Classical versus quantum intensity-field correlations of scattered light from extended cold atomic clouds

We calculate the intensity-field correlations in the light scattered by $N$ cold atoms driven by a quasiresonant laser field. Fundamental differences occur if the atomic state is an entangled single-excitation state or a coherent factorized state. We provide analytic expressions for the two-time field and intensity correlation functions for the timed Dicke state and the quasi-Bloch state. The comparison with multiatom simulations shows good agreement between numerical and analytic solutions.

Figure 1

$R$ vs $\sigma =k_0{\sigma }_r$ for $N={10}^3$ and $\theta ={90}^{\circ }$, averaged over ${10}^4$ iterations; solid black line: numerical simulation; dashed red line: analytic solution.

Figure 2

$g^{\left(2\right)}\left(\tau \right)$ vs ${\mathrm{\Gamma }}_N\tau$ for $R=2$ and two different values of detuning: $\mathrm{\Delta }=5{\mathrm{\Gamma }}_N$ (solid black line) and $\mathrm{\Delta }=0$ (red dashed line).

Figure 3

$g^{\left(2\right)}\left(\tau \right)$ vs ${\mathrm{\Gamma }}_N\tau$ from Eq. (67) for $\mathrm{\Delta }=5{\mathrm{\Gamma }}_N$, $N={10}^6$, $k_0{\sigma }_r=20$ and angles $\theta ={12}^{\circ }$ (dashed black line), $\theta ={11}^{\circ }$ (continuous red line), $\theta ={10}^{\circ }$ (dashed-dotted blue line), and $\theta =9^{\circ }$ (dotted green line).

Figure 4

$g^{\left(2\right)}\left(\tau \right)$ vs $\mathrm{\Gamma }\tau$, calculated from Eq. (24), for $N=100$, $k_0{\sigma }_r=5$, $\mathrm{\Delta }=5\mathrm{\Gamma }$, $\theta ={90}^{\circ }$ and average after 20 iterations (continuous blue line). The dashed red line is the analytic expression of Eq. (44), with $R=1.7$.

Figure 5

$g^{\left(2\right)}\left(\tau \right)$ vs $\mathrm{\Gamma }\tau$, calculated from Eq. (44), for $N=100$, $k_0{\sigma }_r=5$, $\mathrm{\Delta }=5\mathrm{\Gamma }$, $\theta =16.{26}^{\circ }$ and average after 20 iterations (continuous blue line). The dashed red line is the analytic expression of Eq. (67), with $R=1.025$, $Q=-0.042$, and ${\mathrm{\Gamma }}_N=2\mathrm{\Gamma }$.