Abstract
We investigate quantum gravity corrections due to the generalized uncertainty principle on three-dimensional weakly interacting Bose gases at both zero and finite temperatures using the time-dependent Hatree–Fock–Bogoliubov theory. We derive useful formulas for the depletion, the anomalous density, and some thermodynamic quantities such as the chemical potential, the ground-state energy, the free energy, and the superfluid density. It is found that the presence of a minimal length leads to modify the fluctuations of the condensate and its thermodynamic properties in the weak and strong quantum gravitational regimes. Unexpectedly, the interplay of quantum gravity effects and quantum fluctuations stemming from interactions may lift both the condensate and the superfluid fractions. We show that quantum gravity minimizes the interaction force between bosons leading to the formation of ultradilute Bose condensates. Our results which can be readily probed in current experiments may offer a new attractive possibility to understand gravity in the framework of quantum mechanics.
Similar content being viewed by others
Data Availability Statement
The data generated and/or analyzed during the current study are not publicly available for legal/ethical reasons but are available from the corresponding author on reasonable request.
References
R. Penrose, On the gravitization of quantum mechanics 1: quantum state reduction. Found. Phys. 44, 557 (2014)
D. Kafri, J.M. Taylor, G.J. Milburn, A classical channel model for gravitational decoherence. New J. Phys. 16, 065020 (2014)
S. Bose, A. Mazumdar, G.W. Morley, H. Ulbricht, M. Torós, M. Paternostro, A. Geraci, P. Barker, M. Kim, G. Milburn, Phys. Rev. Lett. 119, 240401 (2017)
C. Marletto, V. Vedral, Phys. Rev. Lett. 119, 240402 (2017)
T. Krisnanda, M. Zuppardo, M. Paternostro, T. Paterek, Phys. Rev. Lett. 119, 120402 (2017)
C. Marletto, V. Vedral, Phys. Rev. D 98, 046001 (2018)
R. Howl, V. Vedral, D. Naik, M. Christodoulou, C. Rovelli, A. Iyer, Phys. Rev. X Quantum 2, 010325 (2021)
K. Shiraishi, Prog. Theor. Phys. 77, 975 (1987)
S. Das, E.C. Vagenas, Phys. Rev. Lett. 101, 221301 (2008)
F. Briscese, M. Grether, M. de Llano, Europhys. Lett. 98, 6 (2012)
F. Briscese, Phys. Lett. B 718, 214 (2012)
J. Hansson, S. Francois, Int. J. Mod. Phys. D 26, 1743003 (2017)
M. Jaffe, P. Haslinger, V. Xu, P. Hamilton, A. Upadhye, B. Elder, J. Khoury, H. Müller, Nat. Phys. 13, 938 (2017)
S.A. Haine, New J. Phys. 23, 033020 (2021)
M. Maggiore, Phys. Lett. B 304, 65 (1993)
M. Maggiore, Phys. Lett. B 319, 83 (1993)
M. Maggiore, Phys. Rev. D 49, 5182 (1994)
A. Kempf, G. Mangano, R.B. Mann, Phys. Rev. D 52, 1108 (1995)
F. Scardigli, Phys. Lett. B 452, 39 (1999)
L.N. Chang, D. Minic, N. Okamura, T. Takeuchi, Phys. Rev. D 65, 125028 (2002)
A.F. Ali, S. Das, E.C. Vagenas, Phys. Rev. D 84, 044013 (2011)
M. Sprenger, P. Nicolini, M. Bleicher, Class. Quantum Grav. 28, 235019 (2011)
I. Pikovski, M.R. Vanner, M. Aspelmeyer, M. Kim, C. Brukner, Nat. Phys. 8, 393 (2012)
V. Husain, S. Seahra, S. Webster, Phys. Rev. D 88, 024014 (2013)
P. Pedram, Phys. Rev. D 91, 063517 (2015)
Z. Feng, H.L. Li, X.T. Zu, S.Z. Yang, Eur. Phys. J. C 76, 1 (2016)
H. Shababi, W.S. Chung, Phys. Lett. B 770, 445 (2017)
G. Gecim, Y. Sucu, Phys. Lett. B 773, 391 (2017)
F. Scardigli, G. Lambiase, E.C. Vagenas, Phys. Lett. B 767, 242 (2017)
M.C. Braidotti, Z.H. Musslimani, C. Conti, Phys. D 338, 34 (2017)
P. Bosso, S. Das, I. Pikovski, M.R. Vanner, Phys. Rev. A 96, 023849 (2017)
