Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2501.19044 · Physics Letters B

Testing quantum gravity with dilute dipolar Bose gases

Asma Tahar Taiba, Abdelâali Boudjemâa

Published Jan 28, 2025• 3 citations
arXivHTMLPDF

Abstract

We systematically investigate the effects of quantum gravity on the ground-state properties of dilute homogeneous dipolar Bose gases using the Hartree-Fock-Bogoliubov theory based on the generalized uncertainty principle. We calculate quantum gravity corrections to the condensed fraction, the equation of state , the critical temperature and the superfluid fraction. Improved upper bounds on the generalized uncertainty principle parameters are found. We compare our predictions with previous experimental and theoretical results.

DOI
10.1016/j.physletb.2025.139291

Related papers

Quantum gravity phenomenology in quadrupolar Bose-Einstein condensates: Finite-temperature thermodynamics and projected bounds

Asma Tahar Taiba, Abdelâali Boudjemâa

We study the thermodynamics of quadrupolar Bose-Einstein condensates in the realm of the generalized uncertainty principle (GUP) for the quest of understanding and testing quantum gravity (QG). Using both quadratic GUP (QGUP) and linear-quadratic GUP (LQGUP) which incorporate modified density of states, we calculate corrections to the condensed fraction, critical temperature, equation of state and other thermodynamic quantities. We find that the intriguing interplay of quadrupole-quadrupole interactions (QQIs) and the GUP may strongly modify the finite-temperature properties of the condensate, with the LQGUP generally predicting larger corrections than the QGUP, although their relative magnitudes depend on the chosen parameters and the validity of the perturbative expansion. We further estimate the sensitivity of the critical temperature to GUP-induced effects by imposing an assumed fractional temperature resolution which provides projected upper bounds on the GUP deformation parameters. Our findings demonstrate that quadrupole-quadrupole interacting Bose gases provide a promising platform for testing GUP-induced deviations from standard quantum mechanics and for probing QG phenomenology through measurements of finite-temperature many-body observables. They also motivate future studies using realistic system-specific parameters.

arXiv:2610.37930•Oct 27, 2026•0 citations

Quantum nature of gravity in self-bound quantum droplets

Asma Tahar Taiba, Abdelâali Boudjemâa

We explore the possibility of testing the quantum nature of the gravitational field with an ultracold self-bound quantum droplet of one-dimensional Bose-Bose mixtures. To this end, we solve variationally and numerically the underlying generalized Gross-Pitaevskii equation which includes the effects of quadratic and cubic nonlinearities. We derive the associated generalized uncertainty principle and its corresponding minimal length. The obtained modified uncertainty relation enables us to search for the quantum gravity signatures in both small and large droplets. We place bounds on the parameter using existing experimental data from recent experiment of dilute droplets of potassium. Improved upper bounds on the generalized uncertainty principle parameters are found from our analysis.

