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

Abstract

-We analyze the consequences caused by a deformed dispersion relation, suggested in several quantum gravity models, upon a bosonic gas. Concerning the ground state of the Bogoliubov space of this system, we deduce the corrections in the pressure, the speed of sound, and the corresponding healing length. Indeed, we prove that the corrections in the relevant thermodynamic properties associated with the ground state, defines a non trivial function of the density of particles and the deformation parameters, allowing us to constrain, in principle, the form of the modified energy-momentum dispersion relation.Introduction. -The possibility of a deformation in the dispersion relation of microscopic particles, appears in connection with the quest for a quantum theory of gravity [1-5, 9-12]. In some schemes, the possibility that the space-time could be quantized, can be characterized, from a phenomenological point of view, as a modification in the dispersion relation of microscopic particles [2,3,[5][6][7][8] (and references therein). A modified dispersion relation emerges as an adequate tool in the search for phenomenological consequences caused by this type of quantum gravity models. Nevertheless, the most difficult aspect in searching experimental hints relevant for the quantumgravity problem is the smallness of the involved effects [3,4]. If this kind of deformations are characterized by some Planck scale, then the quantum gravity effects become very small [2,5].In the non-relativistic limit, the deformed dispersion relation can be expressed as follows [5,9]

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

“…Recently, the use of many-body systems as theoretical tools in searching some possible Planck scale manifestations has become a very interesting line of research [1][2][3][4][5][6]. 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.…”

“…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.…”

Effect of the Minimal Length on Bose—Einstein Condensation in the Relativistic Ideal Bose Gas

“…It is also possible to test quantum gravity effects using cold or slow atoms, where particles exist in the non-relativistic regime [18][19][20][21]. In [20][21][22][23][24], quantum gravity effects of non-traped and harmonically trapped Bose-Einstein condensates are examined respectively using the deformed non-relativistic free-particle energy-momentum dispersion relation. Quantum gravity effects cause an explicit shift in the condensation temperature, and then ultraprecise measurements of the condensation temperature make it possible to upper-bound the deformation parameter.…”