Genuine quantum non-Gaussianity and metrological sensitivity of Fock states prepared in a mechanical resonator

TL;DR

This paper demonstrates the preparation of high Fock states in a mechanical resonator, verifies their genuine quantum non-Gaussianity, and shows their enhanced sensitivity in quantum sensing applications despite decoherence.

Contribution

It introduces a method to generate and verify high Fock states in a mechanical resonator and assesses their metrological advantages over lower Fock states.

Findings

Prepared Fock states up to |6⟩ in a mechanical resonator.

Confirmed genuine quantum non-Gaussianity of the states.

Achieved displacement sensitivity surpassing that of |3⟩ Fock state.

Abstract

Fock states of the quantum harmonic oscillator are fundamental to quantum sensing and information processing, serving as key resources for exploiting bosonic degrees of freedom. Here, we prepare high Fock states in a high-overtone bulk acoustic wave resonator (HBAR) by coupling it to a superconducting qubit and applying microwave pulses designed using quantum optimal control. We characterize the experimentally realized states by employing a criterion for genuine quantum non-Gaussianity (QNG) designed to reveal multiphonon contributions. Although energy relaxation and decoherence limit the achievable fidelities, we demonstrate genuine QNG features compatible with Fock state $\vert 6\rangle$, confirming that the prepared states cannot be generated through Gaussian operations on states with up to Fock state $\vert 5\rangle$ contributions. We further investigate the robustness of these QNG features to losses and their utility in sensing displacement amplitudes. In particular, we introduce a hierarchy based on the quantum Fisher information and show that, despite decoherence and measurement imperfections, the prepared states achieve a displacement sensitivity surpassing that of an ideal Fock state $\vert 3\rangle$. Our results have immediate applications in quantum sensing and simulations with HBAR devices.