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≃ξ1mcp/2Mp produces a shift in the condensation temperature Tc of about ΔTc/Tc0≃10−6ξ1 for typical laboratory conditions. Such a shift allows to bound the deformation parameter up to |ξ1|≲104. Moreover we show that it is possible to enlarge ΔTc/Tc0 and improve the bound on ξ1 lowering the frequency of the harmonic trap. Finally we compare the Planck-scale induced shift in Tc with similar effects due to interboson interactions and finite size effects.