Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale

Luciano Petruzziello,Fabrizio Illuminati

doi:10.1038/s41467-021-24711-7

Luciano Petruzziello, Fabrizio Illuminati

Open Access

https://doi.org/10.1038/s41467-021-24711-7

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Abstract

Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared to other schemes of gravitational decoherence, we find that the decoherence rate predicted by our model is extremal, being minimal in the deep quantum regime below the Planck scale and maximal in the mesoscopic regime beyond it. We discuss possible experimental tests of our model based on cavity optomechanics setups with ultracold massive molecular oscillators and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.

Highlights

Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition
We have investigated the decoherence process associated with the existence of a minimal length at the Planck scale and the corresponding deformed quantum uncertainty relations
Assuming that the minimal spatial scale of length and the ensuing deformation parameter β are fixed only on average by space-time quantum fluctuations and are fluctuating random quantities, we have derived a master equation for the averaged quantum density matrix, showing that such quantum open dynamics can be cast in a Lindblad form, which guarantees complete positivity and trace preserving

Summary

Introduction

Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Recalling the above hypothesis on the stochastic nature of the deformation parameter β entering in the DCCRs and the associated GUP, in the following we obtain a master equation in Lindblad form for the quantum density matrix averaged over the fluctuations of β.

Results

Conclusion