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 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.
Abstract Significant evidence is available to support the quantum effects of gravity that lead to the generalized uncertainty principle (GUP) and the minimum observable length. Usually in quantum mechanics, statistical physics does not take gravity into account. Thermodynamic properties of ideal Bose gases in different external power-law potentials are studied under the GUP with a statistical physical method. Critical temperature, internal energy, heat capacity, entropy, particle number of ground state and excited state are calculated analytically to ideal Bose gases in the external potentials under the GUP. Below the critical temperature, taking the rubidium and sodium atoms, ideal Bose gases whose particle densities are under standard and experimental conditions, respectively, as examples, the relations of internal energy, heat capacity and entropy with temperature are analyzed numerically. Theoretical and numerical calculations show that: (1) the GUP leads to an increase in the critical temperature. (2) When the temperature is lower than the critical temperature and slightly higher than 0 K, the GUP’s amendments to internal energy, heat capacity and entropy etc are positive. As the temperature increases to a certain value, these amendments become negative. (3) The external potentials can increase or decrease the influence of the GUP on thermodynamic properties. When ε = 1 J, ε is the quantity that reflects the external potential intensity, and atomic density n = 2.687 × 10 25 m −3 , the GUP’s amendments to the internal energy, heat capacity and entropy of the rubidium atoms ideal Bose gas first decrease and then increase with the increase of X (where X ≡ Σ i 1/ t i is sum of the reciprocal of the exponents of the power function). In three-dimensional harmonic potential, the relative correction term of the GUP is 26 orders of magnitude larger than that of a free-particle system in a fixed container. (4) When ε ≈10 −31 J and n ≈ 10 20 m −3 (which are the experimental data when BEC was first verified by sodium atomic gas), the influence of the GUP can be completely ignored. (5) Under certain conditions, GUP may become the dominant factor governing the thermodynamic properties of the system.
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.
Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.
Several theories of quantum gravity propose the existence of a minimal measurable length and maximum measurable momentum near the Planck scale. When integrated into the framework of quantum mechanics, such restrictions lead to the generalization of the Heisenberg uncertainty principle, which is commonly referred to as the generalized uncertainty principle (GUP). The GUP has been applied to a plethora of physical models in order to provide further insights on our understanding of the Universe, both in the macroscopic and the microscopic regime. Nevertheless, the corrections related to GUP are expected to be extremely small, which thus renders experimental verification a difficult task. Therefore, phenomenological approaches on a qualitative level are typically addressed with the aim of enhancing our possibility of detecting these tiny effects. Motivated by a recent work on a universal decoherence mechanism stemming from the standard formulation of GUP, we extend the ideas contained therein by considering a more general form of GUP which includes linear and quadratic momentum terms to examine its implications. To achieve such a picture, we equip the deformation parameter appearing in front of all momentum terms with a stochastic nature, so that the effective decoherence mechanism emerges by taking the average over fluctuations. We find that, despite the apparently small differences among the two generalizations of the Heisenberg uncertainty principle, the consequences at the level of the universal decoherence mechanism they entail is significant, as they predict decoherence times that are completely uncorrelated and distinct.
The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Uncertainty Principle predicted by several theories of quantum gravity. In this work, we compute GUP corrections to the well-known Jaynes-Cummings Model (JCM) with the aim of eventually observing quantum gravity effects in quantum optical systems. To this end, we first analytically solve the GUP-corrected JCM and obtain the corrected Rabi frequency in the quadratic GUP model. Following this, we calculate the effects of a dispersive interaction with light in a coherent state and show that this gives rise to photon-added coherent states that were first studied by Agarwal and Tara in 1991. The latter causes a change in the value of the Wigner function, which if detected in the laboratory, would in effect be a signature of quantum gravity.
We examine quantum gravity effects on entanglement by a straightforward application of the generalized uncertainty principle (GUP) to continuous-variable systems. In particular, we study the following cases: the modified uncertainty relation of two identical entangled particles (Rigolin, 2002), and the inseparability conditions for entangled particles in the bipartite (Duan, Giedke, Cirac and Zoller, 2000) and tripartite (van Loock and Furusawa, 2003) cases. Rigolin showed a decrease in the lower bound of the product of the uncertainties of the position and momentum for two identical entangled particles while Duan and van Loock derived inseparability conditions for EPR-like operators. In all three cases, the GUP correction resulted in a higher value of the bounds: a higher lower bound for the Rigolin's result and a higher upper bound for the inseparability condition in Duan's and van Loock's relations. In Rigolin's case, the GUP correction decreased the disagreement with the Heisenberg uncertainty relation while in Duan's and Loock's cases,the inseparability and entanglement conditions are enhanced. Interestingly, the GUP corrections tend to make quantum mechanical effects more pronounced.