Quantum Imaging with Incoherent Photons

We propose a technique to obtain subwavelength resolution in quantum imaging with potentially 100% contrast using incoherent light. Our method requires neither path-entangled number states nor multiphoton absorption. The scheme makes use of $N$ photons spontaneously emitted by $N$ atoms and registered by $N$ detectors. It is shown that for coincident detection at particular detector positions a resolution of $\lambda /N$ can be achieved.

Figure 1

Atomic arrangement and detection scheme: $N$ identical two-level atoms at ${\mathbf{R}}_1,\dots ,{\mathbf{R}}_N$ spontaneously emit $N$ photons after excitation by a laser pulse. The photons are recorded in the far field by $N$ detectors positioned at ${\mathbf{r}}_1,\dots ,{\mathbf{r}}_N$. The figure exemplifies the case $N=4$ (for additional symbols see text).

Figure 2

Left (a)–(c): density plots of $G^{(2)}({\mathbf{r}}_1,{\mathbf{r}}_2)$ for two atoms versus $\delta ({\mathbf{r}}_1)$ and $\delta ({\mathbf{r}}_2)$; left (d): density plot of $G^{(4)}({\mathbf{r}}_1,{\mathbf{r}}_2,{\mathbf{r}}_3,{\mathbf{r}}_4)$ for four atoms versus $\delta ({\mathbf{r}}_1)$ and $\delta ({\mathbf{r}}_2)$, with $\delta ({\mathbf{r}}_3)=\pi /2$ and $\delta ({\mathbf{r}}_4)=-\pi /2$. Right: cuts through the density plots along the indicated lines, i.e., for (a) $\delta ({\mathbf{r}}_2)=\delta ({\mathbf{r}}_1)$, (b) $\delta ({\mathbf{r}}_2)=\mathrm{const}$, and (c),(d) $\delta ({\mathbf{r}}_2)=-\delta ({\mathbf{r}}_1)$.

Figure 3

$G^{(1)}({\mathbf{r}}_1)$ and $G^{(4)}({\mathbf{r}}_1)$ as a function of $\delta ({\mathbf{r}}_1)$ for a chain of 4 atoms. The interval [$-2\pi$, $2\pi$] corresponds to the maximal range of variation of $\delta ({\mathbf{r}}_1)$ for an interatomic distance $d=\lambda$ [see Eq. (6)]. The dashed lines indicate the corresponding range in case of $d=\lambda /4$.