R. Casadio, F. cardigli, Phys. Lett. B 807, 135558 (2020)
T. Fityo, Phys. Lett. A 372, 5872 (2008)
B. Vakili, M.A. Gorji, J. Stat. Mech. P10013 (2012)
E. Castellanos, C. Laemmerzahl, Phys. Lett. B 731, 1 (2014)
X. Zhang, C. Tian, Chin. Phys. Lett. 32, 010303 (2015)
H.L. Li, J.X. Ren, W.W. Wang, B. Yang, H.J. Shen, J. Stat. Mech. 2018, 023106 (2018)
S. Dey, V. Hussin, Int. J. Theor. Phys. 58, 3138 (2019)
S. Das, M. Fridman, Phys. Rev. D 104, 026014 (2021)
M. Novello, M. Visser, G. Volovik (eds.), Artificial Black Holes (World Scientific, 2002)
A. Boudjemâa, Degenerate Bose Gas at Finite Temperatures (Lambert Academic Publishing, Saarbrücken, 2017)
A. Boudjemâa, M. Benarous, Eur. Phys. J. D 59, 427 (2010)
A. Boudjemâa, M. Benarous, Phys. Rev. A 84, 043633 (2011)
A. Boudjemâa, Phys. Rev. A 86, 043608 (2012)
A. Boudjemâa, Phys. Rev. A 88, 023619 (2013)
A. Boudjemâa, Phys. Rev. A 90, 013628 (2014)
A. Boudjemâa, Phys. Rev. A 91, 063633 (2015)
A. Boudjemâa, Commun. Nonlinear Sci. Numer. Simul. 33, 85 (2016)
A. Boudjemâa, Commun. Nonlinear Sci. Numer. Simul. 48, 376 (2017)
A. Boudjemâa, Phys. Rev. A 94, 053629 (2016)
A. Boudjemâa, N. Guebli, J. Phys. A: Math. Theor. 50, 425004 (2017)
A. Boudjemâa, Phys. Rev. A 98, 033612 (2018)
A. Boudjemâa, Phys. Rev. A 97, 033627 (2018)
A. Boudjemâa, N. Guebli, Phys. Rev. A 102, 023302 (2020)
N. Guebli, A. Boudjemâa, Phys. Rev. A 104, 023310 (2021)
A. Boudjemâa, Sci. Rep. 11, 21765 (2021)
S.T. Beliaev, Sov. Phys. JETP 7, 289 (1958)
A. Griffin, H. Shi, Phys. Rep. 304, 1 (1998)
C.J. Pethick, H. Smith, Bose–Einstein Condensation in Dilute Gases, 2nd edn. (Cambridge University Press, 2008)
A. Boudjemâa, J. Phys. B: At. Mol. Opt. Phys. 48, 035302 (2015)
J.O. Andersen, Theory of the weakly interacting Bose gas. Rev. Mod. Phys. 76, 599 (2004)
V. Yukalov, Phys. Part. Nucl. 42, 460 (2011)
A. Boudjemâa, J. Phys. A: Math. Theor. 49, 285005 (2016)
R. Balian, M. Vénéroni, Ann. Phys. (NY) 187, 29 (1988)
R. Balian, M. Vénéroni, Ann. Phys. (NY) 195, 324 (1989)
R. Balian, M. Vénéroni, Ann. Phys. (NY) 362, 838 (2015)
C. Martin, Phys. Rev. D 52, 7121 (1995)
M. Benarous, H. Flocard, Ann. Phys. 273, 242 (1999)
F. Scardigli, R. Casadio, Eur. Phys. J. C 75, 425 (2015)
D. Gao, M. Zhan, Phys. Rev. A 94, 013607 (2016)
Z.W. Feng, S.Z. Yang b, H.L. Li, X.T. Zu, Phys. Lett. B 768, 81 (2017)
J.C.S. Neves, Eur. Phys. J. C 80, 343 (2020)
A. Das, S. Das, N.R. Mansour, E.C. Vagenas, Phys. Lett. B 819, 136429 (2021)
N.N. Bogolubov, J. Phys. (Moscow) 11, 23 (1947)
A.D. Lange, K. Pilch, A. Prantner, F. Ferlaino, B. Engeser, H.-C. Nägerl, R. Grimm, C. Chin, Phys. Rev. A 79, 013622 (2009)
P.O. Fedichev, G.V. Shlyapnikov, Phys. Rev. A 58, 3146 (1998)
T.D. Lee, K. Huang, C.N. Yang, Phys. Rev. 106, 1135 (1957)
I.M. Khalatnikov, An Introduction to the Theory of Superfluidity (Benjamin, New York, 1965)
E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Part 2 (Pergamon Press, Oxford, 1980)
R. Lopes, C. Eigen, N. Navon, D. Clément, R.P. Smith, Z. Hadzibabic, Phys. Rev. Lett. 119, 190404 (2017)
C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)
L. Menculini, O. Panella, P. Roy, Phys. Rev. D 87, 065017 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boudjemâa, A. Weakly interacting Bose gases with generalized uncertainty principle: Effects of quantum gravity. Eur. Phys. J. Plus 137, 256 (2022). https://doi.org/10.1140/epjp/s13360-022-02475-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-022-02475-3