Higher-Order Quantum Ghost Imaging with Ultracold Atoms

Ghost imaging is a quantum optics technique that uses correlations between two beams to reconstruct an image from photons that do not interact with the object being imaged. While pairwise (second-order) correlations are usually used to create the ghost image, higher-order correlations can be utilized to improve the performance. In this Letter, we demonstrate higher-order atomic ghost imaging, using entangled ultracold metastable helium atoms from an $s$-wave collision halo. We construct higher-order ghost images up to fifth order and show that using higher-order correlations can improve the visibility of the images without impacting the resolution. This is the first demonstration of higher-order ghost imaging with massive particles and the first higher-order ghost imaging protocol of any type using a quantum source.

Figure 1

Schematic of atomic higher-order ghost imaging. A halo (gray-shaded ring) of back-to-back correlated atoms is produced via pairwise $s$-wave collisions to produce correlated atoms with momenta $\mathbf{k}$ and $-\mathbf{k}$. The detector is divided in two, with atoms on the bucket port side of the halo passed through a mask (here ANU), with only the arrival times of atoms that pass through recorded and all spatial information of these atoms discarded. These arrival times are then correlated with the arrival times of atoms in the image port, which are measured with full 3D resolution, to match groups of 2, 3, 4, or 5 atoms around $\mathbf{k}$ and $-\mathbf{k}$, depending on the order of ghost imaging being used. The $x$ and $y$ components of these image port atoms form the ghost image. Insets show how higher-order imaging can improve the visibility: when an additional correlated atom (green dot in upper inset) beyond the first one (blue dot) is detected in the bucket port, the location of the second atom will most likely lie within a correlation length $l_{\mathrm{corr}}$ of the first one, although it must also pass through the mask, so the red shaded regions outside the mask open area are excluded. An atom detected in the image port, which is correlated with both bucket port atoms, is thus most likely to lie within the radius of the correlation length of the corresponding position of both of these (small dashed circles). This restricts image port atoms to a smaller area (indicated in cyan) than the area they could be found if there was only one correlated atom in the bucket port (either the large blue or green dashed circles). This makes the image atoms more likely to be located in the corresponding image region, rather than outside it, thus improving the visibility.

Figure 2

A selection of atomic ghost images created using a transmission mask comprising the letters ANU. There is only one case (a) for second-order ghost imaging, consisting of 1 atom in each port ($1_I$, $1_B$). In contrast, for three-atom ghost imaging there are two configurations, with either (b) two atoms in the image port ($2_I$, $1_B$) or (c) two atoms in the bucket port ($1_I$, $1_B$). Higher orders have correspondingly more possible configurations, of which one is shown (d) for four atoms, with three of these atoms detected in the image port ($3_I$, $1_B$). The background semicircular arc corresponding to the halo is visible in each image and is due to random, uncorrelated atoms. The scale of the images is given in terms of the collisional recoil momentum $k_r$, while the number of atoms in each pixel is shown by the color bars for each image. All images are the result of $\sim 45000$ experimental runs, and the increasingly stringent correlation criteria means that each image (a) to (d) has fewer total counts than the previous, leading to case (c) appearing less clear by eye than case (b), despite the calculated visibility being higher.

Figure 3

The experimentally measured (circles) and numerically simulated (bands) visibilities for a range of different types and orders ($N$) of ghost imaging, with labels showing the number of atoms in the image ($I$) and bucket ($B$) ports, represented in the diagrams for the 3 atom cases. Blue visibilities are for the optimal cases, with one atom in the image port and the rest in the bucket (mask) port, with the reverse cases shown in yellow (green points are for intermediate cases). Error bars show the variance in intensity, due to shot-to-shot variations in $B$ and $I$.

Figure 4

Resolution of ghost imaging using different orders $N$. The resolution is calculated by forming a ghost image of a square mask, integrating along the $y$ dimension and then fitting a Gaussian function convolved with a top hat of the width of the mask. Insets show these plots for the two third-order cases (the left inset shows the case of one atom in the image, the right inset is two atoms in the image). In all cases the resolution does not significantly change for different methods within error.