2016/05/31 by Hao Guo, Yan He, Chih-Chun Chien
Mathematics · Physics and Astronomy · #Algebraic number #Bose–Einstein condensate #Boson #Cold Atom Physics and Bose-Einstein Condensates #Fermion #Geometric phase #Ground state #Mathematical physics #Mathematics #Physics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Superfluidity #cond-mat.quant-gas #cond-mat.supr-con #math-ph #math.MP
paper · pdf · doi:10.1016/j.physleta.2016.11.014
published as Phys. Lett. A 381, 351 (2017) · 14 pages, no figure, revised version
openalex created_date 2016/09/16 · arxiv created 2016/10/12 · openalex publication_date 2016/11/15 · arxiv updated 2016/12/23 · openalex updated_date 2026/08/05
By using Bogoliubov transformations to construct the ground states of fermionic Bardeen-Cooper-Schrieffer (BCS) superfluids and weakly-interacting Bose gases supporting Bose Einstein Condensation (BEC), their algebraic structures and implications can be analyzed in detail. Both ground states are generalized squeezed coherent states saturating a generalized Heisenberg uncertainty relation, and they acquire quantized Berry phases when the corresponding systems are transported along a closed path in their parameter spaces. While the Berry phase of the BCS ground state depends on the total particle number, the Berry phase of the BEC ground state depends only on the particles outside the BEC. The Berry phases are associated with magnetic monopoles in the parameter spaces and we found that the Dirac quantization condition is satisfied. Moreover, both ground states are entangled states of the fermion or boson quanta and we found the entanglement entropy quantifying the internal correlations. A fixed particle-number approach of fermionic superfluids does not saturate the generalized uncertainty relation, exhibits internal entanglement, and gives corresponding Berry phase. In addition, the algebraic structures of the ground states can be classified by the q-deformed Hopf algebra, \bigopluskh_qk(1) for bosons and q-deformed Hopf superalgebra \bigopluskh_qk(1|1) for fermions, respectively.