Few-Body Systems

, 58:159 | Cite as

Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

  • Daniel PęcakEmail author
  • Mariusz Gajda
  • Tomasz Sowiński
Open Access


A system of a two-flavour mixture of ultra-cold fermions confined in a one-dimensional harmonic trap is studied. Using the well-known properties of the centre-of-mass frame we present a numerical method of obtaining energetic spectra in this frame for an arbitrary mass ratio of fermionic species. We identify a specific invariant encoded in many-body correlations which may be helpful to determine an eigenstate of the Hamiltonian and to label excitations of the centre of mass. The tool presented can be easily applied and thus may be particularly useful in an experimental analysis of the interparticle interactions which do not affect the centre of mass excitations in a harmonic potential.


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of PhysicsPolish Academy of SciencesWarsawPoland

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