Abstract
We study the thermodynamic phases of a Bose gas of spin-1/2 atoms in the Hartree-Fock approximation. Our main result is that, for repulsive or weakly attractive inter-component interaction strength, the superfluid and ferromagnetic phase transitions occur at the same temperature. For strongly attractive inter-component interaction strength, however, the ferromagnetic phase transition occurs at a higher temperature than the superfluid phase transition. We also find that the presence of a condensate acts as an effective magnetic field that polarizes the normal cloud. We finally comment on the validity of the Hartree-Fock approximation in describing different phenomena in this system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
CJ. Myatt EA. Burt RW. Ghrist EA. Cornell CE. Wieman (1997) Phys. Rev. Lett. 78 586 Occurrence Handle10.1103/PhysRevLett.78.586
HJ. Lewandowski DM. Harber DL. Whitaker E.A. Cornell (2002) Phys. Rev. Lett. 88 070403 Occurrence Handle10.1103/PhysRevLett.88.070403 Occurrence Handle11863871
JM. McGuirk HJ. Lewandowski DM. Harber T. Nikuni J.E. Williams EA. Cornell (2002) Phys. Rev. Lett. 89 090402 Occurrence Handle10.1103/PhysRevLett.89.090402 Occurrence Handle12190382
JM. McGuirk DM. Harber HJ. Lewandowski EA. Cornell (2003) Phys. Rev. Lett. 91 150402 Occurrence Handle14611452
M.Ö. Oktel and Levitov LS., Phys. Rev. Lett. 88, 230403 (2002); Fuchs JN., Gangardt DM., and F. Laloë: Phys. Rev Lett. 88: 230404 (2002); Williams JE., Nikuni T., and C. W Clark, Phys. Rev. Lett. 88: 230405 (2002); A. S. Bradley and C. W Gardiner, J. Phys. B. 20: 4299 (2002)
T. Nikuni JE. Williams (2003) J. Low Temp. Phys. 133 323
J. Stenger S. Inouye D.M. Stamper-Kurn HJ. Miesner A.P. Chikkatur W. Ketterle (1998) Nature 396 345
T. Ohmi K. Machida (1998) J. Phys. Soc. Jpn. 67 1822
TL. Ho (1998) Phys. Rev. Lett. 81 742
CK. Law H. Pu NP. Bigelow (1998) Phys. Rev. Lett. 81 5257
AE. Leanhardt Y. Shin D. Kielpinski DE. Pritchard W. Ketterle (2003) Phys. Rev. Lett. 90 140403 Occurrence Handle12731900
H. Pu CK. Law S. Raghavan JH. Eberly NP. Bigelow (1999) Phys. Rev. A. 60 1463
H. Schmaljohann M. Erhard J. Kronjager M. Kottke S. Staa Particlevan L. Cacciapuoti JJ. Arlt K. Bongs K. Sengstock (2004) Phys. Rev. Lett. 92 040402 Occurrence Handle14995355
MS. Chang CD. Hamley MD. Barrett JA. Sauer KM. Fortier W. Zhang L. You MS. Chapman (2004) Phys. Rev. Lett. 92 140403 Occurrence Handle15089521
IJ. Bonalde TM. Brill W. Yao BJ. Verhaar IF. Silvera (1998) J. Low Temp. Phys. 113 211
E.D. Siggia AE. Ruckenstein (1980) Phys. Rev. Lett. 44 1423
T.-L. Ho L. Yin (2000) Phys. Rev. Lett. 84 2302 Occurrence Handle11018870
K. Yang YQ. Li (2003) Int. J. Mod. Phys. B. 17 1027
Q. Gu and Klemm RA., Phys. Rev. A. 68: 031604(R) (2003)
G. Baym G. Grinstein (1977) Phys. Rev. D. 15 2897
See e.g. A. L. Fetter and Walecka JD., Quantum Theory of Many-Particle Systems. (McGraw-Hill, New York, 1971)
The reason why we are restricting our analysis to states where the numbers of atoms in the ↑ and ↓ states are equal is to simplify the algebra. In the regimes of interest to us, the state of the system that minimizes the free energy will satisfy that condition even if it is not imposed externally
K. Huang (1963) Statistical Mechanics John Wiley & Sons New York
F. Dalfovo S. Giorgini LP. Pitaevskii S. Stringari (1999) Rev. Mod. Phys. 71 463
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ashhab, S. Superfluid vs Ferromagnetic Behavior in a Bose Gas of Spin-1/2 Atoms. J Low Temp Phys 140, 51–65 (2005). https://doi.org/10.1007/s10909-005-6011-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10909-005-6011-8