Quantum non-Gaussianity of multi-phonon states of a single atom

TL;DR

This paper develops criteria for identifying quantum non-Gaussian states in single-atom phonon states and demonstrates their application to states with up to 10 phonons, highlighting their importance for quantum technologies.

Contribution

The paper derives the most challenging hierarchy of quantum non-Gaussian criteria for mechanical Fock states and applies it to characterize single trapped-ion oscillator states.

Findings

Quantum non-Gaussian features are crucial for quantum advantage.

Criteria successfully characterize states up to 10 phonons.

Mechanical heating affects the depth of quantum non-Gaussian features.

Abstract

Quantum non-Gaussian mechanical states from inherently nonlinear quantum processes are already required in a range of applications spanning from quantum sensing up to quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates - Fock states. Despite the progress in their preparation, the remaining imperfections can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant in the applications. We derive the most challenging hierarchy of quantum non-Gaussian criteria for the individual mechanical Fock states and demonstrate its implementation on the characterization of single trapped-ion oscillator states up to 10~phonons. We analyze the depth of quantum non-Gaussian features under mechanical heating and predict their application in quantum sensing. These results uncover that the crucial quantum non-Gaussian features are demanded to reach quantum advantage in the applications.