arXiv:2508.12838•Aug 18, 2025•0 citations

Equilibrium and Non-Equilibrium Properties of Dilute Bose Gases

Oldenburg, Jakob Felix

Quantum systems consisting of many particles are both interesting from the physics and the mathematics perspective. One aspect that makes them fascinating from the physics point of view is that they can exhibit quantum effects on macroscopic scales such as Bose-Einstein condensation. This phenomenon, first predicted 100 years ago by Bose [19] and Einstein [44], occurs when a dilute gas of bosons is cooled down to very low temperatures. Below a certain critical temperature a condensate forms, meaning that a macroscopic fraction of the particles is in the same one-particle state, and thus, quantum phenomena become relevant on length scales much larger than the individual atom. The occurrence of Bose-Einstein condensation is also related to superfluidity as suggested in [88]. Bose-Einstein condensation has been achieved experimentally independently by the groups of Cornell and Wieman [3] and Ketterle [40] earning them a Nobel prize in 2001. While Bose and Einstein analyzed theoretically the non-interacting gas, an effective theory describing weakly interacting Bose gases was proposed by Bogoliubov in 1947 with the goal of explaining the occurrence of superfluidity in liquid helium [18]. Using assumptions such as that condensation indeed occurs, his theory yields predictions for the low-energy states of the system. Seen from the mathematics perspective, describing the Bose gas is an interesting challenge due to the strong correlations between particles introduced by the interaction making this case much harder to study than the non-interacting one. In particular, a proof that Bose-Einstein condensation occurs in the thermodynamic limit for continuous systems is still out of reach. However, there has been a lot of work regarding the rigorous analysis of bosonic systems in various relevant regimes. This thesis contains three new contributions establishing rigorous results on bosonic systems in different, physically relevant settings. It is based on the articles [37, 27, 31]. The first result concerns the time-evolution of initially trapped Bose gases in the ultra-dilute Gross-Pitaevskii regime. Under some assumptions on the initial data satisfied in particular by a class of states that are expected to approximate the ground state in a trap, we derive a quasi-free approximation that is close to the true solution in $L^2$-norm. In particular, we show that this approximate wave function is described in terms of a Bose-Einstein condensate in a one-particle state following the time-dependent Gross-Pitaevskii equation together with pair excitations with respect to this condensate. As a corollary, we establish a central limit theorem for bounded one-particle observables. The second result is a simple proof of Bose-Einstein condensation for interacting, ultra-dilute gases. More specifically, we consider scalings interpolating between the Gross-Pitaevskii regime and the thermodynamic limit. While condensation had been shown to hold in these regimes before, the advantage of the method used here is its simplicity. Lastly, the third result establishes an upper bound on the ground state energy of a dilute Bose gas in the thermodynamic limit. It captures rigorously the third order correction to the energy per unit volume for sufficiently low densities as predicted in the physics literature first by Wu and subsequently others. $\textit{Full-text embargoed until: 2026-01-01}$

•Dec 9, 2025•0 citations

Theory of the weakly interacting Bose gas

Jens O. Andersen

This article reviews recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective-field-theory methods are used to formulate a systematic perturbative framework that can be used to calculate the properties of a system at $T=0.$ The perturbative expansion of these properties is essentially an expansion in the gas parameter $\sqrt{{\mathrm{na}}^{3}},$ where $a$ is the $s$-wave scattering length and $n$ is the number density. In particular, the leading quantum corrections to the ground-state energy density, the condensate depletion, and long-wavelength collective excitations are rederived in an efficient and economical manner. Nonuniversal effects are also discussed. These effects are higher-order corrections that depend on properties of the interatomic potential other than the scattering length, such as the effective range. The article critically examines various approaches to the dilute Bose gas in equilibrium at finite temperature. These include the Bogoliubov approximation, the Popov approximation, the Hartree-Fock-Bogoliubov approximation, the \ensuremath{\Phi}-derivable approach, optimized perturbation theory, and renormalization-group techniques. The article ends with a look at recent calculations of the critical temperature of the dilute Bose gas, which include $1/N$ techniques, lattice simulations, self-consistent calculations, and variational perturbation theory.

arXiv:cond-mat/0305138•Reviews of Modern Physics•Jul 1, 2004•506 citations

Theory of excitations of dipolar Bose–Einstein condensate at finite temperature

Abdelâali Boudjemâa

We present a systematic study of dilute three-dimensional dipolar Bose gas employing a finite temperature perturbation theory (beyond the mean field). We analyze in particular the behavior of the anomalous density, we find that this quantity has a finite value in the limit of weak interactions at both zero and finite temperatures. We show that the presence of the dipole–dipole interaction enhances fluctuations, the second order correlation function and thermodynamic quantities such as the chemical potential, the ground state energy, the compressibility and the superfluid fraction. We identify the validity criterion of the small parameter of the theory for Bose-condensed dipolar gases.

arXiv:1310.6722•Journal of Physics B Atomic Molecular and Optical Physics•Jan 13, 2015•35 citations

