Bogoliubov space of a Bose-Einstein condensate and quantum spacetime fluctuations.

In this work, we consider the role that metric fluctuations could have upon the properties of a Bose-Einstein condensate. In particular, we consider the Bogoliubov space associated with it and show that there are, at least, two independent ways in which the average size of these metric fluctuations could be, experimentally, determined. Indeed, we prove that the pressure and the speed of sound of the ground state define an expression allowing us to determine the average size of these fluctuations. Afterward, an interferometric experiment involving Bogoliubov excitations of the condensate and the pressure (or the speed of sound of the ground state) provides a second and independent way in which this average size could be determined, experimentally. [ABSTRACT FROM AUTHOR]