Tests of quantum gravity-induced non-locality: Hamiltonian formulation of a non-local harmonic oscillator

Year: 2019

Authors: Belenchia A., Benincasa D., Marin F., Marino F., Ortolan A., Paternostro M., Liberati S.

Autors Affiliation: Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queens University, Belfast BT7 1NN, United Kingdom; School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland; Dipartimento di Fisica e Astronomia, University of Florence, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy; CNR-Istituto Nazionale di Ottica, Largo E. Fermi 6,I-50125 Firenze, Italy.
INFN, Sez. di Firenze., Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy; European Laboratory for Non-Linear Spectroscopy (LENS), Via Carrara 1, I-50019 Sesto Fiorentino (FI), Italy; INFN, Laboratori Nazionali di Legnaro, Viale dell’Università, 2, 35020 Legnaro, Padova, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, Italy; INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy; IFPU-Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy.

Abstract: Motivated by the development of on-going optomechanical experiments aimed at constraining non-local effects inspired by some quantum gravity scenarios, the Hamiltonian formulation of a non-local harmonic oscillator, and its coupling to a cavity field mode(s), is investigated. In particular, we consider the previously studied model of non-local oscillators obtained as the nonrelativistic limit of a class of non-local Klein–Gordon operators, f (\Box), with f an analytical function. The results of previous works, in which the interaction was not included, are recovered and extended by way of standard perturbation theory. At the same time, the perturbed energy spectrum becomes available in this formulation, and we obtain the Langevin’s equations characterizing the interacting system.

Journal/Review: CLASSICAL AND QUANTUM GRAVITY

Volume: 36 (15)      Pages from: 155006-1  to: 155006-20

More Information: AB thanks Marco Letizia for useful discussions. AB is supported by H2020 through the MSCA IF pERFEcTO (Grant No. 795782). MP acknowledges support from the DfE-SFI Investigator Programme (Grant No. 15/IA/2864), the H2020 Collaborative Project TEQ (Grant Agreement No. 766900), and the Leverhulme Trust Research Project Grant.
KeyWords: quantum gravity; quantum optomechanics; phenomenology; non-local field theory
DOI: 10.1088/1361-6382/ab2c0a

ImpactFactor: 3.071
Citations: 9
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