Certify vacuum origin and entanglement of analog cosmological pair creation
In plain words
In an expanding universe, empty space should produce pairs of particles; ramping or expanding a condensate produces pairs of sound waves in the same way. Experiments see the pairs, but have not yet shown that they come from quantum vacuum fluctuations and are entangled rather than amplified heat.
Precise statement
In a 2D BEC or a quantum fluid of light with an effective scale factor $a(t)$ set by expansion or an interaction ramp, phonons at momenta $k$ and $-k$ acquire occupation $n_k$ and anomalous correlation $c_k = \langle b_k b_{-k}\rangle$. Determine whether $\mid c_k\mid > n_k$ (non-separability for the symmetric two-mode state) holds after accounting for the initial thermal occupation, and whether $n_k$ matches the vacuum Bogoliubov coefficient $\mid\beta_k\mid^2$ for the imposed $a(t)$. An answer is a measurement establishing or excluding the inequality with stated confidence and a measured initial temperature.
What would settle it
Quadrature-resolved or momentum-correlation measurements of phonon pairs violating the separability bound, with the initial thermal population measured independently.
Status in the literature
Unverified note
Pair production has been observed in atomic BECs (Viermann et al., Nature 2022, power-law expansion; Sparn et al., PRL 2024), and Steinhauer and coworkers (Nat. Commun. 2022) claimed spontaneous creation in a quantum fluid of light, but to the extent checked no experiment had certified entanglement or vacuum origin as of 2026.