Planck-scale–induced speed of sound in a trapped Bose-Einstein condensate

Abstract

In the present work, we analyze the corrections caused by an anomalous dispersion relation, suggested in several quantum gravity models, upon the speed of sound in a weakly interacting Bose-Einstein Condensate, trapped in a potential of the form V (r) ∼ r 2 . We show that the corresponding ground state energy and consequently, the associated speed of sound, present corrections respect to the usual case, which may be used to explore the sensitivity to Planck-scale effects on these relevant properties associated with the condensate. Indeed, we stress that this type of macroscopic bodies may be more sensitive, under certain conditions, to Planck-scale manifestations than its constituents. In addition, we prove that the inclusion of a trapping potential, together with manybody contributions, improves the sensitivity to Planck-scale signals, compared to the homogeneous system.

Planck-scale traces from the interference pattern of two Bose-Einstein condensates

“…In particular, due to its quantum properties, and also to its high experimental precision, Bose-Einstein condensates become an excellent tool in the search of traces from Planck-scale physics, and has produced several interesting works in this direction [4][5][6][7][8][9][10][11], and references therein.…”

“…For instance, in Refs. [5,6] it was demonstrated that the corrections arising from the quantum structure of spacetime, characterized by a deformed dispersion relation, on some relevant properties associated with a Bose-Einstein condensate scales as a non-trivial function of the number of particles.…”

“…Additionally, it is quiet remarkable that the inclusion of a trapping potential improves the sensitivity to Planck scale signals, compared to a condensate in a box [6]. These facts suggest that the properties associated with many-body systems, in particular some properties associated with a Bose-Einstein condensate could be used, in principle, to obtain representative bounds on the deformation parameters [4,[8][9][10] or to explore the sensitivity for these systems to Planck scale signals [5][6][7]12]. Thus, it is quite interesting to explore the sensitivity to Planck scale signals on certain properties of the condensate, in which the corrections caused by the quantum structure of space-time can be amplified, instead of being suppressed.…”

Planck scale physics and Bogoliubov spaces in a Bose-Einstein condensate

“…Usually, the confinement of the condensate can be obtained by using harmonic traps, among others [18,40] and the use of generic potentials, under certain conditions, could be used to constrain Planck scale physics in this context, by changing the shape of the trap [28,29]. In other words, the analysis of a system trapped in generic potential within the Bogoliubov formalism deserves further investigation, and will be presented elsewhere [33]. Finally, we must add that the measurement of the corrections caused by the deformation parameter α, could be out of the current technology.…”

Polymer Quantization in the Bogoliubov’s Regime for a Homogeneous One-Dimensional Bose-Einstein Condensate

“…One interesting feature, related to Bose-Einstein condensates, is its possible use as test tools in gravitational physics [1][2][3][4][5][6][7][8][9][10][11][12]. The quantum properties associated with this N-body system suggest that this phenomenon could be taken as a serious candidate to explore some features related to a possible quantum structure of space-time.…”