Applied Physics B

, Volume 117, Issue 3, pp 785–796 | Cite as

How bosonic is a pair of fermions?

  • Malte C. Tichy
  • P. Alexander Bouvrie
  • Klaus Mølmer


Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indicator for bosonic quality is the composite boson normalisation ratio \(\chi _{N+1}/\chi _{N}\) of a state of \(N\) composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large composite numbers \(N\). Here, we provide an efficient characterisation in terms of the purity \(P\) and the largest eigenvalue \(\lambda _1\) of the reduced single-fermion state. We find the states that extremise \(\chi _N\) for given \(P\) and \(\lambda _1\), and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic quality of a composite particle and the entanglement of its constituents.


Normalisation Factor Pauli Principle Schmidt Decomposition Composite Boson Saturable Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank Florian Mintert, Łukasz Rudnicki, Alagu Thilagam and Nikolaj Th. Zinner for stimulating discussions, and Christian K. Andersen, Durga Dasari, Jake Gulliksen, Pinja Haikka, David Petrosyan and Andrew C. J. Wade for valuable feedback on the manuscript. M.C.T. gratefully acknowledges support by the Alexander von Humboldt-Foundation through a Feodor Lynen Fellowship. K.M. gratefully acknowledges support by the Villum Foundation. P.A.B. gratefully acknowledges support by the Progama de Movilidad Internacional CEI BioTic en el marco PAP-Erasmus.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Malte C. Tichy
    • 1
  • P. Alexander Bouvrie
    • 2
  • Klaus Mølmer
    • 1
  1. 1.Department of Physics and AstronomyUniversity of AarhusAarhus CDenmark
  2. 2.Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y ComputacionalUniversidad de GranadaGranadaSpain

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