Regular Article

Probing quantum gravity effects with quantum mechanical oscillators^★,

¹ Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division, I-38123 Povo, Trento, Italy
² Istituto Nazionale di Fisica Nucleare (INFN), Trento Institute for Fundamental Physics and Application, I-38123 Povo, Trento, Italy
³ CNR-INO, L.go E. Fermi 6, I-50125 Firenze, Italy
⁴ INFN, Sezione di Firenze, Via Sansone 1, I-50019 Sesto, Fiorentino (FI), Italy
⁵ School of Science and Technology, Physics Division, University of Camerino, Via Madonna delle Carceri, 9, I-62032 Camerino (MC), Italy
⁶ INFN, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
⁷ Laboratory of Electronic Components Technology and Materials (ECTM), Department of Microelectronics, Delft University of Technology, Feldmanweg 17, 2628 CT Delft, The Netherlands
⁸ Dipartimento di Fisica, Università di Trento, I-38123 Povo, Trento, Italy
⁹ European Laboratory for Non-Linear Spectroscopy (LENS), Via N. Carrara 1, I-50019 Sesto Fiorentino (FI), Italy
¹⁰ Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy

^a e-mail: francesco.marin@unifi.it

Received: 30 March 2020
Received in final form: 21 July 2020
Published online: 1 September 2020

Abstract

Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization.