Fig. 4

Nonclassical correlations of photons emitted from the quantum memory. a, b Second-order cross-correlation function \(g_{{\mathrm{S,AS}}}^{(2)}\) measured for different positions of ROI in S and AS arms, for zero memory storage time. Nonclassical correlations are observed only between conjugate modes, confirming the highly-multimode character of our quantum memory. Data corresponds to S photon probability p _S = 2 × 10⁻⁴ per ROI. Standard deviation error maps are included as Supplementary Fig. 1. c \(g_{{\mathrm{S,AS}}}^{(2)}\) for Stokes and anti-Stokes photons measured at t = 0 storage time using different sizes of ROI in the analysis. Smaller ROIs correspond to lower p _S and consequently give higher values of \(g_{{\mathrm{S,AS}}}^{(2)}\). Our theoretical prediction for \(g_{{\mathrm{S,AS}}}^{(2)}\) calculated for the measured mode size closely adheres to experimental results (see Methods for details). Other curves correspond to the maximum value of \(g_{{\mathrm{S,AS}}}^{(2)}\) without noise in the AS arm and the maximum theoretical result for two-mode squeezed vacuum state (TMSV) with given probability p _S. Gray dashed lines mark the regime of operation used in the measurement shown in a, b. d Second-order correlation as a function of storage time, measured for two different angles of scattering corresponding to stored spin waves with different K _x . Data was taken with a higher than in (a–c) S photon detection probability of p _S = 1.9 × 10⁻³ and thus the value of the correlation function is smaller. Nonclassical correlations for spin waves with smaller wavenumber are confirmed for the storage time t up to 50 μs. Theoretical model of the time evolution of \(g_{{\mathrm{S,AS}}}^{(2)}\) (solid lines, see Methods for derivation) exhibits good agreement with experimental data, except for the initial drop that we attribute to an increase of noise fluorescence of thermal atoms. Errobars in c, d correspond to one standard deviation drawn from an ensemble of multiple conjugate region pairs