Directional Dicke Subradiance with Nonclassical and Classical Light Sources

We investigate Dicke subradiance of $N\ge 2$ distant quantum sources in free space, i.e., the spatial emission patterns of spontaneously radiating noninteracting multilevel atoms or multiphoton sources, prepared in totally antisymmetric states. We find that the radiated intensity is marked by a full suppression of spontaneous emission in particular directions. In resemblance to the analogous, yet inverted, superradiant emission profiles of $N$ distant two-level atoms prepared in symmetric Dicke states, we call the corresponding emission patterns directional Dicke subradiance. We further derive that higher-order intensity correlations of the light emitted by statistically independent thermal light sources display the same directional Dicke subradiant behavior and show that it stems from the same interference phenomenon as in the case of quantum sources. We finally present measurements of directional Dicke subradiance for $N=2,\dots ,5$ distant thermal light sources corroborating the theoretical findings.

Figure 1

Setup considered for the oberservation of directional Dicke subradiance: $N$ light sources are aligned along the $x$ axis equidistantly at positions ${\mathbf{R}}_l$, $l=1,\dots ,N$, with separation $d\gg \lambda$. In the far field of the sources, $N$ detectors measure the $N$th-order correlation function at positions ${\mathbf{r}}_j$, $j=1,\dots ,N$.

Figure 2

Experimental setup to measure $g_{N\mathrm{TLS}}^{(N)}$ with $N$ pseudothermal light sources. $M$, mirror; $L$, lens. For details, see the text and Ref. [14].

Figure 3

Experimental results. (a) Average intensity $I_{2\mathrm{TLS}}({\delta }_1)$ of $N=2$ TLS demonstrating that the pseudothermal light sources are spatially incoherent in first order. (b)–(e) Measurement of the normalized $N$th-order correlation function $g_{N\mathrm{TLS}}^{(N)}({\delta }_1,{\delta }_j=2\pi [(j-1)/N];j=2,\dots ,N)={\mathrm{G}}_{N\mathrm{TLS}}^{(N)}({\delta }_1,{\delta }_j=2\pi [(j-1)/N];j=2,\dots ,N)/[I_{N\mathrm{TLS}}({\delta }_1)\prod _{j=2}^N{I}_{N\mathrm{TLS}}({\delta }_j=2\pi [(j-1)/N])]$ for $N=2,\dots ,5$ as a function of the first detector at ${\delta }_1$ (the red solid curves). The suppression of incoherently emitted radiation at ${\delta }_1=0$ after $N-1$ photons have been recorded at the SP at ${\delta }_j=2\pi [(j-1)/N]$, $j=2,\dots ,N$, is clearly visible. The theoretical predictions of Eq. (16) are displayed by the black (dashed) curves.