Quantum fluctuations in dipolar Bose gases

Aristeu R. P. Lima, Axel Pelster

We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov--de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the condensate and the excited particles. This allows to obtain the Bogoliubov spectrum analytically in the limit of large particle numbers. After discussing the condensate depletion and the ground-state energy correction, we derive quantum-corrected equations of motion for harmonically trapped dipolar Bose gases by using superfluid hydrodynamics. These equations are subsequently applied to analyze the equilibrium configuration, the low-lying oscillation frequencies, and the time-of-flight dynamics. We find that both atomic magnetic and molecular electric dipolar systems offer promising scenarios for detecting beyond mean-field effects.

arXiv:1103.4128•Physical Review A•Oct 14, 2011•260 citations
We systematically investigate the effects of quantum gravity on the ground-state properties of dilute homogeneous dipolar Bose gases using the Hartree-Fock-Bogoliubov theory based on the generalized uncertainty principle. We calculate quantum gravity corrections to the condensed fraction, the equation of state , the critical temperature and the superfluid fraction. Improved upper bounds on the generalized uncertainty principle parameters are found. We compare our predictions with previous experimental and theoretical results.
We study the thermodynamics of quadrupolar Bose-Einstein condensates in the realm of the generalized uncertainty principle (GUP) for the quest of understanding and testing quantum gravity (QG). Using both quadratic GUP (QGUP) and linear-quadratic GUP (LQGUP) which incorporate modified density of states, we calculate corrections to the condensed fraction, critical temperature, equation of state and other thermodynamic quantities. We find that the intriguing interplay of quadrupole-quadrupole interactions (QQIs) and the GUP may strongly modify the finite-temperature properties of the condensate, with the LQGUP generally predicting larger corrections than the QGUP, although their relative magnitudes depend on the chosen parameters and the validity of the perturbative expansion. We further estimate the sensitivity of the critical temperature to GUP-induced effects by imposing an assumed fractional temperature resolution which provides projected upper bounds on the GUP deformation parameters. Our findings demonstrate that quadrupole-quadrupole interacting Bose gases provide a promising platform for testing GUP-induced deviations from standard quantum mechanics and for probing QG phenomenology through measurements of finite-temperature many-body observables. They also motivate future studies using realistic system-specific parameters.
We explore the possibility of testing the quantum nature of the gravitational field with an ultracold self-bound quantum droplet of one-dimensional Bose-Bose mixtures. To this end, we solve variationally and numerically the underlying generalized Gross-Pitaevskii equation which includes the effects of quadratic and cubic nonlinearities. We derive the associated generalized uncertainty principle and its corresponding minimal length. The obtained modified uncertainty relation enables us to search for the quantum gravity signatures in both small and large droplets. We place bounds on the parameter using existing experimental data from recent experiment of dilute droplets of potassium. Improved upper bounds on the generalized uncertainty principle parameters are found from our analysis.
Quantum systems consisting of many particles are both interesting from the physics and the mathematics perspective. One aspect that makes them fascinating from the physics point of view is that they can exhibit quantum effects on macroscopic scales such as Bose-Einstein condensation. This phenomenon, first predicted 100 years ago by Bose [19] and Einstein [44], occurs when a dilute gas of bosons is cooled down to very low temperatures. Below a certain critical temperature a condensate forms, meaning that a macroscopic fraction of the particles is in the same one-particle state, and thus, quantum phenomena become relevant on length scales much larger than the individual atom. The occurrence of Bose-Einstein condensation is also related to superfluidity as suggested in [88]. Bose-Einstein condensation has been achieved experimentally independently by the groups of Cornell and Wieman [3] and Ketterle [40] earning them a Nobel prize in 2001. While Bose and Einstein analyzed theoretically the non-interacting gas, an effective theory describing weakly interacting Bose gases was proposed by Bogoliubov in 1947 with the goal of explaining the occurrence of superfluidity in liquid helium [18]. Using assumptions such as that condensation indeed occurs, his theory yields predictions for the low-energy states of the system. Seen from the mathematics perspective, describing the