Abstract.
For both cases with and without interactions, bipartite entanglement of two fermions from a Fermi gas in a trap is investigated. We show how the entanglement depends on the locations of the two fermions and the total particle number of the Fermi gas. Fermions at the edge of trap have longer entanglement distance (beyond it, the entanglement disappears) than those in the center. We derive a lower limitation to the average overlapping for two entangled fermions in the BCS ground state, it is shown to be \(\sqrt{Q/2M}\), a function of Cooper pair number Q and the total number of occupied energy levels M.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Bouwmeester, A. Ekert, A. Zeilinger, The physics of quantum information, Quantum cryptography, Quantum teleportation, Quantum computation (Springer-Verlag, Berlin, 2000)
M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)
V. Vedral, Centr. Eur. J. Phys. 2, 289 (2003)
S. Oh, J. Kim, Phys. Rev. A 69, 054305 (2004)
C. Lunkes, C. Brukner, V. Vedral, Phys. Rev. Lett. 95, 030503 (2005)
D. Cavalcanti, M.F. Santos, M.O. Terra Cunha, C. Lunkes, V. Vedral, Phys. Rev. A 72, 062307 (2005)
V.E. Korepin, Phys. Rev. Lett. 92, 096402 (2004)
C. Lunkes, C. Brukner, V. Vedral, Phys. Rev. A 71, 034309 (2005)
V. Vedral, New J. Phys. 6, 22 (2004)
W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1997)
In the light of well-established and elementary many-body physics, this can be understood as follows. For a free Fermi gas in one spatial direction, the particle density n and the Fermi momentum kf are related via n=2kf/π. Thus, the larger the density, the larger kf, and in turn, the shorter the entanglement distance. Also the observation that the entanglement between two particles depend on both their coordinates and not just on their diffenence, is an consequence of the lack of translational symmetry in the harmonic trap.
R.K. Pathria, Statistical mechanics (Elsevier, 2001)
J. Dukelsky, G. Sierra, Phys. Rev. B 61, 12302 (2000)
J. von Delft, D.C. Ralph, Phys. Rep. 345, 61 (2001)
J. von Delft et al., Phys. Rev. Lett. 77, 3189 (1996)
C. Dunning, J. Links, H.Q. Zhou, Phys. Rev. Lett. 94, 227002 (2005)
A. Peres, Phys. Lett. A 202, 16 (1995)
F. Braun et al., Phys. Rev. Lett. 79, 921 (1997)
S. Dusuel, J. Vidal, Phys. Rev. A 71, 060304 (2005)
M.A. Martin-Delgado, e-print arXiv:quant-ph/0207026
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yi, X. Entanglement of Fermi gases in a harmonic trap. Eur. Phys. J. D 39, 465–469 (2006). https://doi.org/10.1140/epjd/e2006-00162-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2006-00162-7