 Referenced 152

J. Zinn Justin Quantum Field Theory and Critical Phenomena (Oxford Univ. Press Oxford 1996).
10.1103/PhysRevLett.83.1703
10.1103/PhysRevLett.87.120401
10.1103/PhysRevLett.87.120402
10.1103/PhysRevA.64.053609
10.1007/BF00682285
M. J. Adriaans, D. R. Swanson, J. A. Lipa, Physica B194, 733 (1993). / Physica B (1993)
10.1103/PhysRevB.68.174518
10.1103/PhysRevA.59.4595
K. Huang Statistical Mechanics (Wiley New York 1987).
In the general d -dimensional case 〈Ψ † ( r )Ψ(0) 〉 ∝ r –( d –2+η) exp(– r /ξ) where η is a critical exponent. The calculated and measured values of η are on the order of 10 –2 and therefore we neglect η in our analysis.
For a noninteracting gas the critical exponent can be calculated as ν = 1 for homogeneous systems and ν = ½ for harmonically trapped systems.
10.1103/PhysRev.65.117
10.1103/PhysRevA.54.R4633
The numerical coefficient may be different for a trapped gas and has been omitted in ( 25 ).
10.1103/PhysRevA.69.053625
10.1103/PhysRevA.73.053604
10.1103/PhysRevLett.92.130403
10.1038/nature02530
10.1126/science.1100700
10.1038/nature04851
10.1038/35003132
10.1063/1.2216907
10.1103/PhysRevA.73.043602
10.1209/epl/i1996-00179-4
10.1103/PhysRevLett.84.4894
10.1103/PhysRevB.63.214503
10.1103/PhysRevB.74.132502
10.1016/0031-9163(66)90088-6
We thank G. Blatter F. Brennecke A. Kuklov G. Shlyapnikov M. Troyer and W. Zwerger for insightful discussions. Supported by a European Union Marie Curie fellowship under contract MEIF-CT-2005-023612 (T.B.) SEP Information Sciences the Optical Lattices and Quantum Information (OLAQUI) project of the European Union and the Quantum Systems for Information Technology (QSIT) project of ETH Zürich.

Dates

Type	When
Created	18 years, 5 months ago (March 15, 2007, 4:29 p.m.)
Deposited	1 year, 7 months ago (Jan. 10, 2024, 2:55 a.m.)
Indexed	4 weeks ago (Aug. 6, 2025, 8:52 a.m.)
Issued	18 years, 5 months ago (March 16, 2007)
Published	18 years, 5 months ago (March 16, 2007)
Published Print	18 years, 5 months ago (March 16, 2007)

Funders 0

None

BibTeX

@article{Donner_2007, title={Critical Behavior of a Trapped Interacting Bose Gas}, volume={315}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.1138807}, DOI={10.1126/science.1138807}, number={5818}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Donner, T. and Ritter, S. and Bourdel, T. and Öttl, A. and Köhl, M. and Esslinger, T.}, year={2007}, month=mar, pages={1556–1558} }

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