Probing low-energy Lorentz violation from high-energy modified dispersion in dipolar Bose-Einstein condensates

We theoretically propose an experimentally viable scheme to use an impurity atom in a dipolar Bose-Einstein condensate, in order to probe analogue low-energy Lorentz violation from the modified dispersion at high energies as suggested by quantum theories of gravity. We show that the density fluctuations in the dipolar Bose-Einstein condensate possess a Lorentz-violating Bogoliubov spectrum ωk = c0|k|f(c0|k|/M*⋆), with recovery of approximate Lorentz invariance at energy scales well below M⋆. When f is adjusted to dip below unity somewhere, the impurity, analogously dipole coupled to the density fluctuations, experiences analogous drastic Lorentz violation at arbitrarily low energies, reproducing the same response of the Unruh-DeWitt detector to Lorentz-violating quantum fields. Being a fundamentally quantum mechanical device, our quantum fluid platform provides an experimentally realizable test field to verify whether the effective low-energy theory can reveal unexpected imprints of the theory's high-energy structure, in quantum field theory.