Sub-Rayleigh quantum imaging using single-photon sources

We propose a technique capable of imaging a distinct physical object with sub-Rayleigh resolution in an ordinary far-field imaging setup using single-photon sources and linear optical tools only. We exemplify our method for the case of a rectangular aperture and two or four single-photon emitters obtaining a resolution enhanced by a factor of 2 or 4, respectively.

Figure 1

(Color online) Setup used for far-field quantum imaging: in a single measurement cycle both emitters at ${\mathbf{R}}_1$ and ${\mathbf{R}}_2$ each emits a single photon. Between the source and the detection plane, the field is diffracted by an object (in the case illustrated by the figure, a rectangular aperture of height $a$ and width $b$). The two detectors are placed in the far-field region of the aperture at positions ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$.

Figure 2

(Color online) (a) Enhanced two-photon imaging setup employing different detector positions. Plot shows the diffraction pattern of second order for $x$ and $y$ directions as derived in Eq. (8) for the $x$ component. (b) By using a lens in the Fourier plane of the object and a two-photon absorbing medium our scheme is able to reconstruct the object with sub-Rayleigh resolution without relying on a postselection mechanism.

Figure 3

(Color online) Diffraction signal in the Fourier plane of a double slit aperture showing intensity pattern (dashed red line), intensity squared (dotted-dashed green line), and second-order correlation function (solid blue line). For the range of observation shown, corresponding to a fixed numerical aperture, only the $G^{\left(2\right)}$ function is able to resolve a whole period of the diffraction pattern and thereby to reconstruct the double slit.