image: Figure | Principle of classical SHWS and PCB-SHWS. a, classical SHWS. The inset shows a focused spot inside a microlens aperture. b, PCB-SHWS. At the microlens and its back focal plane respectively, two balls with the same color represent one entangled photon pair. A tilt phase leads to the centroid displacement. The inset is the biphoton centroid marginal distribution inside an aperture.
Credit: Yi Zheng et al.
Entangled photon pairs, also known as biphotons, are widely used in quantum optical techniques. Quantum imaging enables several nonclassical imaging features. In particular, biphotons with a strong position correlation (i.e., they are roughly at the same transverse position) can realize quantum super-resolution imaging or quantum image distillation from the stray light. However, like classical imaging, a phase aberration can severely degrade the image. In recent years, the biphoton spatial aberration has been measured by detecting the aberration source with classical lights or scanning the correction phase till the biphoton anticorrelation in the far field revives. More efficient biphoton phase measurement methods are crucial for quantum adaptive imaging.
In a new paper published in Light: Science & Applications, a team of scientists, led by Professors Jin-Shi Xu and Chuan-Feng Li from Laboratory of Quantum Information, University of Science and Technology of China, have introduced position-correlated biphoton Shack–Hartmann wavefront sensing (PCB-SHWS). Classical SHWS uses a microlens array to map the local obliquity of a light field to the focused spot displacement at its back focal plane. Then, the phase of the light field can be reconstructed from its gradient distribution. Based on the team's previous work on a biphoton spatial wavefunction reconstruction technique named quantum SHWS which utilizes the biphoton joint probability distribution at the back focal plane of a microlens array and cannot be applied to biphotons with a strong position correlation, a new theoretical framework and data processing method were developed to reconstruct the phase added to position-correlated biphotons.
The basic idea is from the Einstein–Podolsky–Rosen (EPR) paper. If the biphotons have a perfect position correlation and a constant intensity, adding the phase of an oblique plane wave to each photon leads to the displacement of the anticorrelation center in the momentum space, which means the biphoton centroid marginal distribution after a Fourier lens is peaked, whose position corresponds to the local phase gradient. When photons at the whole microlens array arrive at its back focal plane, if the phase inside each aperture can be approximated by an oblique plane wave and the dynamic range of SHWS is satisfied (the phase gradient is not too large), photon pairs from different apertures have distinct centroids inside their own aperture, and the whole centroid distribution is an array of sharp peaks, similar as the image in classical SHWS, which can be used to extract the gradient distribution and reconstruct the phase. In the realistic case, the finite width of a microlens weakens the momentum anticorrelation, and the biphoton position correlation is not perfect, which are analyzed in the article.
In the experiments, the biphotons are created by degenerate type-I spontaneous parametric down-conversion. Researchers first loaded phase patterns on a spatial light modulator (SLM) and measured them. Then, a plastic film was pasted on the SLM as the aberration source, and the added phase on biphotons was measured. Finally, the camera was moved to the imaging plane (the far-field). By imaging an object, the aberration from the film was corrected after loading the correction phase on the SLM. These scientists summarize the features of PCB-SHWS:
“We use a microlens array to measure the phase of position-correlated biphotons. This new method is inspired by classical SHWS and the EPR state, and handles an important type of biphoton state in quantum imaging, which cannot be properly measured by our previous quantum SHWS method. It only requires the biphoton field, so the aberration source can be unreachable. Most importantly, it is single-shot and highly efficient, so we believe that with a more advanced biphoton coincidence counting technique, real-time biphoton phase measurement can be realized for future quantum microscopy and remote imaging researches.”
“Finally, we prospect that the microlens array can be further exploited in the future to better characterize the spatial states of quantum optical fields,” they added.
Article Title
Position-correlated biphoton wavefront sensing for quantum adaptive imaging