Abstract
We study the phase separated state of an ultracold atomic Fermi gas confined in a three-dimensional quantum harmonic trap with a BCS pairing interaction. Examining various finite-temperature phase diagrams, we investigate the interplay between the filling of the quantum trap energy levels and the pairing energy. We find that a low (high) filling leads to a large (small) critical population imbalance for the superfluid/normal transition, together with a fully (partially) polarized normal part. We also show that the decrease of the density leads to a changeover of the shape of the superfluid core from an equipotential form to a deformed one. Moreover, we clarify the intrinsic mechanisms that lead to the deformation, providing a unified scenario for phase separation and deformation in a trapped Fermi gas, allowing for a possible interpretation of the apparently controversial experimental findings.
Similar content being viewed by others
References
S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008) and references therein
G.B. Partridge, W. Li, R.I. Karmar, Y.A. Liao, R.G. Hulet, Science 311, 503 (2006)
G.B. Partridge, W. Li, Y.A. Liao, R.G. Hulet, M. Haque, H.T.C. Stoof, Phys. Rev. Lett. 97, 190407 (2006)
M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle, Nature 442, 54 (2006)
Y. Shin, M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle, Phys. Rev. Lett. 97, 030401 (2006)
M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006)
Y. Shin, C.H. Schunck, A. Schirotzek, W. Ketterle, Nature 451, 689 (2008)
C.H. Schunk, Y. Shin, A. Schirotzek, M.W. Zwierlein, W. Ketterle, Science 316, 867 (2007)
P.F. Bedaque, H. Caldas, G. Rupak, Phys. Rev. Lett. 91, 247002 (2003)
H. Müther, A. Sedrakian, Phys. Rev. Lett. 88, 252503 (2002)
A. Sedrakian, J. Mur-Petit, A. Polls, H. Müther, Phys. Rev. A 72, 013613 (2005)
W.V. Liu, F. Wilczek, Phys. Rev. Lett. 90, 047002 (2003)
M.M. Forbes, E. Gubankova, W.V. Liu, F. Wilczek, Phys. Rev. Lett. 94, 017001 (2005)
K.B. Gubbels, M.W.J. Romans, H.T.C. Stoof, Phys. Rev. Lett. 97, 210402 (2006)
K. Machida, T. Mizushima, M. Ichioka, Phys. Rev. Lett. 97, 120407 (2006)
R. Casalbuoni, G. Nardulli, Rev. Mod. Phys. 76, 263 (2004)
A. Schirotzek, C.-H. Wu, A. Sommer, M.W. Zwierlein, Phys. Rev. Lett. 102, 230402 (2009)
Y. Liao, A.S.C. Rittner, T. Paprotta, W. Li, G.B. Partridge, R.G. Hulet, S.K. Baur, E.J. Mueller, arXiv:0912.0092
F. Chevy, C. Mora, arXiv:1003.0801
J. Kinnunen, L.M. Jensen, P. Torma, Phys. Rev. Lett. 96, 110403 (2006)
R. Sensarma, W. Schneider, R.B. Diener, M. Randeria, arXiv:0706.1741
T.N. De Silva, E.J. Mueller, Phys. Rev. Lett. 97, 070402 (2006)
M. Haque, H.T.C. Stoof, Phys. Rev. Lett. 98, 260406 (2007)
M. Haque, H.T.C. Stoof, Phys. Rev. A 74, R011602 (2006)
X.W. Guan, M.T. Batchelor, C. Lee, M. Bortz, Phys. Rev. B 76, 085120 (2007)
F. Chevy, Phys. Rev. Lett. 96, 130401 (2006)
Q. Chen, Y. He, C.-C. Chien, K. Levin, Phys. Rev. A 74, 063603 (2006)
C.-C. Chien, Q. Chen, Y. He, K. Levin, Phys. Rev. Lett. 98, 110404 (2007)
W. Yi, L.-M. Duan, Phys. Rev. A 74, 013610 (2006)
Z.-J. Ying, M. Cuoco, C. Noce, H.-Q. Zhou, Phys. Rev. Lett. 100, 140406 (2008)
D.E. Sheehy, L. Radzihovsky, Phys. Rev. Lett. 96, 060401 (2006)
L.M. Jensen, J. Kinnunen, P. Torma, Phys. Rev. A 76, 033620 (2007)
X. Liu, H. Hu, P.D. Drummond, Phys. Rev. A 75, 023614 (2007)
Y. Shin, C.H. Schunck, A. Schirotzek, W. Ketterle, Nature 451, 689 (2007)
J. Carlson, S. Reddy, Phys. Rev. Lett. 95, 060401 (2005)
J.R. Engelbrecht, M. Randeria, C.A.R.S. de Melo, Phys. Rev. B 55, 15153 (1997)
J. Carlson, S. Reddy, Phys. Rev. Lett. 100, 150403 (2008)
J. Carlson, S.-Y. Chang, V.R. Pandharipande, K.E. Schmidt, Phys. Rev. Lett. 91, 050401 (2003)
F. Chevy, Phys. Rev. A 74, 063628 (2006)
G. Bruun, Y. Castin, R. Dum, K. Burnett, Eur. Phys. J. D 7, 433 (1999)
A. Perali, P. Pieri, G.C. Strinati, Phys. Rev. Lett. 93, 100404 (2004)
M.M. Parish, D.A. Huse, Phys. Rev. A 80, 063605 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ying, ZJ., Cuoco, M., Noce, C. et al. Phase diagram and deformed phase separation for a trapped Fermi gas with population imbalance and BCS pairing interaction. Eur. Phys. J. B 78, 43–49 (2010). https://doi.org/10.1140/epjb/e2010-10515-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2010-10515-0