Trapped Bose-Einstein condensates with Planck-scale induced deformation of the energy-momentum dispersion relation

We show that harmonically trapped Bose-Einstein condensates can be used to constrain Planck-scale physics. In particular we prove that a Planck-scale induced deformation of the Minkowski energy-momentum dispersion relation δE≃ξ 1mcp/2M p produces a shift in the condensation temperature T c of about δTc/Tc0≃10-6ξ1 for typical laboratory conditions. Such a shift allows to bound the deformation parameter up to |ξ 1|≲10 4. Moreover we show that it is possible to enlarge δTc/Tc0 and improve the bound on ξ 1 lowering the frequency of the harmonic trap. Finally we compare the Planck-scale induced shift in T c with similar effects due to interboson interactions and finite size effects. © 2012 Elsevier B.V.