Measurement of Non-classical Photon-Phonon States in a Superfluid Optomechanical System*

Non-classical states with a negative Glauber-Sudarshan P-function can offer metrological advantages and can outperform sensitivity bounds associated with coherent states [1]. They also play an important role in quantum communication, quantum sensing, and fundamental tests of quantum mechanics. Here, we demonstrate the creation and observation of non-classical photon-phonon states using an optomechanical device that consists of a fiber cavity filled with superfluid helium [2]. We use photon-counting techniques to demonstrate the violation of a classical bound on photon-phonon correlations that is set by the Cauchy-Schwarz inequality, thereby revealing the state's P-function negativity [3,4]. We find that the non-classical correlations decay with a time constant of ~50us, which is set by the phonon mode lifetime. With an effective mass ~6 ng, this system is one of the most massive objects to demonstrate P-function negativity.

[1] A. Shukur et. al., Nat. Comm. 11, 3775 (2020)
[2] A. D. Kashkanova et. al., Nat. Phys. 13, 74 (2017)
[3] A. Kuzmich et. al., Nature 423, 731 (2003)
[4] R. Riedinger et. al., Nature 530, 313 (2016)