Planck-scale effects on Bose-Einstein condensates

The effects of a Planck-scale deformation of the Minkowski energy-momentum dispersion relation on the phenomenology of non-trapped Bose-Einstein condensates (BECs) are examined. Such a deformation is shown to cause a shift in the condensation temperature Tc of the BEC and, for a specific functional form of deformation, this shift can be as large as the current measured precision on Tc. For a 8537Rb cold-atom BEC with a particle density n≃1012cm−3 we find a fractional shift of order 10−4, but this can be much larger for even more dilute BECs. We discuss the possibility of planning specific experiments with BECs that might provide phenomenological constraints on Planck-scale physics. These corrections to Tc are found to be extremely small for ultrarelativistic BECs implying that, in some cases, Planck-scale effects may be more important in low- rather than high-energy processes.