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Journal of Physics Conference Series

Searching for Planck scale effects from the free expansion of a Bose–Einstein Condensate

Elías Castellanos, Peter Sloane

Published May 1, 2018• 0 citations
Publisher

Abstract

The free expansion of a Bose–Einstein condensate is analyzed, assuming that the single particle energy spectrum is modified due to some quantum structure of space time. The condensate’s free velocity expansion leads in a natural way to a deformed uncertainty principle. We show that large expansion times are required in order to amplify some possible traces of the Planck scale regime. The analysis presented in this work opens up the opportunity to use Bose–Einstein condensates as tools in quantum gravity phenomenology with a solid experimental basis.

DOI
10.1088/1742-6596/1030/1/012003

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The free expansion of a Bose–Einstein condensate is analyzed, assuming that the single particle energy spectrum is modified due to some quantum structure of space time. The condensate’s free velocity expansion leads in a natural way to a deformed uncertainty principle. We show that large expansion times are required in order to amplify some possible traces of the Planck scale regime. The analysis presented in this work opens up the opportunity to use Bose–Einstein condensates as tools in quantum gravity phenomenology with a solid experimental basis.
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We analyze the possible effects arising from the Planck scale regime upon the interference pattern of two noninteracting Bose-Einstein condensates. We start with the analysis of the free expansion of a condensate, and have taken into account the effects produced by a deformed dispersion relation, suggested in several quantum-gravity models. The analysis of the condensate free expansion, in particular, the modified free velocity expansion, suggests in a natural way, a modified uncertainty principle that could lead to new phenomenological implications related to the quantum structure of space-time. Finally, we analyze the corresponding separation between the interference fringes after the two condensates overlap, in order to explore the sensitivity of the system to possible signals caused by the Planck scale regime.
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 TcT_{c}Tc​ of the BEC and, for a specific functional form of deformation, this shift can be as large as the current measured precision on TcT_{c}Tc​. For a 3785Rb_{37}^{85}Rb3785​Rb cold-atom BEC with a particle density n≃1012cm−3n\simeq 10^{12}cm^{-3}n≃1012cm−3 we find a fractional shift of order 10−410^{-4}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 TcT_{c}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.
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.
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 . We show that the corresponding ground-state energy and consequently, the associated speed of sound, present corrections with 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 many-body contributions, improves the sensitivity to Planck-scale signals, compared to the homogeneous system.