Correlation measurement of few-phonon interference

The interferometer is a vital technology in achieving coherent control and measurement in quantum systems. In this study, we present a few -phonon interferometer based on an optomechanical crystal cavity, which is cooled down with several phonons even less. Through the phonon counting, the competition between the thermal and coherent phonons is demonstrated by the interference. The interference visibility is monotonically increased with increasing the coherent phonons. However, the interference on second -order correlation g(2)(0) occurs in reverse because of the different statistical properties of thermal and coherent phonons, which also leads to an unnatural interference visibility with great coherent phonons. The investigation of this correlation interference technology will advance the development of cavity optomechanics systems in the quantum precision sensing and quantum information processing fields.