How to read out the phonon number statistics via resonance fluorescence spectroscopy of a single-photon emitter

TL;DR

This paper proposes a method to determine phonon number statistics using resonance fluorescence spectra of a single-photon emitter, enabling quantum state readout in hybrid phononic systems.

Contribution

It introduces an analytical framework for extracting phonon statistics from optical spectra and discusses strategies to improve readout accuracy in noisy conditions.

Findings

Analytical description of optical spectra in low excitation limit.

Identification of conditions causing faulty phonon readout.

Proposed solutions to enhance measurement fidelity.

Abstract

In today's development of quantum technologies a hybrid integration of phononic excitations becomes increasingly attractive. As natural quasi-particle excitations in solid state systems, phonons couple to virtually any other excitation and therefore constitute a useful interaction channel between different building blocks in hybrid quantum systems. This work explores how the efficient light-scattering properties of a single-photon emitter and the appearance of characteristic sidebands in resonance fluorescence spectra, when interfaced with an arbitrary phonon quantum state, can be utilized for acousto-optical transduction. Within reasonable approximations, an analytical description for the optical spectra in the low excitation limit is developed which can be used to read the number statistics of the initial phonon state from a given spectrum. It is shown that the readout is faulty in situations where relevant resonant transitions are forbidden due to vanishing Franck-Condon factors, especially when considering spectra with a noisy background. Two possible solutions to this problem are presented: (A) changing the detuning of the laser relative to the single-photon emitter which modifies the relevant resonant transitions, or (B) increasing dissipation of the single-photon emitter to promote off-resonant transitions.