nLab Bose-Einstein condensate

Idea

A condensate of bosons.

Related concepts

• boson star

• Bose-Einstein condensate dark matter

• superfluid

• superconductivity

• tachyon condensation

• quantum optics

References

General

Textbook accounts:

• Tim Byrnes, Ebubechukwu Ilo-Okeke, Section 2 of: Quantum Atom Optics: Theory and Applications to Quantum Technology, Cambridge University Press 2021 (arXiv:2007.14601, CUP)

See also:

• Wikipedia, Bose-Einstein condensate

Proposal to use BEC for quantum computation:

• Tim Byrnes, Kai Wen, Yoshihisa Yamamoto, Macroscopic quantum computation using Bose-Einstein condensates, Phys. Rev. A 85 (2012) 040306(R) [doi:10.1103/PhysRevA.85.040306]

Realization of quantum entanglement/EPR paradox:

• Paolo Colciaghi, Yifan Li, Philipp Treutlein, Tilman Zibold, Einstein-Podolsky-Rosen experiment with two Bose-Einstein condensates [arXiv:2211.05101]

Discussion of BECs via AdS-CFT in condensed matter physics:

• Yu-Kun Yan, Shanquan Lan, Yu Tian, Peng Yang, Shunhui Yao, Hongbao Zhang, Towards an effective description of holographic vortex dynamics [arXiv:2207.02814]

Defect anyons

Often the concept of anyons is introduced as if a generalization of particle statistics of perturbative quanta like fundamental bosons and fermions. But many (concepts of) types of anyons are really solitonic$\;$defects such as vortices whose braiding phases are adiabatic Berry phases.

The general concept of braiding of defects in solid state physics:

• N. David Mermin, The topological theory of defects in ordered media, Rev. Mod. Phys. 51 (1979) 591 $[$doi:10.1103/RevModPhys.51.591$]$

  (including a review of basic homotopy theory)

and more specifically for vortices:

• Hoi-Kwong Lo, John Preskill, Non-Abelian vortices and non-Abelian statistics, Phys. Rev. D 48 (1993) 4821 $[$doi:10.1103/PhysRevD.48.4821$]$

Explicit discussion as defect anyons:

• Alexei Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321 1 (2006) 2-111 [doi:10.1016/j.aop.2005.10.005]

  ${}$ [p. 4:] “Anyonic particles are best viewed as a kind of topological defects that reveal nontrivial properties of the ground state.”

Anyonic defects which act as genons, changing the effective genus of the ambient 2D surface:

• Maissam Barkeshli, Xiao-Liang Qi: Topological Nematic States and Non-Abelian Lattice Dislocations, Phys. Rev. X 2 031013 (2012) [doi:10.1103/PhysRevX.2.031013, arXiv:1112.3311]

• Maissam Barkeshli, Chao-Ming Jian, Xiao-Liang Qi: Twist defects and projective non-Abelian braiding statistics, Phys. Rev. B 87 (2013) 045130 [doi:10.1103/PhysRevB.87.045130, arXiv:1208.4834]

• Xiao-Liang Qi: Defects in topologically ordered states, talk notes (2014) [pdf, pdf]

• Andrey Gromov: Geometric Defects in Quantum Hall States, Phys. Rev. B 94 085116 (2016) [doi:10.1103/PhysRevB.94.085116]

see also:

• Simon Burton, Elijah Durso-Sabina, Natalie C. Brown: Genons, Double Covers and Fault-tolerant Clifford Gates [arXiv:2406.09951]

and their potential experimental realization:

• Zhao Liu, Gunnar Möller, Emil J. Bergholtz: Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States, Phys. Rev. Lett. 119 (2017) 106801 [doi:10.1103/PhysRevLett.119.106801]

Concrete vortex$\phantom{-}$anyons in Bose-Einstein condensates:

• B. Paredes, P. Fedichev, J. Ignacio Cirac, Peter Zoller: 1/2-Anyons in small atomic Bose-Einstein condensates, Phys. Rev. Lett. 87 (2001) 010402 [doi:10.1103/PhysRevLett.87.010402, arXiv:cond-mat/0103251]

• Julien Garaud, Jin Dai, Antti J. Niemi, Vortex precession and exchange in a Bose-Einstein condensate, J. High Energ. Phys. 2021 157 (2021) [arXiv:2010.04549]

• Thomas Mawson, Timothy Petersen, Joost Slingerland, Tapio Simula, Braiding and fusion of non-Abelian vortex anyons, Phys. Rev. Lett. 123 (2019) 140404 [doi:10.1103/PhysRevLett.123.140404]

and in (other) superfluids:

• Yusuke Masaki, Takeshi Mizushima, Muneto Nitta, Non-Abelian Half-Quantum Vortices in 3P2 Topological Superfluids [arXiv:2107.02448]

and in condensates of non-defect anyons:

• Michele Correggi, Romain Duboscq, Douglas Lundholm, Nicolas Rougerie: Vortex patterns in the almost-bosonic anyon gas, Europhys. Lett. 126 (2019) 20005 [doi:10.1209/0295-5075/126/20005, arXiv:1901.10739]

On analog behaviour in liquid crystals:

• Alexander Mietke, Jörn Dunkel: Anyonic defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals, Phys. Rev. X 12 (2022) 011027 [arXiv:2011.04648, doi:10.1103/PhysRevX.12.011027]

See also Ahn, Park & Yang 19 who refer to the band nodes in the Brillouin torus of a semi-metal as “vortices in momentum space”.

And see at defect brane.