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arXiv:1308.5156 · Europhysics Letters (EPL)

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

E. Castellanos, J. I. Rivas, V. Dominguez-Rocha

Published Jun 1, 2014• 6 citations
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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 . 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.

DOI
10.1209/0295-5075/106/60005

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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.
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.
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 effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. Additionally, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.
In the present work we determine the speed of sound in a Bose-Einstein condensate confined by an isotropic harmonic oscillator trap. The deduction of this physical parameter is done resorting to the NNN-body Hamiltonian operator. The single-particle eigenfunctions that have been employed in this formalism are those stemming from the corresponding harmonic oscillator potential, and an expression for the dependence of this speed on the temperature is also deduced. These functions are used in the calculation of the scaterring length, etc. The situation for a Bose-Einstein condensate of sodium is evaluated and the corresponding speed of sound is obtained and compared against the known experimental outcomes. The possibility that the solution, to the existing discrepancy between experiment and theoretical predictions, could be given by the Zaremba-Nikuni-Griffin formalism is also explored.
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.
We consider the superfluid weight, speed of sound and excitation fraction of a flat band Bose–Einstein condensate (BEC) within multiband Bogoliubov theory. The superfluid weight is calculated by introducing a phase winding and minimizing the free energy with respect to it. We find that the superfluid weight has a contribution arising from the change in the condensate density and chemical potential upon the phase twist that has been neglected in the previous literature. We also point out that the speed of sound and the excitation fraction are proportional to orbital-position-independent generalizations of the quantum metric and the quantum distance, and reduce to the usual quantum metric (Fubini–Study metric) and the Hilbert–Schmidt quantum distance only in special cases. We derive a second-order perturbation correction to the dependence of the speed of sound on the generalized quantum metric, and show that it compares well with numerical calculations. Our results provide a consistent connection between flat band BEC and quantum geometry, with physical observables being independent of the orbital positions for fixed hopping amplitudes, as they should, and complete formulas for the evaluation of the superfluid weight within the Bogoliubov theory. We discuss the limitations of the Bogoliubov theory in evaluating the superfluid weight.