Bose gas is an interesting challenge due to the strong correlations between particles introduced by the interaction making this case much harder to study than the non-interacting one. In particular, a proof that Bose-Einstein condensation occurs in the thermodynamic limit for continuous systems is still out of reach. However, there has been a lot of work regarding the rigorous analysis of bosonic systems in various relevant regimes. This thesis contains three new contributions establishing rigorous results on bosonic systems in different, physically relevant settings. It is based on the articles [37, 27, 31]. The first result concerns the time-evolution of initially trapped Bose gases in the ultra-dilute Gross-Pitaevskii regime. Under some assumptions on the initial data satisfied in particular by a class of states that are expected to approximate the ground state in a trap, we derive a quasi-free approximation that is close to the true solution in L2L^2L2-norm. In particular, we show that this approximate wave function is described in terms of a Bose-Einstein condensate in a one-particle state following the time-dependent Gross-Pitaevskii equation together with pair excitations with respect to this condensate. As a corollary, we establish a central limit theorem for bounded one-particle observables. The second result is a simple proof of Bose-Einstein condensation for interacting, ultra-dilute gases. More specifically, we consider scalings interpolating between the Gross-Pitaevskii regime and the thermodynamic limit. While condensation had been shown to hold in these regimes before, the advantage of the method used here is its simplicity. Lastly, the third result establishes an upper bound on the ground state energy of a dilute Bose gas in the thermodynamic limit. It captures rigorously the third order correction to the energy per unit volume for sufficiently low densities as predicted in the physics literature first by Wu and subsequently others. Full-text embargoed until: 2026-01-01\textit{Full-text embargoed until: 2026-01-01}Full-text embargoed until: 2026-01-01
This article reviews recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective-field-theory methods are used to formulate a systematic perturbative framework that can be used to calculate the properties of a system at T=0.T=0.T=0. The perturbative expansion of these properties is essentially an expansion in the gas parameter na3,\sqrt{{\mathrm{na}}^{3}},na3​, where aaa is the sss-wave scattering length and nnn is the number density. In particular, the leading quantum corrections to the ground-state energy density, the condensate depletion, and long-wavelength collective excitations are rederived in an efficient and economical manner. Nonuniversal effects are also discussed. These effects are higher-order corrections that depend on properties of the interatomic potential other than the scattering length, such as the effective range. The article critically examines various approaches to the dilute Bose gas in equilibrium at finite temperature. These include the Bogoliubov approximation, the Popov approximation, the Hartree-Fock-Bogoliubov approximation, the \ensuremath{\Phi}-derivable approach, optimized perturbation theory, and renormalization-group techniques. The article ends with a look at recent calculations of the critical temperature of the dilute Bose gas, which include 1/N1/N1/N techniques, lattice simulations, self-consistent calculations, and variational perturbation theory.
We present a systematic study of dilute three-dimensional dipolar Bose gas employing a finite temperature perturbation theory (beyond the mean field). We analyze in particular the behavior of the anomalous density, we find that this quantity has a finite value in the limit of weak interactions at both zero and finite temperatures. We show that the presence of the dipole–dipole interaction enhances fluctuations, the second order correlation function and thermodynamic quantities such as the chemical potential, the ground state energy, the compressibility and the superfluid fraction. We identify the validity criterion of the small parameter of the theory for Bose-condensed dipolar gases.
We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov--de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the condensate and the excited particles. This allows to obtain the Bogoliubov spectrum analytically in the limit of large particle numbers. After discussing the condensate depletion and the ground-state energy correction, we derive quantum-corrected equations of motion for harmonically trapped dipolar Bose gases by using superfluid hydrodynamics. These equations are subsequently applied to analyze the equilibrium configuration, the low-lying oscillation frequencies, and the time-of-flight dynamics. We find that both atomic magnetic and molecular electric dipolar systems offer promising scenarios for detecting beyond mean-field effects.